diff --git a/caderno.pdf b/caderno.pdf
index 287710b2c0adc994f9a51831cf88226b60a60b5e..c4990fc0b23c71cafc96aa03b9ea33e086bb1a1d 100644
Binary files a/caderno.pdf and b/caderno.pdf differ
diff --git a/caderno/caderno.tex b/caderno/caderno.tex
index 85692c16f6e31d86732138e813e90d332c3fa721..15ef3e5738d36e861ac594c7898c57f558f9afb8 100644
--- a/caderno/caderno.tex
+++ b/caderno/caderno.tex
@@ -26,7 +26,9 @@
\definecolor{commentgreen}{RGB}{2,112,10}
\definecolor{eminence}{RGB}{210,31,60}
+\DeclareMathOperator{\lcm}{lcm}
\newcommand{\bigO}{\mathcal{O}}
+\newcommand{\compl}[1]{ \color{commentgreen}{$\bigO(#1)$} }
\lstset{
basicstyle=\footnotesize\ttfamily,
showspaces=false,
@@ -213,7 +215,7 @@ $m, n \in \mathbb{N}$ e $m > n$ de tal forma que:
\begin{itemize}
\item Se $G$ tem $k$ componentes conectadas, então $n - m + f = k + 1$.
\item $m \le 3n - 6$. Se $G$ não tem triângulos, $m \le 2n - 4$.
- \item O grau mínimo é $\le 5$. E pode ser 6-colorido em $\mathcal{O}(n+m)$.
+ \item O grau mínimo é $\le 5$. E pode ser 6-colorido em $\bigO(n+m)$.
\end{itemize}
\subsection{Corte mínimo}
@@ -356,7 +358,7 @@ para $a$ e $m$ coprimos.
\lstinputlisting{fontes-com-hash/template.cpp}
\subsection{Teste de estresse}
\lstinputlisting[language=bash]{fontes-com-hash/stress.sh}
-\subsection{Hash de linhas em $[l, r]$}
+\subsection{Hash da entrada padrão}
\lstinputlisting[language=bash]{fontes-com-hash/hash.sh}
\subsection{vimrc}
\lstinputlisting{fontes-com-hash/vimrc}
@@ -368,46 +370,12 @@ para $a$ e $m$ coprimos.
\lstinputlisting{fontes-com-hash/disjoint.h}
\subsection{Árvore de Fenwick}
-\begin{tabular}{l|l|l}
- \hline
- 1-indexada &
- Atualização $\bigO(\lg n)$ &
- Consulta $\bigO(\lg n)$ \\
- \hline
-\end{tabular}
-
-\vspace{4pt}
-\noindent
-\begin{tabular}{lll}
- \hline
- \textbf{Atualização} & \textbf{Consulta} & \textbf{Funções} \\ \hline
- Ponto & Intervalo & \texttt{add} + \texttt{sum\_inclusive} \\
- Intervalo & Ponto & \texttt{add\_inclusive} + \texttt{pref} \\
- \hline
-\end{tabular}
-
\lstinputlisting{fontes-com-hash/fenwick-tree.h}
\subsection{Árvore de Fenwick 2D}
-\begin{tabular}{l|l|l}
- \hline
- 1-indexada &
- Atualização $\bigO(\lg^2 n)$ &
- Consulta $\bigO(\lg^2 n)$ \\
- \hline
-\end{tabular}
-
\lstinputlisting{fontes-com-hash/fenwick-2d-tree.h}
\subsection{Árvore de Fenwick intervalar}
-\begin{tabular}{l|l|l}
- \hline
- 1-indexada &
- Atualização $\bigO(\lg n)$ &
- Consulta $\bigO(\lg n)$ \\
- \hline
-\end{tabular}
-
\lstinputlisting{fontes-com-hash/fenwick-range-tree.h}
\subsection{Tabela esparsa}
@@ -424,7 +392,7 @@ para $a$ e $m$ coprimos.
\subsection{Árvore de segmentos iterativa}
\vspace{4pt}
-\noindent
+\begin{center}
\footnotesize
\begin{tabular}{cccc}
\hline
@@ -434,35 +402,35 @@ para $a$ e $m$ coprimos.
\texttt{FACTOR} & \texttt{(tb - ta + 1)} & \texttt{1} & \texttt{1} \\
\hline
\end{tabular}
+\end{center}
\lstinputlisting{fontes-com-hash/segment-tree.h}
\subsection{Árvore de segmentos preguiçosa iter.}
\lstinputlisting{fontes-com-hash/lazy-segment-tree.h}
-\subsection{Nó de Kadane}
-\lstinputlisting{fontes-com-hash/kadane.h}
+\subsection{K maiores elementos}
+\lstinputlisting{fontes-com-hash/k-elements.h}
\subsection{Hash customizado}
\lstinputlisting{fontes-com-hash/custom-hash.h}
-\subsection{Árvore de segmentos recursiva}
-\lstinputlisting{fontes-com-hash/recursive-segment-tree.h}
+\subsection{Conjunto de intervalos coloridos}
+\lstinputlisting{fontes-com-hash/interval-set.h}
\subsection{Árvore de segmentos preguiçosa rec.}
\lstinputlisting{fontes-com-hash/recursive-lazy-segment-tree.h}
-\subsection{Conjunto de intervalos coloridos}
-\lstinputlisting{fontes-com-hash/interval-set.h}
+\subsection{Árvore de segmentos recursiva}
+\lstinputlisting{fontes-com-hash/recursive-segment-tree.h}
-\subsection{K maiores elementos}
-\lstinputlisting{fontes-com-hash/k-elements.h}
+\subsection{Nó de Kadane}
+\lstinputlisting{fontes-com-hash/kadane.h}
\section{Grafos}
\subsection{Articulações e pontes}
\lstinputlisting{fontes-com-hash/articulations-bridges.h}
-\clearpage
\subsection{Componentes fortes -- Tarjan}
\lstinputlisting{fontes-com-hash/tarjan.h}
@@ -475,31 +443,6 @@ para $a$ e $m$ coprimos.
\subsection{Busca em largura 0-1}
\lstinputlisting{fontes-com-hash/bfs-01.h}
-\subsection{Emparelhamento estável}
-\begin{tabular}{l}
- \hline
- $\bigO(n^2)$ \\
- \hline
-\end{tabular}
-\lstinputlisting{fontes-com-hash/stable-matching.h}
-
-\subsection{Caminho euleriano}
-\lstinputlisting{fontes-com-hash/eulerian-path.h}
-
-\clearpage
-
-\subsection{Stoer-Wagner}
-\lstinputlisting{fontes-com-hash/stoer-wagner.h}
-
-\subsection{Menor no maior}
-\lstinputlisting{fontes-com-hash/small-to-large.h}
-
-\subsection{Árvore geradora mínima -- Prim}
-\lstinputlisting{fontes-com-hash/prim.h}
-
-\subsection{Árvore geradora mínima -- Kruskal}
-\lstinputlisting{fontes-com-hash/kruskal.h}
-
\subsection{Caminho mínimo -- Dijkstra}
\lstinputlisting{fontes-com-hash/dijkstra.h}
@@ -512,6 +455,15 @@ para $a$ e $m$ coprimos.
\subsection{Caminhos mínimos -- Floyd-Warshall}
\lstinputlisting{fontes-com-hash/floyd-warshall.h}
+\subsection{Árvore geradora mínima -- Kruskal}
+\lstinputlisting{fontes-com-hash/kruskal.h}
+
+\subsection{Árvore geradora mínima -- Prim}
+\lstinputlisting{fontes-com-hash/prim.h}
+
+\subsection{Menor no maior}
+\lstinputlisting{fontes-com-hash/small-to-large.h}
+
\subsection{Fluxo máximo}
\lstinputlisting{fontes-com-hash/ford-fulkerson-edmons-karp.h}
@@ -521,55 +473,47 @@ para $a$ e $m$ coprimos.
