[POJ] 3468 A Simple Problem with Integers [线段树区间更新求和]

A Simple Problem with Integers

 

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

 

线段树功能:update:成段增减 query:区间求和

#include<cstdio>
#include<algorithm>

#define clr(x,y) memset(x,y,sizeof(x))
#define LL       long long
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1

const int maxn=1e5+3511;
using namespace std;

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

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


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



int main()
{
    int Q,n,a,b,c;
    char st[10];
    
    scanf("%d%d",&n,&Q);
    build(1,n,1);
    
    while(Q--) {
        scanf("%s",st);
        if(st[0]=='C') {
            scanf("%d%d%d",&a,&b,&c);
            Updata(a,b,c,1,n,1);
        } else {
            scanf("%d%d",&a,&b);
            printf("%lld
",query(a,b,1,n,1));
        }
        
    }
    
    return 0;
}