（poj3468）A Simple Problem with Integers（区间更新）

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.
Source

POJ Monthly–2007.11.25, Yang Yi

分析:区间更新

#include<cstdio>#include<cstring>#include<algorithm>using namespace std;#define lson l,m,rt<<1#define rson m+1,r,rt<<1|1typedef long long LL;const LL N=2e5+5;LL sum[N<<2],a[N],MAX[N<<2],ad[N<<2];void pushup(LL rt){    sum[rt]=sum[rt<<1]+sum[rt<<1|1];    // MAX[rt]=max(MAX[rt<<1],MAX[rt<<1|1]);}void pushdown(int rt,int m){    if(ad[rt])    {        ad[rt<<1]+=ad[rt];        ad[rt<<1|1]+=ad[rt];        sum[rt<<1]+=ad[rt]*(m-(m>>1));        sum[rt<<1|1]+=ad[rt]*(m>>1);        ad[rt]=0; ///标记清除！！！    }}void build(LL l,LL r,LL rt){    ad[rt]=0;    if(l==r)    {        scanf("%lld",&sum[rt]);        return ;    }    LL m=(l+r)>>1;    build(lson);    build(rson);    pushup(rt);}void update(LL L,LL R,LL c,LL l,LL r,LL rt){    if(L<=l&&R>=r)    {        ad[rt]+=c;        sum[rt]+=c*(r-l+1);        return ;    }    pushdown(rt,r-l+1);    LL m=(l+r)>>1;    if(L<=m) update(L,R,c,lson);    if(R>m) update(L,R,c,rson);    pushup(rt);}LL query(LL L,LL R,LL l,LL r,LL rt){    if(L<=l&&R>=r)    {        return sum[rt];    }    pushdown(rt,r-l+1);    LL m=(l+r)>>1;    LL ret=0;    if(L<=m) ret+=query(L,R,lson);    if(R>m) ret+=query(L,R,rson);    return ret;}int main(){    int n,m;    while(~scanf("%d%d",&n,&m))    {        build(1,n,1);        for(int i=0; i<m; i++)        {            char op;            LL a,b,c;            scanf(" %c",&op);            if(op=='Q')            {                scanf("%lld%lld",&a,&b);                printf("%lld\n",query(a,b,1,n,1));            }            else            {                scanf("%lld%lld%lld",&a,&b,&c);                update(a,b,c,1,n,1);            }        }    }    return 0;}