segment tree implementation with lazy propagation in c++

lazy_seg.cpp

#include <bits/stdc++.h>

using namespace std;

int func(int a, int b) {
    // binary function
    // ex) return gcd(a, b);
    // ex) return a * b;
    // ex) return a ^ b;
    // BUT! associated law has to be held
    return a + b;
}

int nest_func(int a, int n) {
    // func(a, func(a, func(a, ...))) (n times)
    // normally O(1) with some functions
    // but you could always do on O(log n)
    return a * n;
}

vector<int> seg, lazy;

void init(vector<int> &vec, int node, int left, int right) {
    if(left == right) {
        seg[node] = vec[left - 1];
        return;
    }
    init(vec, node << 1, left, (left + right) >> 1);
    init(vec, node << 1 | 1, ((left + right) >> 1) + 1, right);
    seg[node] = func(seg[node << 1], seg[node << 1 | 1]);
}

void busy(int node, int left, int right) {
    if(!lazy[node]) return;
    seg[node] = func(seg[node], nest_func(lazy[node], (right - left + 1)));
    if(left != right) {
        lazy[node << 1] = func(lazy[node << 1], lazy[node]);
        lazy[node << 1 | 1] = func(lazy[node << 1 | 1], lazy[node]);
    }
    lazy[node] = 0;
}

void update(int node, int left, int right, int start, int end, int diff) {
    busy(node, left, right);
    if(right < start || end < left) return;
    if(start <= left && right <= end) {
        lazy[node] = diff;
        busy(node, left, right);
        return;
    }
    update(node << 1, left, (left + right) >> 1, start, end, diff);
    update(node << 1 | 1, ((left + right) >> 1) + 1, right, start, end, diff);
    seg[node] = func(seg[node << 1], seg[node << 1 | 1]);
}

int query(int node, int left, int right, int start, int end) {
    busy(node, left, right);
    if(start <= left && right <= end) return seg[node];
    int mid = (left + right) >> 1;
    if(mid < start) return query(node << 1 | 1, mid + 1, right, start, end);
    if(mid + 1 > end) return query(node << 1, left, mid, start, end);
    return func(query(node << 1, left, mid, start, end), query(node << 1 | 1, mid + 1, right, start, end));
}

int main() {
    int size = 4;
    seg.resize(4 * size);
    lazy.resize(4 * size);
    vector<int> vec{1, 2, 3, 4};
    init(vec, 1, 1, size);
    update(1, 1, size, 2, 3, 4);
    cout << query(1, 1, size, 2, 4) << endl;
}