Implementation of segment tree without lazy propagation.

segment_tree.cpp

/**
 * 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];

/**
 * 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(a > b || a > j || b < i) // Current segment is not within range [i, j]
		return;
    
  	if(a == b) { // Leaf node
    		tree[node] += 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(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;
	//array indexed from 0, segTree indexed from 1
	build_tree(1, 0, N-1);

	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]
}

Wouldn't the update be worst case O(n) ?

query_tree() implementation is wrong. lets say your array is of size 8[0..7]
you apply query_tree() on [1..3] , your tree [0:0] will also be updated. which is wrong.

Wouldn't the update be worst case O(n) ?

Yes. That's why lazy propagation was introduced.