Number of path - using O(n) space instead of O(n^2) space, it took me more than 5 minutes to fix the bug - line 26

NumberOfPath_UseO(N)space.cs

using System;

class Solution
{
    public static int NumOfPathsToDest(int n)  // 4
    {
      if( n <= 0) // false 
      {
        return 0; 
      }           
      
      var previous = new int[n]; 
      var current  = new int[n]; 
      
      for(int row = 0; row < n; row++ )  // horizontal 
      {
        for(int col = 0; col < n; col++)  // vertical 
        {
          var firstRow = row == 0; 
          if(firstRow)
          {                   
            current[col] = 1; 
          }
          else 
          {
            current[col] = 0; 
            
            if(row <= col)
            {                            
              current[col] = previous[col] + current[col - 1]; 
            }            
          }
        }        
      
        for(int col = 0; col < n; col++)
        {          
           previous[col] = current[col];          
        }
      }
      
      return current[n - 1]; 
    }

    static void Main(string[] args)
    {
      Console.WriteLine(NumOfPathsToDest(4)); 
    }
}


/*
ok
https://www.linkedin.com/in/jianminchen/

time complexity O(n * n), space complexity is O(n * n), I can reduce space to O(n), 

sure , let me reduce space complexity !

x  x  x  x   14 

x  x  x  5   14     n = 4, output is 5 

x  x  2  5   9 

x   1  2  3   4 

1   1  1  1  1   1    -> go to right, only one way to go to right 

go to first row, 

1  1  1  1   1

and then go to second row

x  1  2  3   4

because it is the sum of left and down - arr[i, j] = arr[i - 1, j] + arr[i, j - 1] if i <= j

*/