Add bit

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

graph/bfs.cpp

+/**
+ * Breadth First Search - BFS
+ * Complexity (Time): O(|V| + |E|)
+ * Complexity (Space): O(|V| + |E|)
+ */
+
 bool cont[MAX];
 vector<int> graph[MAX];
 

graph/dfs.cpp

+/**
+ * Depth First Search - DFS
+ * Complexity (Time): O(|V| + |E|)
+ * Complexity (Space): O(|V| + |E|)
+ */
+
 bool cont[MAX];
 vector<int> graph[MAX];
 

structure/bit.cpp

+/**
+ * Binary Indexed Tree - BIT 
+ * Complexity (Time):
+ *   Update -> O(log n)
+ *   Query  -> O(log n)
+ *
+ * Complexity (Space): O(n)
+ */
+
+int tree[MAX];
+
+// Perform query in array (tree) in the idx position
+int query(int idx) {
+  int sum = 0;
+  for (; idx > 0; idx -= (idx & -idx))
+    sum += tree[idx];
+
+  return sum;
+}
+
+// Add a value (val) to a single position (idx) in the array (tree).
+void update(int idx, int val) {
+  for (; idx <= MAX; idx += (idx & -idx))
+    tree[idx] += val;
+}

structure/bit2d.cpp

+/** 
+ * Binary Indexed Tree 2D - BIT2D
+ * Complexity (Time):
+ *   Update -> O(log^2 n)
+ *   Query  -> O(log^2 n)
+ *
+ * Complexity (Space): O(n^2)
+ */
+
+int tree[MAXN][MAXM];
+
+// Perform query in array (tree) in the (idx,idy) position
+int query(int idx, int idy) {
+  int sum = 0, m;
+  for (; idx > 0; idx -= (idx & -idx))
+    for (m = idy; m > 0; m -= (m & -m))
+      sum += tree[idx][m];
+
+  return sum;
+}
+
+// Add a value (val) to a single position (idx,idy) in the array (tree).
+void update(int idx, int idy, int val) {
+  int m;
+  for (; idx <= MAXN; idx += (idx & -idx))
+    for (m = idy; m <= MAXM; m += (m & -m))
+      tree[idx][m] += val;
+}