[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+;
 using namespace std;

 LL sum[maxn<<],Lazy[maxn<<];

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

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

 void build(int l,int r,int rt)
 {
     int m;
     Lazy[rt]=;
     if(l==r) {
         scanf("%lld",&sum[rt]);
         return;
     }

     m=(l+r)>>;
     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+);
         return;
     }

     PushDown(rt,r-l+);
     m=(l+r)>>;
     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=;
     if(L<=l && r<=R) {
         return sum[rt];
     }

     PushDown(rt,r-l+);
     m=(l+r)>>;
     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[];

     scanf("%d%d",&n,&Q);
     build(,n,);

     while(Q--) {
         scanf("%s",st);
         if(st[]=='C') {
             scanf("%d%d%d",&a,&b,&c);
             Updata(a,b,c,,n,);
         } else {
             scanf("%d%d",&a,&b);
             printf("%lld\n",query(a,b,,n,));
         }

     }

     return ;
 }