题解 | #矩阵的最小路径和#

/**
     * 动态规划公式
     * int m = dp[i - 1][j];
     * int n = dp[i][j - 1];
     * int tmp = Math.min(n, m) + matrix[i][j];
     * dp[i][j] = tmp;
     *
     * @param matrix
     * @return
     */
    public static int minPathSum(int[][] matrix) {
        // write code here
        int[][] dp = new int[matrix.length][matrix[0].length];
        dp[0][0] = matrix[0][0];
        for (int i = 1; i < matrix.length; i++) {
            dp[i][0] = dp[i - 1][0] + matrix[i][0];
        }

        for (int i = 1; i < matrix[0].length; i++) {
            dp[0][i] = dp[0][i - 1] + matrix[0][i];
        }
        for (int i = 1; i < dp.length; i++) {
            for (int j = 1; j < dp[i].length; j++) {
                int m = dp[i - 1][j];
                int n = dp[i][j - 1];
                int tmp = Math.min(n, m) + matrix[i][j];
                dp[i][j] = tmp;
            }
        }
        return dp[matrix.length - 1][matrix[0].length - 1];
    }