\subsection{Fluxo máximo Dinic}
\lstinputlisting{fontes-com-hash/dinic.h}
-\subsection{Ascensão binária}
-\lstinputlisting{fontes-com-hash/binary-lifting.h}
-
-\subsection{Menor anc. comum -- Ancensão binária}
-\lstinputlisting{fontes-com-hash/lca-binary-lifting.h}
+\subsection{Stoer-Wagner}
+\lstinputlisting{fontes-com-hash/stoer-wagner.h}
\subsection{Decomposição pesado-leve}
-\begin{tabular}{l|l}
- \hline
- \multicolumn{2}{l}{
- Precisa de soma de prefixos/árvore de segmentos preguiçosa
- } \\ \hline
- \multicolumn{2}{l}{
- Se usado com pesos nos vértices, use com $\texttt{edge\_wei} = 0$
- } \\ \hline
- Construção $\bigO(|V|\lg|V| + |E|)$ &
- Atualização/Consulta $\bigO(\lg^2 n)$ \\
- \hline
-\end{tabular}
\lstinputlisting{fontes-com-hash/hld.h}
\subsection{Decomposição pesado-leve -- K-ésimo}
\lstinputlisting{fontes-com-hash/hld-kth.h}
-\clearpage
+\subsection{Caminho euleriano}
+\lstinputlisting{fontes-com-hash/eulerian-path.h}
-\subsection{Menor anc. comum -- Offline}
-\lstinputlisting{fontes-com-hash/lca-offline.h}
+\subsection{Ascensão binária}
+\lstinputlisting{fontes-com-hash/binary-lifting.h}
-\subsection{Decomposição centróide}
-\lstinputlisting{fontes-com-hash/centroid.h}
+\subsection{Menor anc. comum -- Ancensão binária}
+\lstinputlisting{fontes-com-hash/lca-binary-lifting.h}
\subsection{Empar. máximo bipartido -- Kuhn}
-\begin{tabular}{l}
- \hline
- As partes tem enumerações distintas
- \\ \hline
-\end{tabular}
\lstinputlisting{fontes-com-hash/kuhn.h}
-\subsection{Emparelhamento Generalizado -- Blossom}
+\clearpage
+
+\subsection{Empar. generalizado -- Blossom}
\lstinputlisting{fontes-com-hash/blossom.h}
-\subsection{Decomposição raiz quadrada de árvore}
-\lstinputlisting{fontes-com-hash/tree-square-root-decomposition.h}
+\subsection{Emparelhamento estável}
+\lstinputlisting{fontes-com-hash/stable-matching.h}
+
+\subsection{Decomposição centróide}
+\lstinputlisting{fontes-com-hash/centroid.h}
\subsection{Menor anc. comum -- Dec. raiz quad.}
\lstinputlisting{fontes-com-hash/lca-square-root-decomposition.h}
+\subsection{Decomposição raiz quadrada de árvore}
+\lstinputlisting{fontes-com-hash/tree-square-root-decomposition.h}
+
+\subsection{Menor anc. comum -- Offline}
+\lstinputlisting{fontes-com-hash/lca-offline.h}
+
\section{Matemática}
\subsection{Operações comuns}
@@ -618,19 +562,14 @@ Gera um conjunto $n/i$ para todo $i$ em $\bigO(\sqrt{n})$.
\lstinputlisting{fontes-com-hash/division-trick.h}
\subsection{Multiplicação -- Karatsuba}
-\begin{tabular}{l}
- \hline
- $\bigO(n^{\log_3 n})$ \\
-\hline
-\end{tabular}
\lstinputlisting{fontes-com-hash/karatsuba.h}
-\subsection{Compressão de coordenadas}
-\lstinputlisting{fontes-com-hash/coordinate-compression.h}
-
\subsection{Inclusão-Exclusão}
\lstinputlisting{fontes-com-hash/inclusion-exclusion.h}
+\subsection{Compressão de coordenadas}
+\lstinputlisting{fontes-com-hash/coordinate-compression.h}
+
\subsection{Mínimo excluído com conjunto}
\lstinputlisting{fontes-com-hash/mexset.h}
@@ -644,11 +583,6 @@ Gera um conjunto $n/i$ para todo $i$ em $\bigO(\sqrt{n})$.
\lstinputlisting{fontes-com-hash/nim.h}
\subsection{Euclides estendido/inv. multiplicativo}
-\begin{tabular}{l}
- \hline
-$\bigO(\lg \min(a, b))$ \\
-\hline
-\end{tabular}
\begin{align*}
ax + by &= \gcd(a, b) \\
ax &= gcd(a, b) \pmod{b} \\
@@ -669,27 +603,12 @@ ax + by = c
\lstinputlisting{fontes-com-hash/diophantine.h}
\subsection{Fatoração por tentativa}
-\begin{tabular}{l}
- \hline
- $\bigO(\sqrt{n})$ \\
-\hline
-\end{tabular}
\lstinputlisting{fontes-com-hash/factorize.h}
\subsection{Crivo de Eratóstenes}
-\begin{tabular}{l}
- \hline
- $\bigO(n \lg\lg n)$ \\
-\hline
-\end{tabular}
\lstinputlisting{fontes-com-hash/sieve.h}
\subsection{Totiente de Euler}
-\begin{tabular}{l}
- \hline
- $\bigO(n \lg \lg n)$ \\
-\hline
-\end{tabular}
\lstinputlisting{fontes-com-hash/euler-totient.h}
\subsection{Eliminação gaussiana}
@@ -702,39 +621,17 @@ ax + by = c
\lstinputlisting{fontes-com-hash/miller-rabin.h}
\subsection{Pollard Rho}
-\begin{tabular}{l}
- \hline
- $\bigO(n^{1/4})$ \\
-\hline
-\end{tabular}
\lstinputlisting{fontes-com-hash/pollard-rho.h}
\subsection{Teorema chinês do resto}
-\begin{tabular}{l}
- \hline
- $\bigO(t \lg(m_1 m_2 \ldots m_t))$ \\
-\hline
-\end{tabular}
\lstinputlisting{fontes-com-hash/chinese-remainder-theorem.h}
\subsection{Teorema chinês do resto generalizado}
-\begin{tabular}{l|l}
- \hline
- $\bigO(t \lg(m_1 m_2 \ldots m_t))$ &
- Infinitas soluções $\pm \text{lcm}(m_1m_2\ldots m_t)$
- \\ \hline
-\end{tabular}
\lstinputlisting{fontes-com-hash/generalized-chinese-remainder-theorem.h}
\section{Strings}
\subsection{KMP}
-\begin{tabular}{l|l}
- \hline
- Pré-computação $\bigO(m)$ &
- Busca $\bigO(n + m)$ \\
- \hline
-\end{tabular}
\lstinputlisting{fontes-com-hash/kmp.h}
\subsection{Algoritmo Z}
@@ -769,19 +666,9 @@ $z[i]$ é o tamanho da maior string que é ao mesmo tempo, um prefixo de $s$ e u
\lstinputlisting{fontes-com-hash/point.h}
\subsection{Fecho convexo de Graham}
-\begin{tabular}{l}
- \hline
- $\bigO(n \lg n)$ \\
- \hline
-\end{tabular}
\lstinputlisting{fontes-com-hash/graham.h}
\subsection{Fecho convexo com corrente monotônica}
-\begin{tabular}{l}
- \hline
- $\bigO(n \lg n)$ \\
- \hline
-\end{tabular}
\lstinputlisting{fontes-com-hash/monotone.h}
\subsection{Medidor giratório}
@@ -866,8 +753,6 @@ Para mudar para superconjunto, use \texttt{\~{}mask} no if.
\subsection{Frequência de frequências/moda com Mo}
\lstinputlisting{fontes-com-hash/freq-freq-mode.h}
-\clearpage
-
\subsection{Rainhas no tabuleiro}
\lstinputlisting{fontes-com-hash/queens.h}
diff --git a/fontes/articulations-bridges.h b/fontes/articulations-bridges.h
index 472c3ca1da8f914a68bb8289696d8d50fb8a3fd8..188ec5b7d8c61a5a0cc149b531a83795da1b9c60 100644
--- a/fontes/articulations-bridges.h
+++ b/fontes/articulations-bridges.h
@@ -1,7 +1,7 @@
int tk = 1; vector<int> tin (N, -1), low (N);
vector<ii> brid; set<int> arti;
-void dfs(int u, int p) {
+void dfs(int u, int p) { //<@\compl{n+m}@>
tin[u] = low[u] = tk++; int ch = 0;
for (auto v : g[u]) {
if (v == p) continue;
diff --git a/fontes/bellman-ford.h b/fontes/bellman-ford.h
index 07b0cb1af47a6fad8802faf678841ff40d909183..7474f1cf19741958fcec1d221de77eab0d82604d 100644
--- a/fontes/bellman-ford.h
+++ b/fontes/bellman-ford.h
@@ -2,7 +2,7 @@ struct edge { int u, v, w; };
vector<edge> edges;
vector<int> d (N, oo);
-int bellman_ford(int src, int dest, int n) {
+int bellman_ford(int src, int dest, int n) { //<@\compl{nm}@>
d[src] = 0;
for (int i = 0; i < n - 1; i++)
for (auto e : edges)
diff --git a/fontes/bfs-01.h b/fontes/bfs-01.h
index d8a12b0d8aa5baa3d06dfa29fb8960a297f19758..2b856bcaaf0d74468e1e5c278634c52ab1f58c6b 100644
