Add segment_tree

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

structure/segment_tree.cpp

+/**
+ * Segment Tree
+ * Complexity (Time):
+ *     Build  -> O(n log n)
+ *     Update -> O(log n)
+ *     Query  -> O(log n)
+ * Complexity (Space): O(n)
+ */
+
+int N, tree[2 * MAX], v[MAX];
+
+// Build tree with elements from v
+void build_tree(int node = 1, int a = 0, int b = N) {
+  if (a > b)
+    return;
+
+  if (a == b) {
+    tree[node] = v[a];
+    return;
+  }
+
+  build_tree(node * 2, a, (a + b) / 2);
+  build_tree(node * 2 + 1, 1 + (a + b) / 2, b);
+
+  tree[node] = tree[node * 2] + tree[node * 2 + 1];
+}
+
+// Update position idx with value val
+void update_tree(int idx, int val, int node = 1, int a = 0, int b = N) {
+  if (a > b || a > idx || b < idx)
+    return;
+
+  if (a == b) {
+    tree[node] = val;
+    return;
+  }
+
+  update_tree(idx, val, node * 2, a, (a + b) / 2);
+  update_tree(idx, val, node * 2 + 1, 1 + (a + b) / 2, b);
+
+  tree[node] = tree[node * 2] + tree[node * 2 + 1];
+}
+
+// Return sum from i to j
+int query_tree(int i, int j, int node = 1, int a = 0, int b = N) {
+  if (a > b || a > j || b < i)
+    return 0;
+
+  if (a >= i && b <= j)
+    return tree[node];
+
+  int res1 = query_tree(i, j, node * 2, a, (a + b) / 2);
+  int res2 = query_tree(i, j, node * 2 + 1, 1 + (a + b) / 2, b);
+
+  return res1 + res2;
+}