前缀和，（一维，二维）

Leetcode 303
class NumArray {
    
    
public:
	vector<int> ans;   //前缀和数组
    NumArray(vector<int>& nums) {
    
    
        int n=nums.size();
        ans.resize(n+1);
        for(int i=0;i<n;i++){
    
    
            ans[i+1]=ans[i]+nums[i];
        }
        
    }
    
    int sumRange(int i, int j) {
    
      //一维区域和检索
        return ans[j+1]-ans[i];
    }
};

Leetcode 304
class NumMatrix {
    
    
public:
    vector<vector<int> >ans;  //前缀和数组
    NumMatrix(vector<vector<int>>& matrix) {
    
    
        int m=matrix.size();      
        if(m>0){
    
    
        int n=matrix[0].size();
        ans.resize(m+1,vector<int>(n+1));
        for(int i=0;i<m;i++){
    
    
            for(int j=0;j<n;j++){
    
    
                ans[i+1][j+1]=ans[i+1][j]+ans[i][j+1]-ans[i][j]+matrix[i][j]; 
                }
            }
        }
    } 
    int sumRegion(int row1, int col1, int row2, int col2) {
    
      //二维区域和检索
        return ans[row2+1][col2+1]-ans[row1][col2+1]-ans[row2+1][col1]+ans[row1][col1];
    }
};