A series of problems about the number of DP paths

 

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



}

 

 

 

class Solution {
         public int minPathSum(int[][] grid) {
        //base case 
        int n=grid.length;
        int m=grid[0].length;
        int dp[][]=new int[n+1][m+1];// Upper left corner to [i][j] The shortest number of steps （ Weighted ）
        //base case
        dp[0][0]=grid[0][0];
        for (int i = 1; i < m; i++) {
            dp[0][i]=dp[0][i-1]+grid[0][i];
        }
        for (int i = 1; i < n; i++) {
            dp[i][0]=dp[i-1][0]+grid[i][0];
        }
        for (int i = 1; i <n; i++) {
            for (int j = 1; j < m; j++) {
                dp[i][j]=grid[i][j]+Math.min(dp[i-1][j],dp[i][j-1]);
            }
        }
        return dp[n-1][m-1];
    }


}