【LBLD】小而美的算法技巧：前缀和数组

一维数组中的前缀和

class NumArray {
private:
    vector<int> preSum;
    
public:
    NumArray(vector<int>& nums) {
        preSum.push_back(0);
        for (int i = 1; i < nums.size()+1; i++) {
            preSum.push_back(nums[i-1]+preSum[i-1]);
        }
    }
    
    int sumRange(int left, int right) {
        return preSum[right+1] - preSum[left];
    }
};

/**
 * Your NumArray object will be instantiated and called as such:
 * NumArray* obj = new NumArray(nums);
 * int param_1 = obj->sumRange(left,right);
 */

二维矩阵中的前缀和

class NumMatrix {
private:
    vector<vector<int>> preSumMatrix;

public:
    NumMatrix(vector<vector<int>>& matrix) {
        // 初始化
        for (int i = 0; i <= matrix.size(); i++)
        {
            vector<int> preSumRow;
            for (int j = 0; j <= matrix[0].size(); j++) {
                preSumRow.push_back(0);
            }
            preSumMatrix.push_back(preSumRow);
        }
        // 计算值
        for (int i = 1; i <= matrix.size(); i++)
        {
            for (int j = 1; j <= matrix[0].size(); j++) {
                preSumMatrix[i][j] = matrix[i-1][j-1] + preSumMatrix[i-1][j] + preSumMatrix[i][j-1] - preSumMatrix[i-1][j-1];
            }
        }
    }
    
    int sumRegion(int row1, int col1, int row2, int col2) {
        return preSumMatrix[row2+1][col2+1] - preSumMatrix[row2+1][col1] - preSumMatrix[row1][col2+1] + preSumMatrix[row1][col1];
    }
};

/**
 * Your NumMatrix object will be instantiated and called as such:
 * NumMatrix* obj = new NumMatrix(matrix);
 * int param_1 = obj->sumRegion(row1,col1,row2,col2);
 */