--- a/fontes/bfs-01.h
+++ b/fontes/bfs-01.h
@@ -1,12 +1,9 @@
vector<int> d (N, oo);
-void bfs01(int s) {
- d[s] = 0;
- deque<int> q;
- q.push_front(s);
+void bfs01(int s) { //<@\compl{n+m}@>
+ d[s] = 0; deque<int> q; q.push_front(s);
while (!q.empty()) {
- int u = q.front();
- q.pop_front();
+ int u = q.front(); q.pop_front();
for (auto [v, w] : g[u]) if (d[u] + w < d[v]) {
d[v] = d[u] + w;
if (w == 1) { q.push_back(v); }
diff --git a/fontes/binary-lifting.h b/fontes/binary-lifting.h
index 8818dd1ef0f3518973071ae01092b10870211f59..1d03e8461bec68e738e6713bfdd027e165d0301d 100644
--- a/fontes/binary-lifting.h
+++ b/fontes/binary-lifting.h
@@ -10,7 +10,7 @@ void bl_euler_tour(int u, int p, int w) {
bl_euler_tour(v, u, w);
}
-void bl_init(int u, int n) {
+void bl_init(int u, int n) { //<@\compl{m + n\lg n}@>
dep[u] = -1; bl_euler_tour(u, u, 0);
// can be put into bl_euler_tour but it will not
// work with cycles (could be useful for online)
@@ -22,7 +22,7 @@ void bl_init(int u, int n) {
}
}
-ll bl_op(int a, int b) {
+ll bl_op(int a, int b) { //<@\compl{\lg n}@>
if (!(dep[a] > dep[b])) { swap(a, b); }
ll res = NEUTRAL;
int diff = dep[a] - dep[b];
diff --git a/fontes/binomial-distribution.h b/fontes/binomial-distribution.h
index 5f73423c80f99899bb43153f2f32cbcef6ae03d9..48d3d8b9a70e7d871d34860e6ff31d38793384e0 100644
--- a/fontes/binomial-distribution.h
+++ b/fontes/binomial-distribution.h
@@ -1,8 +1,7 @@
vector<double> logfact (N);
-
void calc() {
for (int i = 1; i < N; i++)
- logfact[i] = logfact [i-1] + log(i);
+ logfact[i] = logfact[i-1] + log(i);
}
double binom (int n, int k, double p) {
diff --git a/fontes/blossom.h b/fontes/blossom.h
index e835c48ff96dda9b6772a48a8215f77348015798..4ab6ab71f8f5d7c5707c46889e2936c83056f2fd 100644
--- a/fontes/blossom.h
+++ b/fontes/blossom.h
@@ -1,16 +1,14 @@
-int n;
vector<int> match (N), par (N), base (N), vis (N);
-queue<int> q;
+int n; queue<int> q;
void contract(int u, int v, bool first = 1) {
static vector<bool> bloss; static int l;
if (first) {
bloss = vector<bool>(n, 0);
- vector<bool> ok (n, 0);
- int k = u; l = v;
+ vector<bool> ok (n, 0); int k = u; l = v;
while (1) {
ok[k = base[k]] = 1;
- if (match[k] == -1) break;
+ if (match[k] == -1) { break; }
k = par[match[k]];
}
while (!ok[l = base[l]]) l = par[match[l]];
@@ -23,19 +21,20 @@ void contract(int u, int v, bool first = 1) {
contract(v, u, 0);
for (int u = 0; u < n; u++) if (bloss[base[u]]) {
base[u] = l;
- if (!vis[u]) { q.push(u); }
- vis[u] = 1;
+ if (!vis[u]) { q.push(u); } vis[u] = 1;
}
}
int getpath(int s) {
- for (int i = 0; i < n; i++) base[i] = i, par[i] = -1, vis[i] = 0;
+ for (int i = 0; i < n; i++)
+ base[i] = i, par[i] = -1, vis[i] = 0;
vis[s] = 1; q = queue<int>(); q.push(s);
while (q.size()) {
int u = q.front(); q.pop();
for (int i : g[u]) {
- if (base[i] == base[u] || match[u] == i) { continue; }
- if (i == s or (match[i] != -1 && par[match[i]] != -1))
+ if (base[i] == base[u] || match[u] == i)
+ continue;
+ if (i == s || (~match[i] && ~par[match[i]]))
contract(u, i);
else if (par[i] == -1) {
par[i] = u;
@@ -48,13 +47,11 @@ int getpath(int s) {
return -1;
}
-int blossom() {
- int ans = 0;
- fill(all(match), -1);
+int blossom() { //<@\compl{n^3}@>
+ int ans = 0; fill(all(match), -1);
for (int i = 0; i < n; i++) if (match[i] == -1)
for (int j : g[i]) if (match[j] == -1) {
- match[i] = j; match[j] = i; ans++; break;
- }
+ match[i] = j; match[j] = i; ans++; break; }
for (int i = 0; i < n; i++) if (match[i] == -1) {
int j = getpath(i); if (j == -1) { continue; }
ans++;
diff --git a/fontes/bruijn.h b/fontes/bruijn.h
index 5d09f534bfe9ac43c1f5c07080d412cbaeaae938..4560f0bc71bd8f3c920384428d84cef927cc77c4 100644
--- a/fontes/bruijn.h
+++ b/fontes/bruijn.h
@@ -1,5 +1,4 @@
-vector<int> a (K*N, 0);
-vector<int> seq;
+vector<int> a (K*N, 0), seq;
void de_bruijn(int k, int n, int t=1, int p=1) {
if (t > n && n % p == 0)
diff --git a/fontes/centroid.h b/fontes/centroid.h
index 837de3e71496ed6c317f641ce8550824c4b80170..bbf0b14f61dbc7d06cd65d14caf2c4f700700cea 100644
--- a/fontes/centroid.h
+++ b/fontes/centroid.h
@@ -14,10 +14,10 @@ int find_centroid(int u, int p, int n) {
return u;
}
-void centroid_decompose(int u, int p, int d = 0) {
+void centroid_decomp(int u, int p, int d=0) { //<@\compl{n+m}@>
calc_size(u, u);
int c = find_centroid(u, u, sz[u]);
vis[c] = 1; parc[c] = p;
for (int v : g[c]) if (!vis[v])
- centroid_decompose(v, c, d+1);
+ centroid_decomp(v, c, d+1);
}
diff --git a/fontes/chinese-remainder-theorem.h b/fontes/chinese-remainder-theorem.h
index 958010d3356644fc6a5f5f7f6baee028ed5772df..801c79a265253d56ab2b30c6c7c717e81b422437 100644
--- a/fontes/chinese-remainder-theorem.h
+++ b/fontes/chinese-remainder-theorem.h
@@ -1,3 +1,5 @@
+// infinite solutions <@$\pm \lcm(m_1m_2\ldots m_t)$@>
+//<@\compl{t \lg m_1m_2\ldots m_t}@>
ll crt(vector<ll> a, vector<ll> m, int t) {
ll p = 1; for (ll& mi : m) { p *= mi; }
ll ans = 0;
diff --git a/fontes/custom-hash.h b/fontes/custom-hash.h
index e80c99aa5a203869bdbc0f649abb0bf1519d7742..a238efdb3a9adb9a0b8912ee2487b3d2c2ca39fe 100644
--- a/fontes/custom-hash.h
+++ b/fontes/custom-hash.h
@@ -1,16 +1,11 @@
struct custom_hash {
- static uint64_t splitmix64(uint64_t x) {
- // http://xorshift.di.unimi.it/splitmix64.c
- x += 0x9e3779b97f4a7c15;
- x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
- x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
- return x ^ (x >> 31);
- }
-
- size_t operator()(uint64_t x) const {
+ size_t operator()(uint64_t x) const { //<@\compl{1}@>
static const uint64_t FIXED_RANDOM =
chrono::steady_clock::now()
.time_since_epoch().count();
- return splitmix64(x + FIXED_RANDOM);
+ x += FIXED_RANDOM + 0x9e3779b97f4a7c15;
+ x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
+ x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
+ return x ^ (x >> 31);
}
};
diff --git a/fontes/dijkstra.h b/fontes/dijkstra.h
index 2a757a9becd674585f06ee326e1b3370e2263587..a198417e7b09f0244e037578ec1bec758376781a 100644
--- a/fontes/dijkstra.h
+++ b/fontes/dijkstra.h
@@ -1,15 +1,14 @@
-void dijkstra(int src, int dest, int n) {
+void dijkstra(int s, int t, int n) { //<@\compl{(m + n)\lg n}@>
vector<ll> d (n, oo); vector<bool> vis (n);
vector<vector<int>> dag (n);
priority_queue<ii, vector<ii>, greater<ii>> q;
- d[src] = 0; q.push({0, src});
+ d[s] = 0; q.push({0, s});
while (!q.empty()) {
auto [c, u] = q.top(); q.pop();
- if (vis[u]) { continue; }
- vis[u] = 1;
+ if (vis[u]) { continue; } vis[u] = 1;
for (auto [v, w] : gt[u]) if (d[u] == d[v] + w)
dag[v].push_back(u);
- if (u == dest) { break; }
+ if (u == t) { break; }
for (auto [v, w] : g[u])
if (d[v] > d[u] + w) {
d[v] = d[u] + w;
