Day23 leetcode 二维区域和检索

Day 23

题目：二维区域和检索

leetcode链接：二维区域和检索
要点：前缀和

1、Java

class NumMatrix {
    // 定义：preSum[i][j] 记录 matrix 中子矩阵 [0, 0, i-1, j-1] 的元素和
    private int[][] preSum;
    public NumMatrix(int[][] matrix) {
        int m = matrix.length;
        int n = matrix[0].length;
        if(m == 0 || n == 0) return;
        // 构造前缀和矩阵
        preSum = new int[m + 1][n + 1];
        for(int i = 1; i < m + 1; i++){
            for(int j = 1; j < n + 1; j++){
                // 计算每个矩阵 [0, 0, i, j] 的元素和
                preSum[i][j] = preSum[i - 1][j] + preSum[i][j - 1] - preSum[i - 1][j - 1] + matrix[i -1][j - 1];
            }
        }
    }
    
    // 计算子矩阵 [x1, y1, x2, y2] 的元素和
    public int sumRegion(int row1, int col1, int row2, int col2) {
        // 目标矩阵之和由四个相邻矩阵运算获得
        return preSum[row2 + 1][col2 + 1] - preSum[row2 + 1][col1] - preSum[row1][col2 + 1] + preSum[row1][col1];
    }
}

2、python

class NumMatrix:

    def __init__(self, matrix: List[List[int]]):
        m, n = len(matrix), (len(matrix[0]) if matrix else 0)
        self.sums = [[0] * (n + 1) for _ in range(m + 1)]
        _sums = self.sums

        for i in range(m):
            for j in range(n):
                _sums[i + 1][j + 1] = _sums[i][j + 1] + _sums[i + 1][j] - _sums[i][j] + matrix[i][j]

    def sumRegion(self, row1: int, col1: int, row2: int, col2: int) -> int:
        _sums = self.sums

        return _sums[row2 + 1][col2 + 1] - _sums[row1][col2 + 1] - _sums[row2 + 1][col1] + _sums[row1][col1]