POJ - 3468A Simple Problem with Integers （线段树区间更新，区间查询和）

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

解题思路：利用懒惰标记更新区间并求区间和

代码如下：

 #include<iostream>
 #include<stdio.h>
 using namespace std;

 const int MAXN = ;
 int a[MAXN];
 long long int tree[MAXN*];
 long long int lazy[MAXN*];
 int N,Q;
 string s;
 int x , y, z;
 void push_down(int l ,int r ,int rt)
 {
     int m = (l+r)/;

     if(lazy[rt])
     {
         tree[rt*] += lazy[rt]*(m-l+);
         tree[rt*+] += lazy[rt]*(r-m);
         lazy[rt*] += lazy[rt];
         lazy[rt*+] += lazy[rt];
         lazy[rt] = ;
     }
 }
 void bulid_tree(int l ,int r ,int rt)
 {
     if(l==r)
     {
         tree[rt] = a[l];
         return ;
     }
     int m = (l+r)/;

     bulid_tree(l,m,rt*);
     bulid_tree(m+,r,rt*+);
     tree[rt] = tree[rt*]+tree[rt*+];
 }

 long long int Query(int x ,int y ,int l ,int r ,int rt)
 {
     long long sum =  ;
     if(x<=l&&r<=y)
     {
         return tree[rt];
     }
     int m = (l+r)/;
     push_down(l,r,rt);
     if(x<=m)
     {
         sum += Query(x,y,l,m,rt*);
     }
     if(m<y)
     {
         sum += Query(x,y,m+,r,rt*+);
     }
     return sum;
 }
 void Update(int x ,int y ,int k ,int l ,int r ,int rt)
 {
     if(x<=l&&y>=r)
     {
         tree[rt] += k*(r-l+);
         lazy[rt] += k;
         return ;
     }
     push_down(l,r,rt);
     int m = (l+r)/;
     if(x<=m)
     {
         Update(x,y,k,l,m,rt*);
     }
     if(y>m)
     {
         Update(x,y,k,m+,r,rt*+);
     }
     tree[rt] = tree[rt*]+tree[rt*+];
 }
 int main()
 {
     scanf("%d%d",&N,&Q);
     for(int i =  ; i <= N;i++)
     {
         scanf("%d",&a[i]);
     }
     bulid_tree(,N,);
     while(Q--)
     {
         cin>>s;
         if(s[]=='Q')
         {
             scanf("%d%d",&x,&y);
             printf("%lld\n",Query(x,y,,N,));

         }
         else
         if(s[]=='C')
         {
             scanf("%d%d%d",&x,&y,&z);
             Update(x,y,z,,N,);
         }
     }
     return ;
 }