One and two dimensional prefix and

• One-dimensional:

 1 #include <iostream>
 2 #include <vector>
 3 
 4 using namespace std;
 5 
 6 vector<int> arr(1e6+10,0);
 7 vector<long long> sum(1e6+10,0);
 8 
 9 int main(){
10     int n, m, l, r;
11     cin >> n >> m;
12     for(int i = 1;i <= n;++i)
13         cin >> arr[i];
14         
15     sum[0] = 0;    
16     for(int i = 1;i <= n;++i)
17         sum[i] = sum[i-1] + arr[i]; 
18     
19         
20     for(int i = 0;i < m;++i){
21         cin >> l >> r;
22         cout << sum[r] - sum[l-1] << endl;
23     }
24     
25     
26 }

code

• Two-dimensional

 1 #include <iostream>
 2 
 3 using namespace std;
 4 
 5 const int N = 1000+10;
 6 int arr[N][N] = {0}, s[N][N] = {0};
 7 int n, m, q; 
 8 
 9 int main(){
10     cin >> n >> m >> q;
11     for(int i = 1;i <= n;++i)
12         for(int j = 1;j <= m;++J)
 13 is              CIN >> ARR [I] [J];
 14      
15      for ( int I = . 1 ; I <= n-; ++ I)
 16          for ( int J = . 1 ; J <= m; ++ J)
 . 17              S [I] [J] = S [I- . 1 ] [J] + S [I] [J- . 1 ] - S [I- . 1 ] [J- . 1 ] + ARR [I] [J]; // equation 
18 is              
. 19      int X1, Y1, X2, Y2; // left and right corners index 
20 is      for ( int I = 0 ; I <Q; ++ I) {
 21 is         cin >> x1 >> y1 >> x2 >> y2;
22         cout << s[x2][y2] - s[x1-1][y2] - s[x2][y1-1] + s[x1-1][y1-1] << endl;
23     }
24         
25     return 0;
26 }

Code