线段树（区间求和+区间更新）（模板）

题目： 传送门
改进： 相较于单点更新，引入lazy数组，lazy[node] = val表示当前节点（node）维护的子区间全部都要加上val（可正可负）。lazy标记在区间更新和区间查询时下传（push_down）
Code：

#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <vector>
#include <map>
#include <queue>
#include <algorithm>

using namespace std;
typedef long long ll;
typedef pair<int, int> P;
const int inf = 0x3f3f3f3f;
const int maxn = 1000007;


int arr[maxn];
ll tree[4*maxn];
ll lazy[4*maxn];
int n, q;

void push_down(int node, int m) {
    
    
    if (lazy[node]) {
    
    
        lazy[2*node] += lazy[node];
        lazy[2*node+1] += lazy[node];
        tree[2*node] += lazy[node] * (m - m/2);
        tree[2*node+1] += lazy[node] * (m/2);
        lazy[node] = 0;
    }
}
void push_up(int node) {
    
    
    tree[node] = tree[2*node] + tree[2*node+1];
}
void build_tree(int node, int l, int r) {
    
    
    if (l == r) {
    
    
        tree[node] = arr[l];
        return;
    }
    lazy[node] = 0;
    int mid = (l + r) / 2;
    build_tree(2*node, l, mid);
    build_tree(2*node+1, mid+1, r);
    push_up(node);
}
ll query_tree(int node, int l, int r, int fl, int fr) {
    
    
    if (l == fl && r == fr) {
    
    
        return tree[node];
    }
    push_down(node, r - l + 1);
    int mid = (l + r) / 2;
    if (fr <= mid) {
    
    
        return query_tree(2*node, l, mid, fl, fr);
    } else if (mid < fl) {
    
    
        return query_tree(2*node+1, mid+1, r, fl, fr);
    } else {
    
    
        return query_tree(2*node, l, mid, fl, mid) + query_tree(2*node+1, mid+1, r, mid+1, fr);
    }
}

void add_tree(int node, int l, int r, int tl, int tr, int val) {
    
    
    if (l == tl && r == tr) {
    
    
        lazy[node] += val;
        tree[node] += (r - l + 1) * val;
        return;
    }
    push_down(node, r - l + 1);

    int mid = (l + r) / 2;
    if (tr <= mid) {
    
    
        add_tree(2*node, l, mid, tl, tr, val);
    } else if (tl > mid) {
    
    
        add_tree(2*node+1, mid+1, r, tl, tr, val);
    } else {
    
    
        add_tree(2*node, l, mid, tl, mid, val);
        add_tree(2*node+1, mid+1, r, mid+1, tr, val);
    }
    push_up(node);
}
int main()
{
    
    
    scanf("%d %d", &n, &q);
    for (int i=1;i<=n;i++) {
    
    
        scanf("%d", &arr[i]);
    }

    build_tree(1, 1, n);

    char op;
    int a, b, c;
    while (q--) {
    
    
        scanf(" %c", &op);
        if (op == 'Q') {
    
    
            scanf("%d %d", &a, &b);
            printf("%lld\n", query_tree(1, 1, n, a, b));
        } else if (op == 'C') {
    
    
            scanf("%d %d %d", &a, &b, &c);
            add_tree(1, 1, n, a, b, c);
        }
    }
    

    return 0;
}