Checking if a vector is a min heap using recursion

Question

I'm trying to write a program that checks if a vector is a min heap. I've been looking at code from here. I understand why they use 2*i+2 to compare to n, since there's a tipping point with the index where values in the vector/array (mine uses a vector) become leaf nodes. What I don't understand is why they keep using 2*i + 1 and 2*i + 2 as the index when they call the function recursively. Shouldn't they be using i+1 to access the left node and i+2 to access the right? But I tried this and I get a segmentation fault.

    bool checkMinHeap(int A[], int i, int n)
    { 
       // if i is a leaf node, return true as every leaf node is a heap
       if (2*i + 2 > n)
       return true;

       // if i is an internal node        

      // recursively check if left child is heap
      bool left = (A[i] <= A[2*i + 1]) && checkMinHeap(A, 2*i + 1, n);

      // recursively check if right child is heap (to avoid array out
     // of bound, we first check if right child exists or not)
     bool right = (2*i + 2 == n) || 
            (A[i] <= A[2*i + 2] && checkMinHeap(A, 2*i + 2, n));

     // return true if both left and right child are heap
     return left && right;
  }

Their test code:

    int main()
    {
       int A[] = {1, 2, 3, 4, 5, 6};
       int n = sizeof(A) / sizeof(int);

       // start with index 0 (root of the heap)
       int index = 0;

       if (checkMinHeap(A, index, n))
           cout << "Given array is a min heap";
       else
           cout << "Given array is not a min heap";

       return 0;
  }

My test code (returns 0, when it should return 1):

   int main (void)
   {
      vector <int> test;
      test.push_back(1);
      test.push_back(2);
      test.push_back(3);
      test.push_back(4);
      test.push_back(5);
      test.push_back(9);
      test.push_back(3);
      test.push_back(19);
      cout << isMinHeap(test,0) << endl;
  }

What do you think of adapting `std::is_heap` for this purpose? It's almost what you need. — John Zwinck, Oct 14 '18 at 02:13
Consider that you check left, then right, and then return true if both left and right are true. You can short-circuit by returning false if left is false. Before checking right. — Jim Mischel, Oct 15 '18 at 15:04

Hiroki · Accepted Answer · 2018-10-14T10:05:22.980

What I don't understand is why they keep using 2*i + 1 and 2*i + 2 as the index when they call the function recursively.

For instance, your heap data structure is following one. These values are stored in an array, say A[i], i = 0, 1, …, 7. In this picture, the blue circles i = 3 = 2*1+1 and i = 4 = 2*1+2 are the children of the green circle i = 1

Like this, in general, the left child of a parent i has an index 2*i+1 and the right one has index 2*i+2. This is very general child-parent relationships in binary heap maps. This is the reason why they keep using 2*i+1 and 2*i+2 as the index when they call the function recursively.

Checking if a vector is a min heap using recursion

1 Answers1