diff --git a/fontes/dinic.h b/fontes/dinic.h
index 00a90e7f52934b6bf6901202fa18789e6c5e946d..5b01160537bcf01dd9c7febd69e0a1c9d74d0a94 100644
--- a/fontes/dinic.h
+++ b/fontes/dinic.h
@@ -32,11 +32,10 @@ ll dfs(int u, int t, ll pushed) {
return 0;
}
-ll dinic /* O(EV^2) */(int s, int t) {
+ll dinic(int s, int t) { //<@\compl{mn^2}@>
ll max_flow = 0;
while (1) {
- fill(all(level), -1);
- level[s] = 0; q.push(s);
+ fill(all(level), -1); level[s] = 0; q.push(s);
if (!minimum_path(s, t)) { break; }
fill(all(ptr), 0);
while (ll pushed = dfs(s, t, 1e18))
diff --git a/fontes/disjoint.h b/fontes/disjoint.h
index fda3eb40ae7a2f150153aa28a6f4ebb8beb9996a..3154000f392ffa2338d4d37204790de83bcd935a 100644
--- a/fontes/disjoint.h
+++ b/fontes/disjoint.h
@@ -1,11 +1,11 @@
vector<int> rep (N), rnk (N), siz (N);
-int ds_find(int u) {
+int ds_find(int u) { //<@\compl{\alpha(n)}@>
if (rep[u] != u) { rep[u] = ds_find(rep[u]); }
return rep[u];
}
-void ds_unite(int u, int v) {
+void ds_unite(int u, int v) { //<@\compl{\alpha(n)}@>
u = ds_find(u); v = ds_find(v);
assert(u != v);
if (!(rnk[u] > rnk[v])) { swap(u, v); }
@@ -14,8 +14,7 @@ void ds_unite(int u, int v) {
siz[u] += siz[v];
}
-void ds_init(int n) {
- for (int u = 0; u < n; u++) {
- rep[u] = u; rnk[u] = 0; siz[u] = 1;
- }
+void ds_init(int n) { //<@\compl{n}@>
+ for (int u = 0; u < n; u++)
+ rep[u] = u, rnk[u] = 0, siz[u] = 1;
}
diff --git a/fontes/euler-totient.h b/fontes/euler-totient.h
index 856870aeaa7be9e4506cb27e4844b41bec677874..7ea7cbe5ca69c853b116e70dd259619cff875d62 100644
--- a/fontes/euler-totient.h
+++ b/fontes/euler-totient.h
@@ -1,5 +1,5 @@
vector<ll> phi (N);
-void totient(int n) {
+void totient(int n) { //<@\compl{n \lg n}@>
for (int i = 1; i <= n; i++) { phi[i] = i; }
for (int i = 2; i <= n; i++) if (phi[i] == i) {
for (int j = i; j <= n; j += i) {
diff --git a/fontes/eulerian-path.h b/fontes/eulerian-path.h
index 9bb3a344d634e450cec9d8c9d565928004d042ca..3b8b6c09023d3a2341f4581d7c06743919501099 100644
--- a/fontes/eulerian-path.h
+++ b/fontes/eulerian-path.h
@@ -1,13 +1,12 @@
-vector<int> eulerian_path(int src, int n) {
+vector<int> eulerian_path(int src, int n) { //<@\compl{n+m}@>
for (int u = 0; u < n; u++)
if (deg[u] % 2) { return {}; }
stack<int> st; st.push(src);
- vector<int> res;
+ vector<int> ans;
while (!st.empty()) {
int u = st.top();
if (g[u].empty()) {
- res.push_back(u);
- st.pop();
+ ans.push_back(u); st.pop();
} else {
int v = *begin(g[u]);
g[u].erase(g[u].find(v));
@@ -17,6 +16,6 @@ vector<int> eulerian_path(int src, int n) {
}
for (int u = 0; u < n; u++) if (g[u].size())
return {};
- reverse(all(res));
- return res;
+ reverse(all(ans));
+ return ans;
}
diff --git a/fontes/extended-euclidean.h b/fontes/extended-euclidean.h
index 61b6a6cb42df1b156e8ae78629a9456bedde2483..6aeb76295a925849c9878cf4418c7591698af49b 100644
--- a/fontes/extended-euclidean.h
+++ b/fontes/extended-euclidean.h
@@ -1,4 +1,4 @@
-ll extgcd(ll a, ll b, ll& x, ll& y) {
+ll extgcd(ll a, ll b, ll& x, ll& y) { //<@\compl{\lg \min(a, b)}@>
if (b == 0) { x = 1; y = 0; return a; }
ll g = extgcd(b, a%b, x, y);
tie(x, y) = make_tuple(y, x - (a/b)*y);
diff --git a/fontes/factorize.h b/fontes/factorize.h
index 1cf040c3dd97634b32f6b9ced3709f84ec197615..4961dcdcae8d6d3114f5622b83035d4105ba422b 100644
--- a/fontes/factorize.h
+++ b/fontes/factorize.h
@@ -1,11 +1,8 @@
-vector<int> factorize(ll n) {
- vector<int> v;
+map<int, int> factorize(ll n) { //<@\compl{\sqrt{n}}@>
+ map<int, int> v;
for (ll i = 2; i*i <= n; i++)
- while (n % i == 0) {
- n /= i;
- v.push_back(i);
- }
- if (n > 1)
- v.push_back(n);
+ while (n % i == 0)
+ n /= i, v[i]++;
+ if (n > 1) { v[n]++; }
return v;
}
diff --git a/fontes/fenwick-2d-tree.h b/fontes/fenwick-2d-tree.h
index 044009d1548633d21fc50f78ad7fa5c983d3abdc..ca0a95f5d163e41d7c1b95e4ba8dacead5571e5a 100644
--- a/fontes/fenwick-2d-tree.h
+++ b/fontes/fenwick-2d-tree.h
@@ -1,12 +1,12 @@
vector<vector<ll>> bit (N, vector<ll>(M));
-void add(int x, int y, ll d) {
+void add(int x, int y, ll d) { //<@\compl{\lg^2 n}@>
for (; x < N; x += x & -x)
for (int j = y; j < M; j += j & -j)
bit[x][j] += d;
}
-ll pref(int x, int y) {
+ll pref(int x, int y) { //<@\compl{\lg^2 n}@>
ll sum = 0;
for (; x > 0; x -= x & -x)
for (int j = y; j > 0; j -= j & -j)
diff --git a/fontes/fenwick-range-tree.h b/fontes/fenwick-range-tree.h
index a8d6142c8b53cb41b81c80bc4f17f85e3993e588..b9df47b63745a2243c17986c0ddc9a0a072edb5d 100644
--- a/fontes/fenwick-range-tree.h
+++ b/fontes/fenwick-range-tree.h
@@ -1,10 +1,10 @@
vector<ll> bit1 (N), bit2 (N);
-void add(vector<ll>& bit, int i, ll d) {
+void add(vector<ll>& bit, int i, ll d) { //<@\compl{\lg n}@>
for (; i < N; i += i & -i) { bit[i] += d; }
}
-ll pref(vector<ll>& bit, int i) {
+ll pref(vector<ll>& bit, int i) { //<@\compl{\lg n}@>
ll sum = 0;
for (; i > 0; i -= i & -i) { sum += bit[i]; }
return sum;
diff --git a/fontes/fenwick-tree.h b/fontes/fenwick-tree.h
index 686efc32997d6bbdd07196cf2c79305db4db8987..d4a9915377ef7745aa79a3728d3a4d9438d1b379 100644
--- a/fontes/fenwick-tree.h
+++ b/fontes/fenwick-tree.h
@@ -1,27 +1,27 @@
vector<ll> bit (N, 0);
-void add(int i, ll d) {
+void add(int i, ll d) { //<@\compl{\lg n}@>
for (; i < N; i += i & -i) { bit[i] += d; }
}
-ll pref(int i) {
+ll pref(int i) { //<@\compl{\lg n}@>
ll sum = 0;
for (; i > 0; i -= i & -i) { sum += bit[i]; }
return sum;
}
int sum_inclusive(int i, int j) {
- return pref(j) - pref(i - 1);
+ return pref(j) - pref(i-1);
}
void add_inclusive(int a, int b, ll d) {
add(a, d); add(b + 1, -d);
}
-int lower_bound(ll t) {
+int lower_bound(ll t) { //<@\compl{\lg n}@>
ll sum = 0; int pos = 0;
for (int p = log2(N); p >= 0; p--) if (
- pos + (1 << p) < N && sum + bit[pos + (1 << p)] < t) {
+ pos + (1<<p) < N && sum + bit[pos + (1<<p)] < t) {
sum += bit[pos + (1 << p)];
pos += (1 << p);
}
diff --git a/fontes/floyd-warshall.h b/fontes/floyd-warshall.h
index df7d13beb6196e1fae48f43135d3528c61d67213..33ddf3537766b1b057c33859adc8f89be3750104 100644
--- a/fontes/floyd-warshall.h
+++ b/fontes/floyd-warshall.h
@@ -1,6 +1,6 @@
vector<vector<ll>> d (N, vector<ll>(N, oo));
-void floydwarshall(int n) {
+void floydwarshall(int n) { //<@\compl{n^3}@>
for (int u = 0; u < n; u++)
d[u][u] = 0;
for (int m = 0; m < n; m++)
diff --git a/fontes/ford-fulkerson-edmons-karp-min-cost.h b/fontes/ford-fulkerson-edmons-karp-min-cost.h
index 97f25d37f22c1e68ebc56b599bc2844b3e204219..de6b718388d374b7ecad3498c8eb7549b4dcfbca 100644
--- a/fontes/ford-fulkerson-edmons-karp-min-cost.h
+++ b/fontes/ford-fulkerson-edmons-karp-min-cost.h
@@ -1,6 +1,5 @@
struct edge { int u, v, cap, cost; };
vector<edge> edges;
-
vector<int> queu (N), ix (N), dist (N), par (N);
