#8 LeetCode ( Q: (62) Unique Paths)

LeetCode 62 Unique Paths, Coding Interview Question
Level : Medium
Challenge : 8/1000

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?

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

Constraints:

• 1 <= m, n <= 100
• It’s guaranteed that the answer will be less than or equal to 2 * 10 ^ 9.

Solution — Java

class Solution {
  private int[][] dp;
  private int m;
  private int n;
  
  public int uniquePaths(int m, int n) {
    this.dp = new int[m][n];    
    this.m = m;
    this.n = n;
    return dfs(0, 0);
  }
  
  private int dfs(int x, int y) {
    if (x > m - 1 || y > n - 1)
      return 0;
    if (x == m - 1 && y == n - 1)
      return 1;
    if (dp[x][y] == 0)     
      dp[x][y] = dfs(x + 1, y) + dfs(x , y + 1);
    return dp[x][y];
  } 
}

Goal : 8 / 1000

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