Java

UniquePath.java

/*
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?



*/

// 1D DP
public class Solution {
    public int uniquePaths(int m, int n) {
        if (m<0||n<0){
            return 0;
        }
        if (m==0 || n==0 ){
            return 1;
        }
        
        int[] arr=new int[n];
        arr[0]=1;
        
        for (int i=0; i<m; i++){
            for (int j=1; j<n; j++){
                arr[j]=arr[j]+arr[j-1];
            }
        }
        
        return arr[n-1];
        
        
    }
}
// 2D DP
public class Solution {
    public int uniquePaths(int m, int n) {
        if (m<0||n<0){
            return 0;
        }
        if (m==0 || n==0 ){
            return 1;
        }
        
        int[][] matrix=new int[m][n];
        for (int i=0; i<m; i++){
            matrix[i][0]=1;
        }
        for (int i=0; i<n; i++){
            matrix[0][i]=1;
        }
        
        for (int i=1; i<m; i++){
            for (int j=1; j<n; j++){
                matrix[i][j]=matrix[i-1][j]+matrix[i][j-1];        
            }
        }
        
        return matrix[m-1][n-1];
        
    }
}