62. Unique Paths
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A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).
The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).
How many possible unique paths are there?
Above is a 3 x 7 grid. How many possible unique paths are there?
Note: m and n will be at most 100.
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Solution:
Tips:
easy dp.
dp[i][j] = dp[i - 1][j] + dp[i][j - 1];Java Code:
public class Solution { public int uniquePaths(int m, int n) { if (m == 0 || n == 0) { return 0; } if (m == 1) { return 1; } int[][] grid = new int[m][n]; // init row Arrays.fill(grid[0], 1); // init column for (int i = 0; i < m; i++) { grid[i][0] = 1; } for (int i = 1; i < m; i++) { for (int j = 1; j < n; j++) { grid[i][j] = grid[i][j - 1] + grid[i - 1][j]; //System.out.printf("%d + %d = %d\n", grid[i][j - 1], grid[i - 1][j], grid[i][j]); } } return grid[m - 1][n - 1]; }}
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