59. Unique Paths

dp[i][j] = dp[i-1][j] + dp[i][j-1]. First row and column are all 1s.

Approach

1. Create m x n DP table.
2. First row and column = 1 (only one way to reach).
3. For each cell: dp[i][j] = dp[i-1][j] + dp[i][j-1].

Complexity

• Time: O(m*n)
• Space: O(m*n)

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