Number of path - use only one row - get advised from the peer only to use one row instead of two rows, previous row and current row.

NumberOfPath_UseOnlyOneRow.cs

using System;

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

    static void Main(string[] args)
    {
     
    }
}

/*
keywords:

go north or go east
go up or go right
cross diagnal 

Ask: number of paths to (n - 1, n - 1)
  
  
  * *  * * *
  * *  * 5 *
  * *  2 5 9
  0 1  2 3 4
  1 1  1 1 1
  
  
  matrix(3, 3) = 5
  Time complexity: (n * n)
  Space complexity: O(n)
    
    Do not need previous row - advised by the peer 
*/