POJ 3468 A Simple Problem with Integers （成端更新)

A Simple Problem with Integers

Time Limit: 5000MS		Memory Limit: 131072K
Total Submissions: 41842		Accepted: 12156
Case Time Limit: 2000MS

Description

You have N integers, A₁, A₂, ... , A_N. 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, ... , A_N. -1000000000 ≤ A_i ≤ 1000000000.
Each of the next Q lines represents an operation.
"C a b c" means adding c to each of A_a, A_a+1, ... , A_b. -10000 ≤ c ≤ 10000.
"Q a b" means querying the sum of A_a, A_a+1, ... , A_b.

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.

Source

POJ Monthly--2007.11.25, Yang Yi

#include<iostream>
#include<cstdio>
#include<cstring>

using namespace std;

const int maxn=100010;

#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1

int n,q;
long long sum[maxn<<2];
long long add[maxn<<2];

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

void Push_Down(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;
    }
}

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

void update(int L,int R,int c,int l,int r,int rt) {
    if (L <= l && r <= R) {
        add[rt] += c;
        sum[rt] += (long long)c * (r - l + 1);
        return ;
    }
    Push_Down(rt , r - l + 1);
    int mid = (l + r) >> 1;
    if (L <= mid) update(L , R , c , lson);
    if (mid < R) update(L , R , c , rson);
    Push_Up(rt);
}

long long query(int L,int R,int l,int r,int rt) {
    if (L <= l && r <= R) {
        return sum[rt];
    }
    Push_Down(rt , r - l + 1);
    int mid = (l + r) >> 1;
    long long ret = 0;
    if (L <= mid) ret += query(L , R , lson);
    if (mid < R) ret += query(L , R , rson);
    return ret;
}

int main(){

    //freopen("input.txt","r",stdin);

    while(~scanf("%d%d",&n,&q)){
        build(1,n,1);
        char op[3];
        int a,b,c;
        while(q--){
            scanf("%s",op);
            if (op[0] == 'Q') {
                scanf("%d%d",&a,&b);
                printf("%I64d\n",query(a , b , 1 , n , 1));
            } else {
                scanf("%d%d%d",&a,&b,&c);
                update(a , b , c , 1 , n , 1);
            }
        }
    }
    return 0;
}