From 8fa1490a34cf7af0a621e60bd7fa31961dd09cd8 Mon Sep 17 00:00:00 2001
From: Bruno Freitas Tissei <bft15@inf.ufpr.br>
Date: Sun, 13 Oct 2019 15:04:52 -0300
Subject: [PATCH] Add SBC14
Signed-off-by: Bruno Freitas Tissei <bft15@inf.ufpr.br>
---
algorithms/math/legendre.cpp | 2 +-
algorithms/structure/disjoint_set.cpp | 2 +-
contests/SBC14/A.cpp | 29 +++++++++
contests/SBC14/B.cpp | 36 +++++++++++
contests/SBC14/C.cpp | 49 +++++++++++++++
contests/SBC14/F.cpp | 62 +++++++++++++++++++
contests/SBC14/G.cpp | 84 +++++++++++++++++++++++++
contests/SBC14/H.cpp | 40 ++++++++++++
contests/SBC14/I.cpp | 89 +++++++++++++++++++++++++++
contests/SBC14/K.cpp | 68 ++++++++++++++++++++
10 files changed, 459 insertions(+), 2 deletions(-)
create mode 100644 contests/SBC14/A.cpp
create mode 100644 contests/SBC14/B.cpp
create mode 100644 contests/SBC14/C.cpp
create mode 100644 contests/SBC14/F.cpp
create mode 100644 contests/SBC14/G.cpp
create mode 100644 contests/SBC14/H.cpp
create mode 100644 contests/SBC14/I.cpp
create mode 100644 contests/SBC14/K.cpp
diff --git a/algorithms/math/legendre.cpp b/algorithms/math/legendre.cpp
index 7be0e3c..229c642 100644
--- a/algorithms/math/legendre.cpp
+++ b/algorithms/math/legendre.cpp
@@ -2,7 +2,7 @@
///
/// Description:
/// Given an interger $n$ and a prime number $p$, find the largest power of
-/// $p$ ($x$) such that $n!$ is divisible by $k^x$. \par
+/// $p$ ($x$) such that $n!$ is divisible by $p^x$. \par
/// Writing $n!$ as $1 \cdot 2 \cdot 3 ... (n-1) \cdot n$ shows that every
/// $k$-th element of the product is divisible by $k$ (i.e. adds $1$ to the
/// answer), the number of such elements is $\lfloor\frac{n}{k}\rfloor$. The
diff --git a/algorithms/structure/disjoint_set.cpp b/algorithms/structure/disjoint_set.cpp
index 7ce7b10..67a7594 100644
--- a/algorithms/structure/disjoint_set.cpp
+++ b/algorithms/structure/disjoint_set.cpp
@@ -8,7 +8,7 @@
struct DisjointSet {
int N;
- vector<int> rnk, par;
+ vector<int> rnk, par, siz;
DisjointSet(int N) :
N(N), rnk(N), par(N), siz(N)
diff --git a/contests/SBC14/A.cpp b/contests/SBC14/A.cpp
new file mode 100644
index 0000000..159d22c
--- /dev/null
+++ b/contests/SBC14/A.cpp
@@ -0,0 +1,29 @@
+#include <bits/stdc++.h>
+
+#define EPS 1e-6
+#define MOD 1000000007
+#define inf 0x3f3f3f3f
+#define llinf 0x3f3f3f3f3f3f3f3f
+
+#define fi first
+#define se second
+#define pb push_back
+#define ende '\n'
+
+#define all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+#define mset(x, y) memset(&x, (y), sizeof(x))
+
+using namespace std;
+
+using ll = long long;
+using ii = pair<int,int>;
+
+int main() {
+ ios::sync_with_stdio(0);
+ cin.tie(0);
+
+ int x, y; cin >> x >> y;
+ cout << ((y - 1) / (y - x)) + 1 << ende;
+ return 0;
+}
diff --git a/contests/SBC14/B.cpp b/contests/SBC14/B.cpp
new file mode 100644
index 0000000..98e0d00
--- /dev/null
+++ b/contests/SBC14/B.cpp
@@ -0,0 +1,36 @@
+#include <bits/stdc++.h>
+
+#define EPS 1e-6
