L64.java

class Solution64 {
    class Solution {
        /**
         * 64. Minimum Path Sum https://leetcode.com/problems/minimum-path-sum/description/
         *
         * @param grid
         * @return
         * @timeComplexity O(m * n)
         * @spaceComplexity O(m * n)
         */
        public int minPathSum(int[][] grid) {
            int m = grid.length;
            int n = grid[0].length;
            int[][] table = new int[m][n];
            int sum = 0;
            // For each position in the first row, store the cumulative sum
            for (int i = 0; i < n; i++) {
                sum += grid[0][i];
                table[0][i] = sum;
            }
            sum = 0;
            // For each position in the first column, store the cumulative sum
            for (int i = 0; i < m; i++) {
                sum += grid[i][0];
                table[i][0] = sum;
            }
            // Choose the best path out of the top and left
            for (int i = 1; i < m; i++) {
                for (int j = 1; j < n; j++) {
                    table[i][j] = grid[i][j] + Math.min(table[i - 1][j], table[i][j - 1]);
                }
            }
            return table[m - 1][n - 1];
        }
    }
}