void link(int u, int v, int cap, int cost) {
diff --git a/fontes/ford-fulkerson-edmons-karp.h b/fontes/ford-fulkerson-edmons-karp.h
index 5def2dedfa683c4709bcc1d5fdd8c2e084f8c448..ee547da42d68a46abe6ec14ba7e41d3f38391af7 100644
--- a/fontes/ford-fulkerson-edmons-karp.h
+++ b/fontes/ford-fulkerson-edmons-karp.h
@@ -26,13 +26,12 @@ bool minimum_path(int s, int t) {
return dist[t] < oo;
}
-pair<int, int> ffek /* O(VE^2) */(int s, int t) {
+pair<int, int> ffek(int s, int t) { //<@\compl{nm^2}@>
int min_cost = 0, max_flow = 0;
while (minimum_path(s, t)) {
int flow = oo;
- for (int u = t; u != s; u = par[u]) {
+ for (int u = t; u != s; u = par[u])
flow = min(flow, edges[ix[u]].cap);
- }
for (int u = t; u != s; u = par[u]) {
edges[ix[u] ].cap -= flow;
edges[ix[u]^1].cap += flow;
diff --git a/fontes/gauss.h b/fontes/gauss.h
index 2abfb8cc4b3161e90bc65998ae98d5b52c07d2b8..329b05246b6148d9e9cf2b36bf0f7e58cc0e0a88 100644
--- a/fontes/gauss.h
+++ b/fontes/gauss.h
@@ -1,5 +1,5 @@
template<typename T>
-pair<int, vector<T>> gauss(
+pair<int, vector<T>> gauss( //<@\compl{mn^2}@>
vector<vector<T>> a, vector<T> b) {
const double eps = 1e-6;
int n = a.size(), m = a[0].size();
diff --git a/fontes/generalized-chinese-remainder-theorem.h b/fontes/generalized-chinese-remainder-theorem.h
index 6fb5fc518c6c6e0abf85a50993fc87184f17714d..abd721e88d237a529b1510c0d987d5eaa5a77de7 100644
--- a/fontes/generalized-chinese-remainder-theorem.h
+++ b/fontes/generalized-chinese-remainder-theorem.h
@@ -1,19 +1,19 @@
ll norm(ll a, ll b) {
- a %= b; return (a < 0) ? a + b : a;
+ a %= b; return (a < 0) ? a + b : a;
}
pair<ll, ll> crt_single(ll a, ll n, ll b, ll m) {
- ll x, y; ll g = extgcd(n, m, x, y);
- if ((a - b) % g) { return {-1, -1}; }
- ll lcm = (m/g) * n;
- return {norm(a + n*(x*(b-a)/g % (m/g)), lcm), lcm};
+ ll x, y; ll g = extgcd(n, m, x, y);
+ if ((a - b) % g) { return {-1, -1}; }
+ ll lcm = (m/g) * n;
+ return {norm(a + n*(x*(b-a)/g % (m/g)), lcm), lcm};
}
ll crt(vector<ll> a, vector<ll> m, int t) {
- ll ans = a[0], lcm = m[0];
- for (int i = 1; i < t; ++i) {
- tie(ans, lcm) = crt_single(ans, lcm, a[i], m[i]);
- if (ans == -1) { return -1; }
- }
- return ans;
+ ll ans = a[0], lcm = m[0];
+ for (int i = 1; i < t; ++i) {
+ tie(ans, lcm) = crt_single(ans, lcm, a[i], m[i]);
+ if (ans == -1) { return -1; }
+ }
+ return ans;
}
diff --git a/fontes/hash.sh b/fontes/hash.sh
index 3990611f3f56cf6e70d14c76ccdf78dfd8d87618..6543aa1ad1404f864f9b21eb2231efeeafd5947b 100644
--- a/fontes/hash.sh
+++ b/fontes/hash.sh
@@ -1,2 +1,7 @@
-sed -n $2','$3' p' $1 | sed '/^#w/d' | cpp -dD -P \
- -fpreprocessed | tr -d '[:space:]' | md5sum | cut -c -3
+while IFS="" read -r l; do
+ h=$(echo "$l" | sed '/^#w/d' |
+ cpp -dD -P -fpreprocessed |
+ tr -d '[:space:]' | md5sum | cut -c -3)
+ [ -z "$l" ] && h=""
+ echo "$h $l"
+done
diff --git a/fontes/hld.h b/fontes/hld.h
index 73d19f0532bbfdeb00df81f23a224406cbc23c27..30e79ab00f1504b4588987042984ec903bfa36bb 100644
--- a/fontes/hld.h
+++ b/fontes/hld.h
@@ -21,7 +21,7 @@ void hld(int u, int h) {
hld(v, v); // new chain
}
-ll hld_op(int u, int v, bool edge_wei = 1) {
+ll hld_op(int u, int v, bool edge_wei = 1) { //<@\compl{\lg q}@>
ll ans = 0;
for (; hds[u] != hds[v]; v = par[hds[v]]) {
if (dep[hds[u]] > dep[hds[v]]) { swap(u, v); }
@@ -31,6 +31,6 @@ ll hld_op(int u, int v, bool edge_wei = 1) {
return OP(ans, op_inclusive(ixs[u] + edge_wei, ixs[v]));
}
-void hld_init(int u, int n) {
+void hld_init(int u, int n) { //<@\compl{n+m+b}@>
cix = 1; hld_fill(u, u); hld(u, u); build(ori, n);
}
diff --git a/fontes/interval-set.h b/fontes/interval-set.h
index 818d3a76542afd2c7f82fa7308a898701841ec1f..8db08b75ade7a399065bbbb4b1c2e833a7b42b88 100644
--- a/fontes/interval-set.h
+++ b/fontes/interval-set.h
@@ -9,7 +9,7 @@ struct itvl {
set<itvl, less<>> si;
-void ins_in(itvl in) {
+void ins_in(itvl in) { //<@\compl{\lg n}@>
auto it = si.lower_bound(in);
int a = in.a, b = in.b, c = in.c;
if (si.size() > 0 && it != begin(si)
@@ -23,7 +23,7 @@ void ins_in(itvl in) {
si.insert(itvl(a, b, c));
}
-void upd_color(int a, int b, int c) {
+void upd_color(int a, int b, int c) { //<@\compl{\lg n}@>
auto it = si.lower_bound(b);
if (it != end(si)) {
itvl ori = *it; si.erase(it);
diff --git a/fontes/josephus.h b/fontes/josephus.h
index 89062e672ccd2b2f083d5291342eb0e918675852..80b00f8c68da71451bf76011735ff88c1c563313 100644
--- a/fontes/josephus.h
+++ b/fontes/josephus.h
@@ -1,13 +1,13 @@
-int josephusrec(int n, int k) {
+int josephusrec(int n, int k) { //<@\compl{n}@>
return n ? (josephusrec(n-1, k) + k) % n : 0;
}
-int josephus /* O(n) */ (int n, int k) {
+int josephus(int n, int k) { //<@\compl{n}@>
int res = 0;
for (int i = 1; i <= n; ++i)
res = (res + k) % i;
return res+1;
}
-int josephusklgn /* O(k log n) */ (int n, int k) {
+int josephusklgn(int n, int k) { //<@\compl{k\lg n}@>
if (n == 1) { return 0; }
if (k == 1) { return n-1; }
if (k > n) { return (josephusklgn(n-1, k) + k) % n; }
diff --git a/fontes/k-elements.h b/fontes/k-elements.h
index 043baed7ba8024fe2a0be6eb4ebf6dc876cc7e7b..3ac64dda75660b3bb567284b9b27b38472c7eafd 100644
--- a/fontes/k-elements.h
+++ b/fontes/k-elements.h
@@ -8,7 +8,7 @@ template <class C = less<>>
struct k_elements {
int k; ord_set<pair<ll, int>, C> s; ll sum;
k_elements(int k) : k(k), sum(0) {};
- void insert(int key, ll value) {
+ void insert(int key, ll value) { //<@\compl{\lg n}@>
int l = s.order_of_key(make_pair(value, key));
s.insert(make_pair(value, key));
if (l >= k) { return; }
@@ -16,7 +16,7 @@ struct k_elements {
if (s.size() > k)
sum -= s.find_by_order(k)->first;
}
- void remove(int key, ll value) {
+ void remove(int key, ll value) { //<@\compl{\lg n}@>
if (s.order_of_key(make_pair(value, key)) < k) {
sum -= value;
if (s.size() > k)
diff --git a/fontes/kadane.h b/fontes/kadane.h
index 76dec7c7df4505528e417d8f92294e13b15cfc14..eb07582aa05a84f2ff0c04c8e100048a1ad34608 100644
--- a/fontes/kadane.h
+++ b/fontes/kadane.h
@@ -1,13 +1,13 @@
struct kadane {
- int sum, pref, suff, ans;
- kadane() : sum(-oo) { pref = suff = ans = 0; }
- kadane(int x) : sum(x) { pref = suff = ans = max(x, 0); }
+ int sum, pre, suf, ans;
+ kadane(int x) : sum(x) { pre = suf = ans = max(x, 0); }
+ kadane() : kadane(-oo) {}
kadane operator+(kadane const& r) {
auto l = *this; kadane a;
a.sum = max(l.sum + r.sum, -oo);
- a.pref = max(l.pref, l.sum + r.pref);
- a.suff = max(r.suff, r.sum + l.suff);
- a.ans = max({ l.ans, r.ans, l.suff + r.pref });
+ a.pre = max(l.pre, l.sum + r.pre);
+ a.suf = max(r.suf, r.sum + l.suf);
+ a.ans = max({ l.ans, r.ans, l.suf + r.pre });
return a;
}
}
diff --git a/fontes/karatsuba.h b/fontes/karatsuba.h
index b9b60e4cec68f416b707164e48f922a1ea5d672d..48e949adc65e6ee6148d51dc8ebdb849fd5bf726 100644