+#define MOD 1000000007
+#define inf 0x3f3f3f3f
+#define llinf 0x3f3f3f3f3f3f3f3f
+
+#define fi first
+#define se second
+#define pb push_back
+#define ende '\n'
+
+#define all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+#define mset(x, y) memset(&x, (y), sizeof(x))
+
+using namespace std;
+
+using ll = long long;
+using ii = pair<int,int>;
+
+int main() {
+ ios::sync_with_stdio(0);
+ cin.tie(0);
+
+ ll n; cin >> n;
+ ll num = 2 % (n + 1);
+ int ans = 1;
+ while (true) {
+ if (num == 1)
+ return cout << ans << ende, 0;
+ num = (num * 2) % (n + 1);
+ ans++;
+ }
+ return 0;
+}
diff --git a/contests/SBC14/C.cpp b/contests/SBC14/C.cpp
new file mode 100644
index 0000000..57cf893
--- /dev/null
+++ b/contests/SBC14/C.cpp
@@ -0,0 +1,49 @@
+#include <bits/stdc++.h>
+
+#define EPS 1e-6
+#define MOD 1000000007
+#define inf 0x3f3f3f3f
+#define llinf 0x3f3f3f3f3f3f3f3f
+
+#define fi first
+#define se second
+#define pb push_back
+#define ende '\n'
+
+#define all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+#define mset(x, y) memset(&x, (y), sizeof(x))
+
+using namespace std;
+
+using ll = long long;
+using ii = pair<int,int>;
+
+struct plane { ll a, b, c, d; };
+
+int main() {
+ ios::sync_with_stdio(0);
+ cin.tie(0);
+
+ int m, n; cin >> m >> n;
+ vector<plane> p(m);
+ for (int i = 0; i < m; ++i) {
+ ll a, b, c, d; cin >> a >> b >> c >> d;
+ p[i] = {a, b, c, d};
+ }
+
+ map<string,int> M;
+ for (int i = 0; i < n; ++i) {
+ string st;
+ ll a, b, c; cin >> a >> b >> c;
+ for (int j = 0; j < m; ++j)
+ st.pb((p[j].a*a + p[j].b*b + p[j].c*c > p[j].d) + '0');
+ M[st] += 1;
+ }
+
+ int ans = 0;
+ for (auto &i : M)
+ ans = max(ans, i.se);
+ cout << ans << ende;
+ return 0;
+}
diff --git a/contests/SBC14/F.cpp b/contests/SBC14/F.cpp
new file mode 100644
index 0000000..af8af4a
--- /dev/null
+++ b/contests/SBC14/F.cpp
@@ -0,0 +1,62 @@
+#include <bits/stdc++.h>
+
+#define EPS 1e-6
+#define MOD 10000
+#define inf 0x3f3f3f3f
+#define llinf 0x3f3f3f3f3f3f3f3f
+
+#define fi first
+#define se second
+#define pb push_back
+#define ende '\n'
+
+#define all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+#define mset(x, y) memset(&x, (y), sizeof(x))
+
+using namespace std;
+
+using ll = long long;
+using ii = pair<int,int>;
+
+ll mat[110*110], ans[110*110], aux[110*110];
+
+void mult(ll *a, ll *b, ll *res, int n) {
+ for (int i = 0; i < n; ++i)
+ for (int j = 0; j < n; ++j) {
+ aux[i*n+j] = 0;
+ for (int k = 0; k < n; ++k)
+ aux[i*n+j] = (aux[i*n+j] + a[i*n+k] * b[k*n+j]) % MOD;
+ }
+
+ memcpy(res, aux, sizeof aux);
+}
+
+void bin_exp(ll e, int n) {
+ mset(ans, 0);
+ for (int i = 0; i < n; ++i)
+ ans[i*n+i] = 1;
+
+ while (e) {
+ if (e & 1) mult(ans, mat, ans, n);
+ e >>= 1;
+ mult(mat, mat, mat, n);
+ }
+}
+
+int main() {
+ int n; ll l;
+ while (scanf("%d %lld", &n, &l) != EOF) {
+ int s, t, x; cin >> s >> t; s--, t--;
+ mset(mat, 0);
+ for (int i = 0; i < n; ++i)
+ for (int j = 0; j < 4; ++j) {
+ scanf("%d", &x); x--;
