From e3ec240763450a947091ef3fd96bcfc906c13752 Mon Sep 17 00:00:00 2001
From: Nishant Tanwar <nishant.tanwar08@gmail.com>
Date: Tue, 3 Oct 2017 04:57:19 +0530
Subject: [PATCH] Added Segment Trees with Lazy Propagation in C++.

---
 segment_tree/segment_trees_lazy.cpp.cpp | 120 ++++++++++++++++++++++++
 1 file changed, 120 insertions(+)
 create mode 100644 segment_tree/segment_trees_lazy.cpp.cpp

diff --git a/segment_tree/segment_trees_lazy.cpp.cpp b/segment_tree/segment_trees_lazy.cpp.cpp
new file mode 100644
index 00000000..8d6be6b3
--- /dev/null
+++ b/segment_tree/segment_trees_lazy.cpp.cpp
@@ -0,0 +1,120 @@
+/**
+ * In this code we have a very large array called arr, and very large set of operations
+ * Operation #1: Increment the elements within range [i, j] with value val
+ * Operation #2: Get max element within range [i, j]
+ * Build tree: build_tree(1, 0, N-1)
+ * Update tree: update_tree(1, 0, N-1, i, j, value)
+ * Query tree: query_tree(1, 0, N-1, i, j)
+ * Actual space required by the tree = 2*2^ceil(log_2(n)) - 1
+ */
+
+#include<iostream>
+#include<algorithm>
+using namespace std;
+
+#include<string.h>
+#include<math.h>
+
+#define N 20
+#define MAX (1+(1<<6)) // Why? :D
+#define inf 0x7fffffff
+
+int arr[N];
+int tree[MAX];
+int lazy[MAX];
+
+/**
+ * Build and init tree
+ */
+void build_tree(int node, int a, int b) {
+    if(a > b) return; // Out of range
+
+    if(a == b) { // Leaf node
+        tree[node] = arr[a]; // Init value
+        return;
+    }
+
+    build_tree(node*2, a, (a+b)/2); // Init left child
+    build_tree(node*2+1, 1+(a+b)/2, b); // Init right child
+
+    tree[node] = max(tree[node*2], tree[node*2+1]); // Init root value
+}
+
+/**
+ * Increment elements within range [i, j] with value value
+ */
+void update_tree(int node, int a, int b, int i, int j, int value) {
+
+    if(lazy[node] != 0) { // This node needs to be updated
+        tree[node] += lazy[node]; // Update it
+
+        if(a != b) {
+            lazy[node*2] += lazy[node]; // Mark child as lazy
+            lazy[node*2+1] += lazy[node]; // Mark child as lazy
+        }
+
+        lazy[node] = 0; // Reset it
+    }
+
+    if(a > b || a > j || b < i) // Current segment is not within range [i, j]
+        return;
+
+    if(a >= i && b <= j) { // Segment is fully within range
+        tree[node] += value;
+
+        if(a != b) { // Not leaf node
+            lazy[node*2] += value;
+            lazy[node*2+1] += value;
+        }
+
+        return;
+    }
+
+    update_tree(node*2, a, (a+b)/2, i, j, value); // Updating left child
+    update_tree(1+node*2, 1+(a+b)/2, b, i, j, value); // Updating right child
+
+    tree[node] = max(tree[node*2], tree[node*2+1]); // Updating root with max value
+}
+
+/**
+ * Query tree to get max element value within range [i, j]
+ */
+int query_tree(int node, int a, int b, int i, int j) {
+
+    if(a > b || a > j || b < i) return -inf; // Out of range
+
+    if(lazy[node] != 0) { // This node needs to be updated
+        tree[node] += lazy[node]; // Update it
+
+        if(a != b) {
+            lazy[node*2] += lazy[node]; // Mark child as lazy
+            lazy[node*2+1] += lazy[node]; // Mark child as lazy
+        }
+
+        lazy[node] = 0; // Reset it
+    }
+
+    if(a >= i && b <= j) // Current segment is totally within range [i, j]
+        return tree[node];
+
+    int q1 = query_tree(node*2, a, (a+b)/2, i, j); // Query left child
+    int q2 = query_tree(1+node*2, 1+(a+b)/2, b, i, j); // Query right child
+
+    int res = max(q1, q2); // Return final result
+
+    return res;
+}
+
+int main() {
+    for(int i = 0; i < N; i++) arr[i] = 1;
+
+    build_tree(1, 0, N-1);
+
+    memset(lazy, 0, sizeof lazy);
+
+    update_tree(1, 0, N-1, 0, 6, 5); // Increment range [0, 6] by 5. here 0, N-1 represent the current range.
+    update_tree(1, 0, N-1, 7, 10, 12); // Incremenet range [7, 10] by 12. here 0, N-1 represent the current range.
+    update_tree(1, 0, N-1, 10, N-1, 100); // Increment range [10, N-1] by 100. here 0, N-1 represent the current range.
+
+    cout << query_tree(1, 0, N-1, 0, N-1) << endl; // Get max element in range [0, N-1]
+}
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