# Highest power of 2 less than or equal to given number

Given a number n, find the highest power of 2 that is smaller than or equal to n.

Examples :

```Input : n = 10
Output : 8

Input : n = 19
Output : 16

Input : n = 32
Output : 32
```

## Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

A simple solution is to start checking from n and keep decrementing until we find a power of 2.

 `// C++ program to find highest power of 2 smaller ` `// than or equal to n. ` `#include ` `using` `namespace` `std; ` ` `  `int` `highestPowerof2(``int` `n) ` `{ ` `    ``int` `res = 0; ` `    ``for` `(``int` `i=n; i>=1; i--) ` `    ``{ ` `        ``// If i is a power of 2 ` `        ``if` `((i & (i-1)) == 0) ` `        ``{ ` `            ``res = i; ` `            ``break``; ` `        ``} ` `    ``} ` `    ``return` `res; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 10; ` `    ``cout << highestPowerof2(n); ` `    ``return` `0; ` `} `

 `// Java code to find highest power  ` `// of 2 smaller than or equal to n. ` `class` `GFG  ` `{ ` `   ``static` `int` `highestPowerof2(``int` `n) ` `   ``{ ` `     ``int` `res = ``0``; ` `     ``for` `(``int` `i = n; i >= ``1``; i--) ` `        ``{ ` `         ``// If i is a power of 2 ` `          ``if` `((i & (i - ``1``)) == ``0``) ` `             ``{ ` `                  ``res = i; ` `                ``break``; ` `             ``} ` `        ``} ` `     ``return` `res; ` `   ``} ` ` `  `   ``// Driver code ` `   ``public` `static` `void` `main(String[] args) ` `   ``{ ` `      ``int` `n = ``10``; ` `      ``System.out.println(highestPowerof2(n)); ` `   ``} ` `} ` `// This code is contributed by prerna saini.  ` ` `

 `# Python3 program to find highest  ` `# power of 2 smaller than or  ` `# equal to n. ` `def` `highestPowerof2(n): ` ` `  `    ``res ``=` `0``; ` `    ``for` `i ``in` `range``(n, ``0``, ``-``1``): ` `         `  `        ``# If i is a power of 2 ` `        ``if` `((i & (i ``-` `1``)) ``=``=` `0``): ` `         `  `            ``res ``=` `i; ` `            ``break``; ` `         `  `    ``return` `res; ` ` `  `# Driver code ` `n ``=` `10``; ` `print``(highestPowerof2(n)); ` `     `  `# This code is contributed by mits `

 `// C# code to find highest power  ` `// of 2 smaller than or equal to n. ` `using` `System; ` ` `  `class` `GFG ` `{ ` `public` `static` `int` `highestPowerof2(``int` `n) ` `{ ` `    ``int` `res = 0; ` `    ``for` `(``int` `i = n; i >= 1; i--) ` `        ``{ ` `        ``// If i is a power of 2 ` `        ``if` `((i & (i - 1)) == 0) ` `            ``{ ` `                ``res = i; ` `                ``break``; ` `            ``} ` `        ``} ` `    ``return` `res; ` `} ` `     `  `    ``// Driver Code ` `    ``static` `public` `void` `Main () ` `    ``{ ` `        ``int` `n = 10; ` `        ``Console.WriteLine(highestPowerof2(n)); ` `    ``} ` `} ` ` `  `// This code is contributed by ajit `

 `= 1; ``\$i``--) ` `    ``{ ` `        ``// If i is a power of 2 ` `        ``if` `((``\$i` `& (``\$i` `- 1)) == 0) ` `        ``{ ` `            ``\$res` `= ``\$i``; ` `            ``break``; ` `        ``} ` `    ``} ` `    ``return` `\$res``; ` `} ` ` `  `// Driver code ` `\$n` `= 10; ` `echo` `highestPowerof2(``\$n``); ` `     `  `// This code is contributed by m_kit ` `?> `

Output :
`8`

Time complexity : O(n). In worst case, the loop runs floor(n/2) times. The worst case happens when n is of the form 2x – 1.

An efficient solution is to use bitwise left shift operator to find all powers of 2 starting from 1. For every power check if it is smaller than or equal to n or not. Below is the implementation of the idea.

 `// C++ program to find highest power of 2 smaller ` `// than or equal to n. ` `#include ` `using` `namespace` `std; ` ` `  `int` `highestPowerof2(unsigned ``int` `n) ` `{ ` `    ``// Invalid input ` `    ``if` `(n < 1) ` `        ``return` `0; ` ` `  `    ``int` `res = 1; ` ` `  `    ``// Try all powers starting from 2^1 ` `    ``for` `(``int` `i=0; i<8*``sizeof``(unsigned ``int``); i++) ` `    ``{ ` `        ``int` `curr = 1 << i; ` ` `  `        ``// If current power is more than n, break ` `        ``if` `(curr > n) ` `           ``break``; ` ` `  `        ``res = curr; ` `    ``} ` ` `  `    ``return` `res; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 10; ` `    ``cout << highestPowerof2(n); ` `    ``return` `0; ` `} `

 `// Java program to find  ` `// highest power of 2 smaller ` `// than or equal to n. ` `import` `java.io.*; ` ` `  `class` `GFG  ` `{ ` `static` `int` `highestPowerof2(``int` `n) ` `{ ` `    ``// Invalid input ` `    ``if` `(n < ``1``) ` `        ``return` `0``; ` ` `  `    ``int` `res = ``1``; ` ` `  `    ``// Try all powers  ` `    ``// starting from 2^1 ` `    ``for` `(``int` `i = ``0``; i < ``8` `* Integer.BYTES; i++) ` `    ``{ ` `        ``int` `curr = ``1` `<< i; ` ` `  `        ``// If current power is  ` `        ``// more than n, break ` `        ``if` `(curr > n) ` `        ``break``; ` ` `  `        ``res = curr; ` `    ``} ` ` `  `    ``return` `res; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args)  ` `{ ` `    ``int` `n = ``10``; ` `    ``System.out.println(highestPowerof2(n)); ` `} ` `} ` ` `  `// This code is contributed aj_36 `