+ mat[i*n+x]++;
+ }
+
+ bin_exp(l, n);
+ printf("%lld\n", ans[s*n + t] % MOD);
+ }
+ return 0;
+}
diff --git a/contests/SBC14/G.cpp b/contests/SBC14/G.cpp
new file mode 100644
index 0000000..b38b7ba
--- /dev/null
+++ b/contests/SBC14/G.cpp
@@ -0,0 +1,84 @@
+#include <bits/stdc++.h>
+
+#define EPS 1e-6
+#define MOD 1000000007
+#define inf 0x3f3f3f3f
+#define llinf 0x3f3f3f3f3f3f3f3f
+
+#define fi first
+#define se second
+#define pb push_back
+#define ende '\n'
+
+#define all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+#define mset(x, y) memset(&x, (y), sizeof(x))
+
+using namespace std;
+
+using ll = long long;
+using ii = pair<int,int>;
+using pii = pair<ii,ii>;
+
+struct elem {
+ int x, y, l, u, d;
+};
+
+ii get(char x) {
+ if (x >= 'a' && x <= 'j')
+ return {1 << (x - 'a'), 0};
+ return {0, 1 << (x - 'A')};
+}
+
+map<pii,int> foi;
+
+int main() {
+ ios::sync_with_stdio(0);
+ cin.tie(0);
+
+ vector<int> dx = {-1, 1, 0, 0};
+ vector<int> dy = {0, 0, 1, -1};
+
+ int n; cin >> n;
+ vector<string> v(n);
+ for (auto &i : v)
+ cin >> i;
+
+ queue<elem> Q;
+ ii val = get(v[0][0]);
+ Q.push({0, 0, val.fi, val.se, 1});
+ foi[pii(ii(0,0),ii(val.fi,val.fi))] = 1;
+ int ans = inf;
+
+ while (!Q.empty()) {
+ elem u = Q.front(); Q.pop();
+ if (u.x == n - 1 && u.y == n - 1)
+ ans = min(ans, u.d);
+
+ for (int i = 0; i < 4; ++i) {
+ int x = u.x + dx[i];
+ int y = u.y + dy[i];
+
+ if (x >= 0 && x < n && y >= 0 && y < n) {
+ val = get(v[x][y]);
+ if (val.fi) {
+ if (!(u.u & val.fi))
+ if (!foi[pii(ii(x,y),ii(val.fi|u.l,u.u))]) {
+ Q.push({x, y, val.fi | u.l, u.u, u.d + 1});
+ foi[pii(ii(x,y),ii(val.fi|u.l,u.u))] = 1;
+ }
+ } else {
+ if (!(u.l & val.se))
+ if (!foi[pii(ii(x,y),ii(u.l,val.se | u.u))]) {
+ Q.push({x, y, u.l, val.se | u.u, u.d + 1});
+ foi[pii(ii(x,y),ii(u.l,val.se|u.u))] = 1;
+ }
+ }
+ }
+ }
+ }
+
+ if (ans == inf) cout << -1 << ende;
+ else cout << ans << ende;
+ return 0;
+}
diff --git a/contests/SBC14/H.cpp b/contests/SBC14/H.cpp
new file mode 100644
index 0000000..6972a43
--- /dev/null
+++ b/contests/SBC14/H.cpp
@@ -0,0 +1,40 @@
+#include <bits/stdc++.h>
+
+#define EPS 1e-6
+#define MOD 1000000007
+#define inf 0x3f3f3f3f
+#define llinf 0x3f3f3f3f3f3f3f3f
+
+#define fi first
+#define se second
+#define pb push_back
+#define ende '\n'
+
+#define all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+#define mset(x, y) memset(&x, (y), sizeof(x))
+
+using namespace std;
+
+using ll = long long;
+using ii = pair<int,int>;
+
+int main() {
+ ios::sync_with_stdio(0);
+ cin.tie(0);
+
+ int ans = 0;
+ int n, m; cin >> n >> m;
+ for (int i = 0; i < n; ++i) {
+ int cnt = 0;
+ for (int j = 0; j < m; ++j) {
+ int x; cin >> x;
+ cnt += (x != 0);
+ }
+ if (cnt == m)
+ ans++;
+ }
+
+ cout << ans << ende;
+ return 0;
+}
diff --git a/contests/SBC14/I.cpp b/contests/SBC14/I.cpp
new file mode 100644
index 0000000..bbc0aff
--- /dev/null
+++ b/contests/SBC14/I.cpp
@@ -0,0 +1,89 @@
