Height of a complete binary tree (or Heap) with N nodes
Consider a Binary Heap of size N. We need to find height of it.
Examples :
Input : N = 6
Output : 2
()
/ \
() ()
/ \ /
() () ()
Input : N = 9
Output :
()
/ \
() ()
/ \ / \
() () () ()
/ \
() ()
Let the size of heap be N and height be h
If we take few examples, we can notice that the value of h in a complete binary tree is ceil(log2(N+1)) – 1.
Examples :
N h --------- 1 0 2 1 3 1 4 2 5 2 ..... .....
C++
// CPP program to find height of complete // binary tree from total nodes. #include <bits/stdc++.h> using namespace std; int height(int N) { return ceil(log2(N + 1)) - 1; } // driver node int main() { int N = 6; cout << height(N); return 0; } |
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Java
// Java program to find height // of complete binary tree // from total nodes. import java.lang.*; class GFG { // Function to calculate height static int height(int N) { return (int)Math.ceil(Math.log(N + 1) / Math.log(2)) - 1; } // Driver Code public static void main(String[] args) { int N = 6; System.out.println(height(N)); } } // This code is contributed by // Smitha Dinesh Semwal |
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Python 3
# Python 3 program to find # height of complete binary # tree from total nodes. import math def height(N): return math.ceil(math.log2(N + 1)) - 1 # driver node N = 6print(height(N)) # This code is contributed by # Smitha Dinesh Semwal |
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C#
// C# program to find height // of complete binary tree // from total nodes. using System; class GFG { static int height(int N) { return (int)Math.Ceiling(Math.Log(N + 1) / Math.Log(2)) - 1; } // Driver node public static void Main() { int N = 6; Console.Write(height(N)); } } // This code is contributed by // Smitha Dinesh Semwal |
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PHP
<?php // PHP program to find height // of complete binary tree // from total nodes. function height($N) { return ceil(log($N + 1, 2)) - 1; } // Driver Code $N = 6; echo height($N); // This code is contributed by aj_36 ?> |
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Output :
2
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