--- a/fontes/karatsuba.h
+++ b/fontes/karatsuba.h
@@ -1,5 +1,5 @@
-vector<ll> karatsuba(const vector<ll> &a,
- const vector<ll> &b) {
+vector<ll> karatsuba /* O(n^{log 3 n})*/(
+ const vector<ll> &a, const vector<ll> &b) {
int n = a.size();
vector<ll> res(n + n);
if (n <= 32) {
diff --git a/fontes/kosaraju.h b/fontes/kosaraju.h
index 1a4d62aed966de20b35cb9f1c7d57f485ae885fe..6f6fe21ea21648efd69545df4afcf34de942809f 100644
--- a/fontes/kosaraju.h
+++ b/fontes/kosaraju.h
@@ -1,10 +1,8 @@
-int cts = 1;
-vector<int> vis (N), rep (N);
+int cts = 1; vector<int> vis (N), rep (N);
stack<int> sinks;
void fill_stack(int u) {
- if (vis[u] == cts) { return; }
- vis[u] = cts;
+ if (vis[u] == cts) { return; } vis[u] = cts;
for (int v : g_t[u]) { fill_stack(v); }
sinks.push(u);
}
@@ -15,10 +13,9 @@ void mark_component(int u, int r) {
for (int v : g[u]) { mark_component(v, r); }
}
-stack<int> kosaraju(int n) {
+stack<int> kosaraju(int n) { //<@\compl{n+m}@>
for (int u = 0; u < n; u++) { fill_stack(u); }
- cts++;
- stack<int> topo;
+ cts++; stack<int> topo;
while (!sinks.empty()) {
int u = sinks.top(); sinks.pop();
mark_component(u, u);
diff --git a/fontes/kruskal.h b/fontes/kruskal.h
index 08633801142cad3f6105fda66c20b29d695231cc..c0f2bddfaae02977e5b28ef341ea7f8eb41e5965 100644
--- a/fontes/kruskal.h
+++ b/fontes/kruskal.h
@@ -3,7 +3,7 @@ struct edge {
bool operator<(struct edge &o) { return w < o.w; }
};
-int kruskal(int n) {
+int kruskal(int n) { //<@\compl{m\alpha(n)}@>
sort(all(edges));
ds_init(n); int components = n; ll sum = 0;
for (auto [u, v, w] : edges) {
diff --git a/fontes/kuhn.h b/fontes/kuhn.h
index 855e504ebb8f30b46d38ccc965db4161161edaac..049c1545d40ffe6ad05e6d722f5ad28651253cd3 100644
--- a/fontes/kuhn.h
+++ b/fontes/kuhn.h
@@ -1,3 +1,4 @@
+// distinct enumeration
vector<vector<int>> g (L);
vector<int> matchr (R, -1);
@@ -10,7 +11,7 @@ int dfs(int u) {
return 0;
}
-int kuhn(int l) {
+int kuhn(int l) { //<@\compl{nm}@>
int ans = 0;
for (int u = 0; u < l; u++) { ans += dfs(u); cts++; }
return ans;
diff --git a/fontes/lazy-segment-tree.h b/fontes/lazy-segment-tree.h
index 9ad17ad67e963b5a32d27d45eab7468a27280c73..64115a750843cfb923a6f37e4093c8d7a66c0ca0 100644
--- a/fontes/lazy-segment-tree.h
+++ b/fontes/lazy-segment-tree.h
@@ -2,7 +2,7 @@ const int L = ceil(log2(N));
struct dlta { int add = 0, set = -1; };
vector<ll> t (2*N); vector<dlta> delta (2*N);
-void build(vector<int>& src, int n) {
+void build(vector<int>& src, int n) { //<@\compl{n}@>
for (int i = 1; i <= n; i++)
t[n+i] = src[i];
for (int ti = n-1; ti > 0; ti--)
@@ -39,7 +39,7 @@ void push(int i) {
}
void apply_inclusive(int l, int r, int n,
- char op = '\0', ll x = 0) {
+ char op = '\0', ll x = 0) { //<@\compl{\lg n}@>
r++; dlta d;
if (op == '+') { d.add = x; }
if (op == '=') { d.set = x; }
@@ -56,7 +56,7 @@ void add_inclusive(int l, int r, int n, ll d) {
apply_inclusive(l, r, n, '+', d);
}
-ll op_inclusive(int l, int r, int n) {
+ll op_inclusive(int l, int r, int n) { //<@\compl{\lg n}@>
r++;
int tl = l += n, tr = r += n, sz = 1;
push(tl); push(tr);
diff --git a/fontes/lca-offline.h b/fontes/lca-offline.h
index 8a87143ff8eff866426dc399316d9973ccb373da..125513909b6c4549ed8684d218d45aebd5150956 100644
--- a/fontes/lca-offline.h
+++ b/fontes/lca-offline.h
@@ -1,7 +1,7 @@
vector<vector<int>> queries (N);
vector<int> anc (N); vector<bool> vis (N);
-void dfs(int u) {
+void dfs(int u) { //<@\compl{n\alpha(n)+m+q\alpha(n)}@>
vis[u] = 1; anc[u] = u;
for (int v : adj[u]) if (!vis[v]) {
dfs(v); ds_unite(u, v); anc[ds_find(u)] = u;
diff --git a/fontes/min-queue.h b/fontes/min-queue.h
index 1c0fd81e5c21023657cca97939dca3d5087c4f2a..99f1f504d4cec8fe5d59084b869f2c27b1b404ff 100644
--- a/fontes/min-queue.h
+++ b/fontes/min-queue.h
@@ -1,10 +1,10 @@
stack<pair<int, int>> s1, s2;
-void enqueue_el(int x) {
+void enqueue_el(int x) { //<@\compl{1}@>
int m = min(x, s1.size() ? s1.top().second : oo);
s1.push({ x, m });
}
-int dequeue_el() {
+int dequeue_el() { //<@\compl{1}@>
if (s2.empty()) while (!s1.empty()) {
int el = s1.top().first; s1.pop();
int m = min(el, s2.size() ? s2.top().second : oo);
@@ -12,7 +12,7 @@ int dequeue_el() {
}
int r = s2.top().first; s2.pop(); return r;
}
-int min_el() {
+int min_el() { //<@\compl{1}@>
return min(
s1.size() ? s1.top().second : oo,
s2.size() ? s2.top().second : oo);
diff --git a/fontes/min-stack.h b/fontes/min-stack.h
index 904b5c2ac3f551dd409f8afbdd2ea052c0798c1f..f879311f8b4d3e2b2708d12acf75dfdd0d9f48c3 100644
--- a/fontes/min-stack.h
+++ b/fontes/min-stack.h
@@ -1,9 +1,12 @@
stack<pair<int, int>> st;
-void push_el(int x) {
+void push_el(int x) { //<@\compl{1}@>
int m = st.empty() ? x : min(x, st.top().second);
st.push({x, m});
}
-int pop_el() {
- int r = st.top().first; st.pop(); return r; }
-int min_el() { return st.top().second; }
+int pop_el() { //<@\compl{1}@>
+ int r = st.top().first; st.pop(); return r;
+}
+int min_el() { //<@\compl{1}@>
+ return st.top().second;
+}
diff --git a/fontes/next-greater-element.h b/fontes/next-greater-element.h
index da7a813ebbf719be6fa2e91c60c4b0e61ead813a..4ed26c44f51af573c143181e67a99be27bd219f6 100644
--- a/fontes/next-greater-element.h
+++ b/fontes/next-greater-element.h
@@ -1,9 +1,11 @@
-stack<int> nge;
-// start from the end for previous
-for (int i = 0; i < n; i++) {
- // < is greater next, > is lesser next
- while (!nge.empty() && v[nge.top()] < v[i]) {
- ans[nge.top()] = i; nge.pop();
+vector<int> next_greater_element(vector<int> v) { //<@\compl{n}@>
+ vector<int> ans (v.size()); stack<int> nge;
+ // start from the end for previous
+ for (int i = 0; i < n; i++) {
+ // < is greater next, > is lesser next
+ while (!nge.empty() && v[nge.top()] < v[i])
+ ans[nge.top()] = i, nge.pop();
+ nge.push(i);
}
- nge.push(i);
+ return ans;
}
diff --git a/fontes/number-theoretic-transform.h b/fontes/number-theoretic-transform.h
index db36cc319de5b6d16651d102429c56d6c5b93024..3c813db35120a6b65e34b440ad3179b2cfad01fc 100644
--- a/fontes/number-theoretic-transform.h
+++ b/fontes/number-theoretic-transform.h
@@ -1,9 +1,8 @@
-void ntt (vector<mint>& a, bool rev) {
+void ntt(vector<mint>& a, bool rev) { //<@\compl{n \lg n}@>
int n = a.size(); auto b = a;
mint g = 1;
while (binary_pow(g, P/2) == 1) g += 1;
if (rev) { g = binary_pow(g.x, P-2); }
-
for (int st = n/2; st; st /= 2) {
mint w = binary_pow(g, P/(n/st)), wn = 1;
for (int i = 0; i < n/2; i += st) {
@@ -15,12 +14,12 @@ void ntt (vector<mint>& a, bool rev) {
}
swap(a, b);
}
-
mint n1 = binary_pow(n, P-2);
if (rev) for (mint& x : a) { x *= n1; }
}
-vector<mint> convolution (vector<mint>& a, vector<mint>& b) {
+vector<mint> convolution (
