POJ 3468 A Simple Problem with Integers（线段树/区间更新）

题目链接: 传送门

A Simple Problem with Integers

Time Limit: 5000MS     Memory Limit: 131072K

Description

You have N integers, A1, A2, ... , AN. You need to deal with two kinds of operations. One type of operation is to add some given number to each number in a given interval. The other is to ask for the sum of numbers in a given interval.

Input

The first line contains two numbers N and Q. 1 ≤ N,Q ≤ 100000.
The second line contains N numbers, the initial values of A1, A2, ... , AN. -1000000000 ≤ Ai ≤ 1000000000.
Each of the next Q lines represents an operation.
"C a b c" means adding c to each of Aa, Aa+1, ... , Ab. -10000 ≤ c ≤ 10000.
"Q a b" means querying the sum of Aa, Aa+1, ... , Ab.

Output

You need to answer all Q commands in order. One answer in a line.

Sample Input

10 5
1 2 3 4 5 6 7 8 9 10
Q 4 4
Q 1 10
Q 2 4
C 3 6 3
Q 2 4

Sample Output

4
55
9
15

HINT

The sums may exceed the range of 32-bit integers.

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
#define lson l ,m , rt << 1
#define rson m + 1 , r ,rt << 1 | 1
typedef __int64 LL;
const int maxn = 100005;
LL sum[maxn<<2],lazy[maxn<<2];

void PushUp(int rt)
{
    sum[rt] = sum[rt<<1] + sum[rt<<1|1];
}

void PushDown(int rt,int m)
{
    if (lazy[rt])
    {
        lazy[rt<<1] += lazy[rt];
        lazy[rt<<1|1] += lazy[rt];
        sum[rt<<1] += (m - (m>>1)) * lazy[rt];
        sum[rt<<1|1] += (m>>1) * lazy[rt];
        lazy[rt] = 0;
    }
}

void build(int l,int r,int rt)
{
    if (l == r)
    {
        scanf("%I64d",&sum[rt]);
        lazy[rt] = 0;
        return;
    }
    int m = (l + r) >> 1;
    build(lson);
    build(rson);
    PushUp(rt);
} 

void upd(int L,int R,int c,int l,int r,int rt)
{
    if (L <= l && r <= R)
    {
        sum[rt] += (LL)(r - l + 1) * c;
        lazy[rt] += c;
        return;
    }
    PushDown(rt,r - l + 1);
    int m = (l + r) >> 1;
    if (L <= m) upd(L,R,c,lson);
    if (R > m)  upd(L,R,c,rson);
    PushUp(rt);
}

LL qry(int L,int R,int l,int r,int rt)
{
    if (L <= l && r <= R)
    {
        return sum[rt];
    }
    PushDown(rt,r - l + 1);
    int m = (l + r) >> 1;
    LL ret = 0;
    if (L <= m) ret += qry(L,R,lson);
    if (R > m)  ret += qry(L,R,rson);
    return ret;
}

int main()
{
    int N,Q,a,b,c;
    char opt;
    while (~scanf("%d%d",&N,&Q))
    {
        build(1,N,1);
        while (Q--)
        {
            getchar();
            scanf("%c",&opt);
            if (opt == 'C')
            {
                scanf("%d%d%d",&a,&b,&c);
                upd(a,b,c,1,N,1);
            }
            else
            {
                scanf("%d%d",&a,&b);
                printf("%I64d\n",qry(a,b,1,N,1));
            }
        }
    }
    return 0;
}