Minimum Path Sum

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

Solution1:

better

public int minPathSum(int[][] grid) { int width = grid[0].length; int height = grid.length; for (int i = 1; i < width; i++) { grid[0][i] += grid[0][i - 1]; } for (int i = 1; i < height; i++) { grid[i][0] += grid[i - 1][0]; for (int j = 1; j < width; j++) { grid[i][j] += Math.min(grid[i - 1][j], grid[i][j - 1]); } } return grid[height - 1][width - 1]; }

Solution2:

public int minPathSum(int[][] grid) { int width = grid[0].length; int height = grid.length; for (int i = 0; i < height; i++) { for (int j = 0; j < width; j++) { if (i == 0 && j != 0) { grid[i][j] = grid[i][j] + grid[i][j - 1]; } else if (i != 0 && j == 0) { grid[i][j] = grid[i][j] + grid[i - 1][j]; } else if (i == 0 && j == 0) { grid[i][j] = grid[i][j]; } else { grid[i][j] = Math.min(grid[i][j - 1], grid[i - 1][j]) + grid[i][j]; } } } return grid[height - 1][width - 1]; }