LeetCode 62. Unique Paths

62. Unique Paths

Difficulty:: Medium

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 7 x 3 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

Example 1:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1\. Right -> Right -> Down
2\. Right -> Down -> Right
3\. Down -> Right -> Right

Example 2:

Input: m = 7, n = 3
Output: 28

Solution

Language: Java

class Solution {
      public int uniquePaths(int m, int n) {
            int[][] dp = new int[m][n];
            Arrays.fill(dp[0], 1);
            for (int i = 0; i < m; i++) {
                  dp[i][0] = 1;
           }
            for (int i = 1; i < m; i++) {
                  for (int j = 1; j < n; j++) {
                        dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
                 }
           }
            return dp[m - 1][n - 1];
     }
}

滚动数组优化

class Solution {
    public int uniquePaths(int m, int n) {
        if (m <= 1 || n <= 1) {
            return 1;
        }
        int[][] dp = new int[2][n];
        Arrays.fill(dp[0], 1);
        dp[1][0] = 1;
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                dp[i % 2][j] = dp[(i - 1) % 2][j] + dp[i % 2][j - 1];
            }
        }
        return dp[(m - 1) % 2][n - 1];
    }
}