Problem 8: Segment Tree with Lazy Propagation

Problem Statement: Implement a segment tree with lazy propagation to support range updates and range queries on an array.

Input

The first line contains n (number of elements) and q (number of queries). The next line has n integers. Each query is either "update l r v" or "query l r".

Output

For each query command "query", output the computed result (e.g., sum) for the range.

Examples


Input:
5 3\n1 2 3 4 5\nupdate 1 3 2\nquery 0 4\nquery 1 2

Output:
17\n7

Solution in C++


#include <iostream>
#include <vector>
using namespace std;

struct SegmentTree{
    int n;
    vector<long long> tree, lazy;
    SegmentTree(int n): n(n) {
        tree.assign(4*n, 0);
        lazy.assign(4*n, 0);
    }
    void build(vector<int>& arr, int idx, int l, int r){
        if(l == r){
            tree[idx] = arr[l]; return;
        }
        int mid = (l+r)/2;
        build(arr, 2*idx, l, mid);
        build(arr, 2*idx+1, mid+1, r);
        tree[idx] = tree[2*idx] + tree[2*idx+1];
    }
    void update(int idx, int l, int r, int ql, int qr, int val){
        if(lazy[idx] != 0){
            tree[idx] += (r-l+1)*lazy[idx];
            if(l != r){
                lazy[2*idx] += lazy[idx];
                lazy[2*idx+1] += lazy[idx];
            }
            lazy[idx] = 0;
        }
        if(r < ql || l > qr) return;
        if(ql <= l && r <= qr){
            tree[idx] += (r-l+1)*val;
            if(l != r){
                lazy[2*idx] += val;
                lazy[2*idx+1] += val;
            }
            return;
        }
        int mid = (l+r)/2;
        update(2*idx, l, mid, ql, qr, val);
        update(2*idx+1, mid+1, r, ql, qr, val);
        tree[idx] = tree[2*idx] + tree[2*idx+1];
    }
    long long query(int idx, int l, int r, int ql, int qr){
        if(lazy[idx] != 0){
            tree[idx] += (r-l+1)*lazy[idx];
            if(l != r){
                lazy[2*idx] += lazy[idx];
                lazy[2*idx+1] += lazy[idx];
            }
            lazy[idx] = 0;
        }
        if(r < ql || l > qr) return 0;
        if(ql <= l && r <= qr) return tree[idx];
        int mid = (l+r)/2;
        return query(2*idx, l, mid, ql, qr) + query(2*idx+1, mid+1, r, ql, qr);
    }
};

int main(){
    int n, q;
    cin >> n >> q;
    vector<int> arr(n);
    for(int i=0;i<n;i++) cin >> arr[i];
    SegmentTree st(n);
    st.build(arr, 1, 0, n-1);
    while(q--) {
        string op;
        cin >> op;
        if(op == "update"){
            int l, r, v;
            cin >> l >> r >> v;
            st.update(1, 0, n-1, l, r, v);
        } else {
            int l, r;
            cin >> l >> r;
            cout << st.query(1, 0, n-1, l, r) << "\n";
        }
    }
    return 0;
}