 `# Python3 program to find highest power of 2 smaller ` `# than or equal to n. ` ` `  `import` `sys ` ` `  `def` `highestPowerof2( n): ` ` `  `    ``# Invalid input ` `    ``if` `(n < ``1``): ` `        ``return` `0` `  `  `    ``res ``=` `1` `  `  `    ``#Try all powers starting from 2^1 ` `    ``for` `i ``in` `range``(``8``*``sys.getsizeof(n)): ` `     `  `        ``curr ``=` `1` `<< i ` `  `  `        ``# If current power is more than n, break ` `        ``if` `(curr > n): ` `             ``break` `  `  `        ``res ``=` `curr ` `  `  `    ``return` `res ` `  `  `# Driver code ` `if` `__name__ ``=``=` `"__main__"``: ` ` `  `    ``n ``=` `10` `    ``print``(highestPowerof2(n)) ` `   `

 `// C# program to find  ` `// highest power of 2 smaller ` `// than or equal to n. ` `using` `System; ` ` `  `class` `GFG ` `{ ` `static` `int` `highestPowerof2(``int` `n) ` `{ ` `    ``// Invalid input ` `    ``if` `(n < 1) ` `        ``return` `0; ` ` `  `    ``int` `res = 1; ` ` `  `    ``// Try all powers  ` `    ``// starting from 2^1 ` `    ``for` `(``int` `i = 0; i < 8 * ``sizeof``(``uint``); i++) ` `    ``{ ` `        ``int` `curr = 1 << i; ` ` `  `        ``// If current power is  ` `        ``// more than n, break ` `        ``if` `(curr > n) ` `        ``break``; ` ` `  `        ``res = curr; ` `    ``} ` ` `  `    ``return` `res; ` `} ` ` `  `// Driver code ` `static` `public` `void` `Main () ` `{ ` `    ``int` `n = 10; ` `    ``Console.WriteLine(highestPowerof2(n)); ` `} ` `} ` ` `  `// This code is contributed ajit `

 ` ``\$n``) ` `        ``break``; ` ` `  `        ``\$res` `= ``\$curr``; ` `    ``} ` ` `  `    ``return` `\$res``; ` `} ` ` `  `// Driver code ` `\$n` `= 10; ` `echo` `highestPowerof2(``\$n``); ` `     `  `// This code is contributed ` `// by m_kit ` `?> `

Output :
`8`

A Solution using Log
Thanks to Anshuman Jha for suggesting this solution.

 `// C++ program to find highest power of 2 smaller ` `// than or equal to n. ` `#include ` `using` `namespace` `std; ` ` `  `int` `highestPowerof2(``int` `n) ` `{ ` `   ``int` `p = (``int``)log2(n); ` `   ``return` `(``int``)``pow``(2, p);  ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 10; ` `    ``cout << highestPowerof2(n); ` `    ``return` `0; ` `} `

 `// Java program to find  ` `// highest power of 2  ` `// smaller than or equal to n. ` `import` `java.io.*; ` ` `  `class` `GFG  ` `{ ` `static` `int` `highestPowerof2(``int` `n) ` `{ ` `     `  `    ``int` `p = (``int``)(Math.log(n) /  ` `                  ``Math.log(``2``)); ` `    ``return` `(``int``)Math.pow(``2``, p);  ` `} ` ` `  `// Driver code ` `public` `static` `void` `main (String[] args)  ` `{ ` `    ``int` `n = ``10``; ` `    ``System.out.println(highestPowerof2(n)); ` `} ` `} ` ` `  `// This code is contributed ` `// by m_kit `

 `# Python3 program to find highest  ` `# power of 2 smaller than or  ` `# equal to n. ` `import` `math ` ` `  `def` `highestPowerof2(n): ` ` `  `    ``p ``=` `int``(math.log(n, ``2``)); ` `    ``return` `int``(``pow``(``2``, p));  ` ` `  `# Driver code ` `n ``=` `10``; ` `print``(highestPowerof2(n)); ` ` `  `# This code is contributed by mits `

 `// C# program to find  ` `// highest power of 2  ` `// smaller than or equal to n. ` `using` `System; ` ` `  `class` `GFG ` `{ ` `static` `int` `highestPowerof2(``int` `n) ` `{ ` `    ``int` `p = (``int``)(Math.Log(n) /  ` `                   ``Math.Log(2)); ` `    ``return` `(``int``)Math.Pow(2, p);  ` `} ` ` `  `// Driver code ` `static` `public` `void` `Main () ` `{ ` `    ``int` `n = 10; ` `    ``Console.WriteLine(highestPowerof2(n)); ` `} ` `} ` ` `  `// This code is contributed ` `// by ajit `

 ` `

Output :
`8`

Application Problem:
Some people are standing in a queue. A selection process follows a rule where people standing on even positions are selected. Of the selected people a queue is formed and again out of these only people on even position are selected. This continues until we are left with one person. Find out the position of that person in the original queue.
Print the position(original queue) of that person who is left.
Examples :

```Input: n = 10
Output:8
Explanation :
1 2 3 4 5 6 7 8 9 10  ===>Given queue
2 4 6 8 10
4 8
8

Input: n = 17
Input: 16
Explanation :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17  ===>Given queue
2 4 6 8 10 12 14 16
4 8 12 16
8 16
16
```

Related Article :
Power of 2 greater than or equal to a given number.

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