线段树 （区间更新，区间查询） poj http://poj.org/problem?id=3468

题目链接

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<string>

using namespace std;
const int N = 100005;
typedef long long int LL;
LL sum[N << 2];
LL add[N << 2];
struct node
{
    int l, r;
    int mid()
    {
        return (l + r) >> 1;
    }
}tree[N << 2];
void PushUp(int rt)
{
    sum[rt] = sum[rt << 1] + sum[rt << 1 | 1];
}
void PushDown(int rt, int m)
{
    if (add[rt]) {
        add[rt << 1] += add[rt];
        add[rt << 1 | 1] += add[rt];
        sum[rt << 1] += add[rt] * (m - (m >> 1));
        sum[rt << 1 | 1] += add[rt] * (m >> 1);
        add[rt] = 0;//更新后要还原，因为递归可能会多次用到这个
    }
}

void build(int l,int r,int rt)
{
    tree[rt].l = l;
    tree[rt].r = r;
    add[rt] = 0;
    if (l == r) {
        scanf("%lld", &sum[rt]);
        return;
    }
    int m = tree[rt].mid();
    build(l, m, rt << 1);
    build(m + 1, r, rt << 1 | 1);
    PushUp(rt); 
}

void updata(int c, int l, int r, int rt)
{
    if (tree[rt].l == l && r == tree[rt].r) {
        add[rt] += c;
        sum[rt] += (LL)(r - l + 1)*c;
        return;//这里没有进行子区间更新，用到lazy标记
    }
    if (tree[rt].l == tree[rt].r) return;
    PushDown(rt, tree[rt].r - tree[rt].l + 1);
    int m = tree[rt].mid();
    if (r <= m) updata(c,l, r, rt << 1);
    else if (l > m) updata(c,l, r, rt << 1 | 1);
    else {
        updata(c, l, m, rt << 1);
        updata(c, m + 1, r, rt << 1 | 1);
    }
    PushUp(rt);

}

LL query(int l, int r, int rt)
{
    if (l == tree[rt].l&&r == tree[rt].r) {
        return sum[rt];
    }
    PushDown(rt, tree[rt].r - tree[rt].l + 1);//标记的特点，用时才进行更新
    int m = tree[rt].mid();
    LL res = 0;
    if (r <= m) res += query(l, r, rt << 1);
    else if (l > m) res += query(l, r, rt << 1 | 1);
    else {
        res += query(l, m, rt << 1);
        res += query(m + 1, r, rt << 1 | 1);
    }
    return res;
}
int main()
{
    int n, m;
    while (scanf("%d %d", &n, &m) == 2) {
        memset(sum, 0, sizeof(sum));
        memset(add, 0, sizeof(add));
        build(1, n, 1);
        while (m--) {
            char ch[10];
            scanf("%s", ch);
            if (ch[0] == 'Q') {
                int a, b;
                scanf("%d %d", &a, &b);
                printf("%lld\n", query(a, b, 1));
            }
            else {
                int a, b, c;
                scanf("%d %d %d", &a, &b, &c);
                updata(c, a, b, 1);
            }
        }
    }

    return 0;
}