My simple java DP solution with explanation


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    public class Solution {
    public int uniquePaths(int m, int n) {
        //s[i][j] denotes number of paths from top-left to (i,j)
        int[][] s = new int[m][n];
        s[0][0] = 1;
        for(int i=0;i<m;i++){
            for(int j =0;j<n;j++){
                //if destination is on the first row or first col, result is 1
                if(i == 0||j == 0) s[i][j] = 1;
                //destination on other nodes
                else s[i][j] = s[i-1][j]+s[i][j-1];
            }
        }
        return s[m-1][n-1];
    }
    

    }


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