Poj 3468 A Simple Problem with Integers （线段树 区间更新 区间求和）

A Simple Problem with Integers

Time Limit: 5000MS		Memory Limit: 131072K
Total Submissions: 37261		Accepted: 10756
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

线段树 区间更新

#include <cstdio>
#include <algorithm>
using namespace std;
#define lson l , m , rt << 1
#define rson m + 1 , r , rt << 1 | 1

const int maxn = 111111;
__int64 add[maxn<<2];
__int64 sum[maxn<<2];
void PushUp(__int64 rt) {
    sum[rt] = sum[rt<<1] + sum[rt<<1|1];
}
void PushDown(__int64 rt,__int64 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(__int64 l,__int64 r,__int64 rt) {
    add[rt] = 0;
    if (l == r) {
        scanf("%I64d",&sum[rt]);
        return ;
    }
    __int64 m = (l + r) >> 1;
    build(lson);
    build(rson);
    PushUp(rt);
}
void update(__int64 L,__int64 R,__int64 c,__int64 l,__int64 r,__int64 rt) {
    if (L <= l && r <= R) {
        add[rt] += c;
        sum[rt] += c * (r - l + 1);
        return ;
    }
    PushDown(rt , r - l + 1);
    __int64 m = (l + r) >> 1;
    if (L <= m) update(L , R , c , lson);
    if (m < R) update(L , R , c , rson);
    PushUp(rt);
}
__int64 query(__int64 L,__int64 R,__int64 l,__int64 r,__int64 rt) {
    if (L <= l && r <= R) {
        return sum[rt];
    }
    PushDown(rt , r - l + 1);
    __int64 m = (l + r) >> 1;
    __int64 ret = 0;
    if (L <= m) ret += query(L , R , lson);
    if (m < R) ret += query(L , R , rson);
    return ret;
}
int main() {
    __int64 N , Q;
    scanf("%I64d%I64d",&N,&Q);
    build(1 , N , 1);
    while (Q --) {
        char op[2];
        __int64 a , b , c;
        scanf("%s",op);
        if (op[0] == 'Q') {
            scanf("%I64d%I64d",&a,&b);
            printf("%I64d\n",query(a , b , 1 , N , 1));
        } else {
            scanf("%I64d%I64d%I64d",&a,&b,&c);
            update(a , b , c , 1 , N , 1);
        }
    }
    return 0;
}