Small fixes

Signed-off-by: Bruno Freitas Tissei <bft15@inf.ufpr.br>

graph/lca.cpp

@@ -11,6 +11,8 @@
  *      *** = used in both * and **
  */
 
+#define MAXLOG 20 //log2(MAX)
+
 vector<int> graph[MAX]; //*** vector<ii>
 
 int h[MAX];

graph/tarjan.cpp

@@ -13,7 +13,7 @@ int ncomp, ind;
 int cont[MAX], parent[MAX];
 int low[MAX], L[MAX];
 
-// Fills scc with strongly connected components of graph
+// Fills SCC with strongly connected components of graph
 void dfs(int x) {
   L[x] = ind;
   low[x] = ind++;

graph/topological_sort.cpp

@@ -28,7 +28,7 @@ bool dfs(int x) {
 }
 
 
-// Returns if graph contains cycle or not, and fills tsort vector with
+// Returns whether graph contains cycle or not, and fills tsort vector with
 // topological sort of the graph
 bool topological_sort(int n, vector<int> &tsort) {
   mset(cont, 0);

math/modular_multiplicative_inverse.cpp

@@ -6,7 +6,7 @@
  */
 
 // ========== Fermat's Little Theorem ==========
-// Used if m is prime
+// Used when m is prime
 
 ll power(ll x, ll y) {
   ll ans = 1;
@@ -31,7 +31,7 @@ ll mod_inverse(ll a) {
 
 
 // ========== Extended Euclidean Algorithm ==========
-// Used if m and a are coprime
+// Used when m and a are coprime
 
 // return gcd(a, b) and find x, y where:
 // a*x + b*y = gcd(a, b)

paradigm/kadane.cpp

 /**
- * Kadane
+ * Kadane - Largest Sum Contiguous Subarray
  *
  * Complexity (Time): O(n + m)
  * Complexity (Space): O(n + m)
@@ -8,6 +8,7 @@
 int v[MAX];
 
 int kadane() {
+
   // Maximum so far (msf), Maximum ending here (meh).
   int msf = -0x3f3f3f3f, meh = 0;
   int start = 0, end = 0, s = 0;
@@ -15,12 +16,16 @@ int kadane() {
   for (int i = 0; i < n; ++i) {
     meh += v[i];
 
+    // Store maximum so far as well as starting and ending position
+    // of the subsequence
     if (msf < meh) {
       msf = meh;
       start = s;
       end = i;
     }
 
+    // If maximum ending here is negative, then it's definitely 
+    // better to restart
     if (meh < 0) {
       meh = 0;
       s = i + 1;

string/kmp.cpp

 /**
- * Knuth-Morris-Pratt - KMP
+ * Knuth-Morris-Pratt (KMP)
  *
  * Complexity (Time): 
  *   preprocess -> O(m)

structure/bit.cpp

 /**
- * Binary Indexed Tree - BIT 
+ * Binary Indexed Tree (BIT)
  *
  * Complexity (Time):
  *   Update -> O(log n)

structure/bit2d.cpp

 /** 
- * Binary Indexed Tree 2D - BIT2D
+ * Binary Indexed Tree 2D (BIT2D)
  *
  * Complexity (Time):
  *   Update -> O(log^2 n)

structure/disjoint_set.cpp

@@ -10,13 +10,13 @@
 
 int par[MAX];
 int h[MAX];
-int sz[MAX];
+int size[MAX];
 
 // Initialize element x
 void make_set(int x) {
   par[x] = x;
   h[x] = 0;
-  sz[x] = 1;
+  size[x] = 1;
 }
 
 
@@ -39,13 +39,12 @@ void union_set(int x, int y) {
 
   if (h[xroot] < h[yroot]) {
     par[xroot] = yroot;
-    sz[yroot] += sz[xroot];
-  } else if (h[xroot] > h[yroot]) {
-    par[yroot] = xroot;
-    sz[xroot] += sz[yroot];
+    size[yroot] += size[xroot];
   } else {
     par[yroot] = xroot;
-    sz[xroot] += sz[yroot];
+    size[xroot] += size[yroot];
+
+    if (h[xroot] == h[yroot])
       h[xroot]++;
   }
 }

structure/policy_tree.cpp

 /**
  * Policy Tree
  *
+ * A set-like STL structure with order statistics
+ *
  * Complexity (Time):
  *   insert        -> O(log n)
  *   erase         -> O(log n)