Minimum path from root node to leaf node - use recursive function, I wrote with a bug in the writing and the peer told me to fix it. I added line 27 to line 32.

RootNodeToLeafNode_Path_minimal.cs

using System;

class Solution
{
  public class Node
  {
    public int cost;
    public Node[] children;     
    
    public Node(int value)
    {
      cost = value; 
    }
  }
    
  public static int getCheapestCost(Node rootNode) // node 0 , 
  {
    // base case 
    if(rootNode == null) // false 
    {
      return 0; 
    }    
    
    var costRoot = rootNode.cost; // 0 
    int minimalPathCost = Int32.MaxValue; 
    
    var hasNoChildren = rootNode.children == null || rootNode.children.Length == 0;      
    
    if(hasNoChildren)
    {
        return costRoot;   
    }
    
    foreach(var item in rootNode.children) // node 5, 3, 6, node 3
    {
      var current = getCheapestCost(item); // 9, 13, 7  
      var cost = costRoot + current; // 0 + 9 = 9, 13, 7
      minimalPathCost = cost < minimalPathCost ? cost : minimalPathCost; // 9, 9, 7 < 9
    }
    
    return minimalPathCost; // 7 
  }

  static void Main(string[] args)
  {
        Console.WriteLine("testing is  here");
        var root0 = new Node(0); 
        var root5 = new Node(5); 
        var root3 = new Node(3); 
        var root6 = new Node(6); 
    
        root0.children = new Node[]{root5, root3, root6}; 
    
        var root4 = new Node(4); 
        root5.children = new Node[]{root4}; // path cost 9
    
        var root1 = new Node(1); 
        root6.children = new Node[]{root1}; // path cost 7
    
        var root10 = new Node(10); 
        root3.children = new Node[]{root10}; // path cost 13
        Console.WriteLine("testing is  here");
        Console.WriteLine("path cost is "+ getCheapestCost(root0)); 
  }
}

// root 0 -> Math.Min(node 5's find mininum, node 3's find minimum, node 6's minimum)
// 7 - path cost