+ vector<mint>& a, vector<mint>& b) {
vector<mint> fa (all(a)), fb (all(b));
int n = 1;
while (n < a.size() + b.size()) { n *= 2; }
diff --git a/fontes/pollard-rho.h b/fontes/pollard-rho.h
index 1bf2067d84db7c7c321d5293938f900e989123d2..1d5ae6737bb37c4850ebdef69ac88a86c6937cfc 100644
--- a/fontes/pollard-rho.h
+++ b/fontes/pollard-rho.h
@@ -1,4 +1,4 @@
-ll pollard(ll n) {
+ll pollard(ll n) { //<@\compl{n^{\frac{1}{4}}}@>
auto f = [n](ll x) {
return (fast_pow(x, x, n) + 1) % n;
};
diff --git a/fontes/prim.h b/fontes/prim.h
index 33dadb076a2836cf68746c914fcb835bb1a6acbe..470533ebc3b83d82704e00039dbd44161e64e27a 100644
--- a/fontes/prim.h
+++ b/fontes/prim.h
@@ -1,4 +1,4 @@
-ll prim(int src, int n) {
+ll prim(int src, int n) { //<@\compl{(m + n)\lg n}@>
vector<bool> vis (n); vector<int> par (n, -1);
vector<ll> d (n, oo); vector<vector<ii>> pt (n);
ll sum = 0;
diff --git a/fontes/recursive-lazy-segment-tree.h b/fontes/recursive-lazy-segment-tree.h
index dd638c60142a41ad77cfdb485cb46cd96c385031..0995ed6286e4c26aee044b8a9b64848696e123b0 100644
--- a/fontes/recursive-lazy-segment-tree.h
+++ b/fontes/recursive-lazy-segment-tree.h
@@ -1,7 +1,7 @@
vector<ll> t (4*N), lazy (4*N), sety (4*N, -1);
void build(vector<int>& src,
- int ti=1, int tl=1, int tr=N) {
+ int ti=1, int tl=1, int tr=N) { //<@\compl{n}@>
if (tl == tr) {
if (tl < src.size()) { t[ti] = src[tl]; }
return;
@@ -28,7 +28,7 @@ void push(int ti, int tl, int tm, int tr) {
}
void update_inclusive(int l, int r, char op, int d,
- int ti=1, int tl=1, int tr=N) {
+ int ti=1, int tl=1, int tr=N) { //<@\compl{\lg n}@>
if (l > r) { return; }
if (l == tl && tr == r) {
if (op == '=') {
@@ -46,7 +46,7 @@ void update_inclusive(int l, int r, char op, int d,
}
ll op_inclusive(int l, int r,
- int ti=1, int tl=1, int tr=N) {
+ int ti=1, int tl=1, int tr=N) { //<@\compl{\lg n}@>
if (l > r) { return NEUTRAL; }
if (l <= tl && tr <= r) { return t[ti]; }
int tm = (tl + tr) / 2; push(ti, tl, tm, tr);
diff --git a/fontes/recursive-segment-tree.h b/fontes/recursive-segment-tree.h
index 10916c2e8681ff14529e904752ff0d0320cde8c3..15953450f9d4234d8fb98c6d5ceac6733591441f 100644
--- a/fontes/recursive-segment-tree.h
+++ b/fontes/recursive-segment-tree.h
@@ -1,7 +1,7 @@
vector<ll> t (4*N);
void build(vector<ll>& src,
- int ti=1, int tl=1, int tr=N) {
+ int ti=1, int tl=1, int tr=N) { //<@\compl{n}@>
if (tl == tr) {
if (tl < src.size()) { t[ti] = src[tl]; }
return;
@@ -13,7 +13,7 @@ void build(vector<ll>& src,
}
ll op_inclusive(int l, int r,
- int ti=1, int tl=1, int tr=N) {
+ int ti=1, int tl=1, int tr=N) { //<@\compl{\lg n}@>
if (l > r) { return NEUTRAL; }
if (l == tl && r == tr) { return t[ti]; }
int tm = (tl + tr) / 2;
@@ -22,12 +22,10 @@ ll op_inclusive(int l, int r,
}
void set_value(int i, ll v,
- int ti=1, int tl=1, int tr=N) {
+ int ti=1, int tl=1, int tr=N) { //<@\compl{\lg n}@>
if (tl == tr) { t[ti] = v; return; }
int tm = (tl + tr) / 2;
- if (i <= tm)
- set_value(i, v, ti*2, tl, tm);
- else
- set_value(i, v, ti*2+1, tm+1, tr);
+ if (i <= tm) { set_value(i, v, ti*2, tl, tm); }
+ else { set_value(i, v, ti*2+1, tm+1, tr); }
t[ti] = OP(t[ti*2], t[ti*2+1]);
}
diff --git a/fontes/segment-tree.h b/fontes/segment-tree.h
index c9869545274e9d18f5f9b7e56331cd30f07bb009..6c96c9c7433f66c83409e16524a1d0306f3a85e3 100644
--- a/fontes/segment-tree.h
+++ b/fontes/segment-tree.h
@@ -1,15 +1,14 @@
vector<int> t (2*N);
-void build(vector<int>& src, int n) {
+void build(vector<int>& src, int n) { //<@\compl{n}@>
for (int i = 1; i <= n; i++)
t[n+i] = src[i];
for (int ti = n-1; ti > 0; ti--)
t[ti] = OP(t[2*ti], t[2*ti+1]);
}
-int op_inclusive(int l, int r, int n) {
- r++;
- int left = NEUTRAL, righ = NEUTRAL;
+int op_inclusive(int l, int r, int n) { //<@\compl{\lg n}@>
+ r++; int left = NEUTRAL, righ = NEUTRAL;
for (l += n, r += n; l < r; l /= 2, r /= 2) {
if (l & 1) left = OP(left, t[l++]);
if (r & 1) righ = OP(t[--r], righ);
@@ -17,7 +16,7 @@ int op_inclusive(int l, int r, int n) {
return OP(left, righ);
}
-void set_value(int i, int v, int n) {
+void set_value(int i, int v, int n) { //<@\compl{\lg n}@>
t[i += n] = v;
for (i /= 2; i > 0; i /= 2)
t[i] = OP(t[i*2], t[i*2+1]);
diff --git a/fontes/sieve.h b/fontes/sieve.h
index 31440de6b614641f75c1c620a8a754d65a083508..b31a6f2897b8e89298002858135b1aaa2365010d 100644
--- a/fontes/sieve.h
+++ b/fontes/sieve.h
@@ -1,5 +1,5 @@
vector<bool> sieve (1e7+15, 1);
-void eratosthenes(int n) {
+void eratosthenes(int n) { //<@\compl{n \lg \lg n}@>
for (int i = 2; i * i <= n; i++) if (sieve[i])
for (int j = i * i; j <= n; j += i)
sieve[j] = 0;
diff --git a/fontes/small-to-large.h b/fontes/small-to-large.h
index e098a046ca50bf15d7bfd7aecc212fabe4bf360a..5488fe70b5e19fecaceaf3720014ba687f8a243c 100644
--- a/fontes/small-to-large.h
+++ b/fontes/small-to-large.h
@@ -1,5 +1,4 @@
-vector<int> hvy (N);
-vector<int> sz (N, 1);
+vector<int> hvy (N), sz (N, 1);
int calc_size(int u, int p) {
for (int v : g[u]) if (v != p)
@@ -8,12 +7,12 @@ int calc_size(int u, int p) {
}
void dfs_add(int u, int p, int x) {
- // add
+ // implement add
for (int v : g[u]) if (v != p && !hvy[v])
dfs_add(v, u, x);
}
-void small_large(int u, int p, bool keep) {
+void small_large(int u, int p, bool keep) { //<@\compl{n\lg n}@>
int mx = -1, h = -1;
for (int v : g[u]) if (v != p && sz[v] > mx) {
mx = sz[v]; h = v;
@@ -22,7 +21,7 @@ void small_large(int u, int p, bool keep) {
small_large(v, u, 0);
if (h != -1) { small_large(h, u, 1); hvy[h] = 1; }
dfs_add(u, p, +1);
- // solve queries
+ // solve queries for u
if (h != -1) { hvy[h] = 0; }
if (keep == 0) { dfs_add(u, p, -1); }
}
diff --git a/fontes/sparse-table.h b/fontes/sparse-table.h
index c54a2a8504ec6870677756be8f3769b38a14a97f..c42a221988914fcbafb537bc05a09c0a4446a136 100644
--- a/fontes/sparse-table.h
+++ b/fontes/sparse-table.h
@@ -1,19 +1,15 @@
const int K = 25;
-vector<int> lg (N+1);
vector<vector<int>> st (N, vector<int>(K+1));
-void build(vector<int>& src) {
- lg[1] = 0;
- for (int i = 2; i <= N; i++) { lg[i] = lg[i/2] + 1; }
+void build(vector<int>& src) { //<@\compl{n \lg n}@>
for (int i = 0; i < src.size(); i++)
st[i][0] = src[i];
-
for (int j = 1; j <= K; j++)
for (int i = 0; i + (1 << j) <= N; i++)
st[i][j] = min(st[i][j-1], st[i+(1 << (j-1))][j-1]);
}
-int min_inclusive(int l, int r) {
- int j = lg[r-l+1];
+int min_inclusive(int l, int r) { //<@\compl{1}@>
+ int j = __lg(r-l+1);
return min(st[l][j], st[r-(1 << j)+1][j]);
}
diff --git a/fontes/spfa.h b/fontes/spfa.h
index 661c124255953598361e3501dc067da7963cb2b8..58cd40d8f986ce9fe531c8884cd7cee2fd0e3a0b 100644
--- a/fontes/spfa.h
+++ b/fontes/spfa.h
@@ -1,4 +1,4 @@
-bool spfa(int src, int n) {
+bool spfa(int src, int n) { //<@\compl{nm}@>