+#include <bits/stdc++.h>
+
+#define EPS 1e-6
+#define MOD 1000000007
+#define inf 0x3f3f3f3f
+#define llinf 0x3f3f3f3f3f3f3f3f
+
+#define fi first
+#define se second
+#define pb push_back
+#define ende '\n'
+
+#define all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+#define mset(x, y) memset(&x, (y), sizeof(x))
+
+using namespace std;
+
+using ll = long long;
+using ii = pair<int,int>;
+
+vector<int> sieve(int n) {
+ vector<int> primes;
+ vector<int> is_prime(n + 1, 1);
+
+ for (int p = 2; p*p <= n; ++p)
+ if (is_prime[p])
+ for (int i = p*p; i <= n; i += p)
+ is_prime[i] = false;
+
+ for (int p = 2; p <= n; ++p)
+ if (is_prime[p])
+ primes.pb(p);
+
+ return primes;
+}
+
+struct ans_t { ll x, y, d; };
+
+ans_t ext_gcd(ll a, ll b) {
+ if (a == 0) return {0, 1, b};
+ ans_t e = ext_gcd(b % a, a);
+ return {e.y - (b/a)*e.x, e.x, e.d};
+}
+
+int extended_euclidean(int a, int m) {
+ ans_t g = ext_gcd(a, m);
+ return (g.x % m + m) % m;
+}
+
+ll bin_exp(ll a, ll e, ll M = MOD) {
+ ll x = 1;
+ while (e) {
+ if (e & 1) x = (x * a) % M;
+ e >>= 1;
+ a = (a * a) % M;
+ }
+ return x % M;
+}
+
+int main() {
+ ios::sync_with_stdio(0);
+ cin.tie(0);
+
+ ll n, e, c; cin >> n >> e >> c;
+ vector<int> primes = sieve((int) sqrt(n)+1);
+
+ for (int i = 0; i < primes.size() && primes[i]*primes[i] <= n; ++i) {
+ if (n % primes[i] == 0) {
+ ll p = primes[i];
+ ll q = n / p;
+
+ if (p % 2 == 0 || q % 2 == 0)
+ continue;
+
+ ll phi = (p - 1) * (q - 1);
+ if (e >= phi || __gcd(phi, e) != 1)
+ continue;
+
+ ll d = extended_euclidean(e, phi);
+ ll m = bin_exp(c, d, n);
+
+ if (bin_exp(m, e, n) == c && m > 0)
+ return cout << m << ende, 0;
+ }
+ }
+
+ return 0;
+}
diff --git a/contests/SBC14/K.cpp b/contests/SBC14/K.cpp
new file mode 100644
index 0000000..007b9e7
--- /dev/null
+++ b/contests/SBC14/K.cpp
@@ -0,0 +1,68 @@
+#include <bits/stdc++.h>
+
+#define EPS 1e-6
+#define MOD 1000000007
+#define inf 0x3f3f3f3f
+#define llinf 0x3f3f3f3f3f3f3f3f
+
+#define fi first
+#define se second
+#define pb push_back
+#define ende '\n'
+
+#define all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+#define mset(x, y) memset(&x, (y), sizeof(x))
+
+using namespace std;
+
+using ll = long long;
+using ii = pair<int,int>;
+
+int main() {
+ ios::sync_with_stdio(0);
+ cin.tie(0);
+
+ double c;
+ int n; cin >> c >> n;
+
+ vector<double> v(n);
+ for (auto &i : v) cin >> i;
+
+ double l = v[0] + EPS, r = v[1];
+ for (int i = 0; i < 30; ++i) {
+ double m = (l + r) / 2.0;
+ double cc = m + (c / n);
+
+ int k = 1;
+ int whi = 0;
+ for (int j = 1; j < n; j = k) {
+ while (k < n && v[k] < cc) k++;
+ if (k == n)
+ if (v[0] + c < cc)
+ k++;
+
+ if (k - j > 1) {
+ whi = 1;
+ break;
+ }
+
+ if (k - j == 0) {
+ whi = 2;
+ break;
+ }
+
+ cc += (c / n);
+ }
+
+ if (whi == 0) {
+ return cout << "S" << ende, 0;
+ } else if (whi == 1)
+ r = m;
+ else
+ l = m;
+ }
+
+ cout << "N" << ende;
+ return 0;
+}
--
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