3468-A Simple Problem with Integers 线段树（区间增减，区间求和）

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
题意：n个数字，q次操作，每次可以区间增减，或者查询区间的和

 #include<cstdio>
 #define lson l,m,rt<<1
 #define rson m+1,r,rt<<1|1
 #define MAXN 100100
 #define LL long long
 LL sum[MAXN<<];
 LL add[MAXN<<];
 int n,q;
 char s[];
 void putup(int rt)
 {
     sum[rt] = sum[rt<<]+sum[rt<<|];
 }
 void putdown(int rt,int m)
 {
     if (add[rt])
     {
         add[rt<<] += add[rt];
         add[rt<<|] += add[rt];
         sum[rt<<] += (m-(m>>))*add[rt];
         sum[rt<<|] += (m>>)*add[rt];
         add[rt] = ;
     }
 }
 void build(int l,int r,int rt)
 {
     add[rt] = ;
     if (l==r)
     {
         scanf("%lld",&sum[rt]);
         return ;
     }
     int m = (l+r)>>;
     build(lson);
     build(rson);
     putup(rt);
 }
 void update(int l,int r,int rt,int L,int R,int c)
 {
     if (L<=l && r<=R)
     {
         add[rt] += c;
         sum[rt] += (LL)c*(r-l+);
         return ;
     }
     putdown(rt,r-l+);
     int m = (l+r)>>;
     if (L<=m) update(lson,L,R,c);
     if (R>m)  update(rson,L,R,c);
     putup(rt);
 }
 LL query(int l,int r,int rt,int L,int R)
 {
     if (L<=l && r<=R)
     {
         return sum[rt];
     }
     putdown(rt,r-l+);
     LL ret = ;
     int m = (l+r)>>;
     if (L<=m) ret += query(lson,L,R);
     if (R>m)  ret += query(rson,L,R);
     return ret;
 }
 int main()
 {
     scanf("%d%d",&n,&q);
     build(,n,);
     while (q--)
     {
         int x,y,z;
         scanf("%s",s);
         if (s[]=='C')
         {
             scanf("%d%d%d",&x,&y,&z);
             update(,n,,x,y,z);
         }
         else
         {
             scanf("%d%d",&x,&y);
             printf("%lld\n",query(,n,,x,y));
         }
     }
     return ;
 }