vector<int> cnt (n); vector<bool> queu (n);
vector<ll> d (n, oo);
queue<int> q; q.push(src); d[src] = 0;
diff --git a/fontes/stable-matching.h b/fontes/stable-matching.h
index ff39bf1a9f7a0d42eb2dc44dde7eb025052ac2c2..18a49d54e71d62de9f4d010d8ef9bd146ae8338c 100644
--- a/fontes/stable-matching.h
+++ b/fontes/stable-matching.h
@@ -3,12 +3,10 @@ vector<vi> pwix (N, vi(N+1)); // [w][m] = j
vector<bool> single (N, 1);
vector<int> match (N, -1), watch (N, N);
-vector<ii> galeshapley(int n) {
- // sentinel
+vector<ii> galeshapley(int n) { //<@\compl{n^2}@>
for (int w = 0; w < n; w++) { pwix[w][n] = n; }
bool done = 0;
- while (!done) {
- done = 1;
+ while (!done) { done = 1;
for (int m = 0; m < n; m++) if (single[m]) {
done = 0; match[m] += 1;
int w = pm[m][match[m]];
diff --git a/fontes/stoer-wagner.h b/fontes/stoer-wagner.h
index 65a50eecc31e79813896ba4d3788a58900e6b501..5a6f76f2a528f38783c894fd3a2530f2b61114a7 100644
--- a/fontes/stoer-wagner.h
+++ b/fontes/stoer-wagner.h
@@ -22,7 +22,7 @@ int contract(int n, int &s, int &t) {
return mincut;
}
-int stoer_wagner(int n) {
+int stoer_wagner(int n) { //<@\compl{nm + n^2\lg n}@>
int mincut = oo, s, t;
for (int i = 0; i < n-1; i++) {
mincut = min(mincut, contract(n, s, t));
diff --git a/fontes/suffix-array-radix.h b/fontes/suffix-array-radix.h
index 0837d4f35d9e1af2e60066e759f9fd6640d3c652..7c2739f5644cc3ad9748abb84c012bae4ac47e26 100644
--- a/fontes/suffix-array-radix.h
+++ b/fontes/suffix-array-radix.h
@@ -3,7 +3,7 @@ pair<vector<int>, vector<int>> build_sa(string s, int n) {
vector<pair<int, int>> a (n);
for (int i = 0; i < n; i++) { a[i] = { s[i], i }; }
sort(all(a));
- for (int i = 0; i < n; i++) { tie(sk[i], sa[i]) = a[i]; }
+ for (int i = 0; i < n; i++) { tie(sk[i],sa[i]) = a[i]; }
vector<int> nsk(n);
for (int i = 1, r = 0; i < n; i++)
nsk[sa[i]] = (sk[i-1] == sk[i] ? r : ++r);
diff --git a/fontes/tarjan.h b/fontes/tarjan.h
index 1b549b84a9bf6ea092c87c93fb08e24c9fe773df..321b7772f5acb3ae6aacf8efa7016bf83d8b6aae 100644
--- a/fontes/tarjan.h
+++ b/fontes/tarjan.h
@@ -1,6 +1,5 @@
vector<int> tin (N, -1), lowlnk (N, -1), rep (N);
-stack<int> st, topo;
-int cts = 1;
+stack<int> st, topo; int cts = 1;
void dfs_tarjan(int u) {
if (tin[u] != -1) { return; }
@@ -19,7 +18,7 @@ void dfs_tarjan(int u) {
}
}
-stack<int> tarjan(int n) {
+stack<int> tarjan(int n) { //<@\compl{n+m}@>
for (int u = 0; u < n; u++) { dfs_tarjan(u); }
return topo;
}
diff --git a/fontes/topological-order.h b/fontes/topological-order.h
index dbf4edb3b648d8c9a6ef00fab13ec5316738c283..613421f43182686483133043daed20f09a273e68 100644
--- a/fontes/topological-order.h
+++ b/fontes/topological-order.h
@@ -7,7 +7,7 @@ void dfs_topo(int u) {
st.push(u);
}
-vector<int> toposort(int n) {
+vector<int> toposort(int n) { //<@\compl{n+m}@>
fill(begin(vis), begin(vis)+n, 0);
vector<int> topo;
for (int u = 0; u < n; u++) { dfs_topo(u); }
diff --git a/fontes/tree-square-root-decomposition.h b/fontes/tree-square-root-decomposition.h
index 5a9f3b9a7abcfe134cdbf858e0c3f6d7d8ba638b..416a7eb01c1613d7cc33ad448fc1618e066d2d90 100644
--- a/fontes/tree-square-root-decomposition.h
+++ b/fontes/tree-square-root-decomposition.h
@@ -1,7 +1,7 @@
vector<int> up (N), bup (N), depth (N);
vector<ll> weiop (N), bweiop (N);
-void stdt_decompose(int u, int p, int w) {
+void stdt_decompose(int u, int p, int w) { //<@\compl{n+m}@>
up[u] = p; weiop[u] = w;
depth[u] = depth[p] + 1;
bup[u] = depth[u] % B ? bup[p] : p;
@@ -10,7 +10,7 @@ void stdt_decompose(int u, int p, int w) {
stdt_decompose(v, u, w);
}
-int stdt_op(int a, int b) {
+int stdt_op(int a, int b) { //<@\compl{\sqrt{n}}@>
int ans = NEUTRAL;
if (!(depth[a]/B > depth[b]/B)) { swap(a, b); }
while (depth[a]/B > depth[b]/B) {
diff --git a/fontes/voronoi.h b/fontes/voronoi.h
index 580a713211b69276214871a0a4a72f5b9d568063..cb1fbf6a200cdacc359cdce05d63f7ed0f292513 100644
--- a/fontes/voronoi.h
+++ b/fontes/voronoi.h
@@ -18,15 +18,15 @@ pt line_intersect(pt a, pt b, pt u, pt v) {
pt circumcenter(pt a, pt b, pt c) {
b = (a + b) * ld(.5);
c = (a + c) * ld(.5);
- return point_in_line_line(
- seg(b, b + rot(vec(a, b))), seg(c, c + rot(vec(a, c))));
+ return point_in_line_line(seg(b, b + rot(vec(a, b))),
+ seg(c, c + rot(vec(a, c))));
}
ld parab_intersect(pt l, pt r, ld sw) {
if (abs(l.py - r.py) < abs(l.px - r.px) * EPS) {
int sign = l.px < r.px ? 1 : -1;
pt m = 0.5l * (l+r);
- pt v = line_intersect(m, rot(r-l), pt(0, sw), pt(1, 0));
+ pt v = line_intersect(m, rot(r-l), pt(0,sw), pt(1,0));
pt w = line_intersect(m, rot(l-v), v, l-v);
ld l1 = abs(v-w);
ld l2 = sqrt(sq(sw-m.py) - norm(m-w));
@@ -116,13 +116,13 @@ struct beach {
}
}; using arc = beach::arc;
-struct event {
- event(ld sw, int ix)
+struct ev {
+ ev(ld sw, int ix)
: type(0), sw(sw), ix(ix) {}
- event(ld sw, arc* c) : type(1), sw(sw),
+ ev(ld sw, arc* c) : type(1), sw(sw),
prv(c->prv->ix), cur(c), nxt(c->nxt->ix) {}
int type, ix, prv, nxt; arc* cur; ld sw;
- bool operator>(const event &l) const { return sw > l.sw; }
+ bool operator>(const ev& l) const { return sw > l.sw; }
};
struct voronoi_t {
@@ -132,7 +132,7 @@ struct voronoi_t {
voronoi_t fortune(vector<pt> &ps) {
voronoi_t ans; beach line;
- priority_queue<event, vector<event>, greater<event>> e;
+ priority_queue<ev, vector<ev>, greater<ev>> e;
auto add_edge = [&](int u, int v, int a, int b,
arc* c1, arc* c2) {
@@ -145,8 +145,8 @@ voronoi_t fortune(vector<pt> &ps) {
if (ix % 2 == 0) { ans.dy[ix/2].first = v; }
else { ans.dy[ix/2].second = v; }
};
- auto add_event = [&](arc* cur) {
- ld nxt; if (line.get(cur, nxt)) { e.emplace(nxt, cur); }
+ auto add_event = [&](arc* cur) { ld nxt;
+ if (line.get(cur, nxt)) { e.push({nxt, cur}); }
};
int n = ps.size(), cnt = 0;
@@ -176,7 +176,7 @@ voronoi_t fortune(vector<pt> &ps) {
} else { e.emplace(psi[i].first.py, i); }
}
while (e.size()) {
- event q = e.top(); e.pop();
+ ev q = e.top(); e.pop();
arc *prv, *cur, *nxt, *si;
int v = ans.v.size(), ix = q.ix;
line.sw = q.sw;
diff --git a/generate.sh b/generate.sh
index 6f9a08a10f435c547f24fec75bdc9f690f2247f0..c07ed3342d60a736927de41bc11e91a7bfc574a9 100644
--- a/generate.sh
+++ b/generate.sh
@@ -1,11 +1,9 @@
mkdir -p fontes-com-hash
for arq in fontes/*; do
- arq=$(basename $arq)
- cat </dev/null >fontes-com-hash/$arq
- n=1
- while IFS="" read -r line || [ -n "$line" ]; do
- hashed=$(bash fontes/hash.sh fontes/$arq 1 $n)
- echo "$hashed <@\$`printf %02d $n`\$@> $line" >>fontes-com-hash/$arq
- n=$((n+1))
- done <fontes/$arq
+ echo $(basename $arq)
+ if [ ! -z "$(tail -c 1 <"$arq")" ]; then
+ echo "WARNING: $arq does not end with a newline"
+ fi
+ grep --color '.\{59\}' $arq
+ bash fontes/hash.sh <$arq >fontes-com-hash/$(basename $arq)
done