# Find all powers of 2 less than or equal to a given number

Given a positive number **N**, the task is to find out all the perfect powers of two which are less than or equal to the given number **N**.

**Examples:**

Input:N = 63Output:32 16 8 4 2 1Explanation:

There are total of 6 powers of 2, which are less than or equal to the given number N.

Input:N = 193Output:128 64 32 16 8 4 2 1Explaination:

There are total of 8 powers of 2, which are less than or equal to the given number N.

**Naive Approach:** The idea is to traverse each number from N to 1 and check if it is a perfect power of 2 or not. If yes, then print that number.

**Another Approach:** The idea is to find all powers of 2 and simply print the powers that are lesser than or equal to N.

**Another Approach:** The idea is based on the concept that all powers of 2 has all bits set, in its binary form. Bitset function is used in this approach solve the above problem. Below are the steps:

- Find the largest power of 2(say
**temp**) which is used to evaluate the number less than or equal to**N**. - Initialise an bitset array
**arr[]**of maximum size**64**, to store the binary representation of the given number**N**. - Reset all the bits in the bitset array using reset() function.
- Iterate a loop from
**total to 0**, and sequentially make each bit**1**, and find the value of that binary expression and then reset the bit.

Below is the implementation of the above approach:

`// C++ program for the above approach` ` ` `#include <bits/stdc++.h>` `using` `namespace` `std;` `const` `int` `MAX = 64;` ` ` `// Function to return max exponent of` `// 2 which evaluates a number less` `// than or equal to N` `int` `max_exponent(` `int` `n)` `{` ` ` `return` `(` `int` `)(log2(n));` `}` ` ` `// Function to print all the powers` `// of 2 less than or equal to N` `void` `all_powers(` `int` `N)` `{` ` ` `bitset<64> arr(N);` ` ` ` ` `// Reset all the bits` ` ` `arr.reset();` ` ` ` ` `int` `total = max_exponent(N);` ` ` ` ` `// Iterate from total to 0` ` ` `for` `(` `int` `i = total; i >= 0; i--) {` ` ` ` ` `// Reset the next bit` ` ` `arr.reset(i + 1);` ` ` ` ` `// Set the current bit` ` ` `arr.set(i);` ` ` ` ` `// Value of the binary expression` ` ` `cout << arr.to_ulong() << ` `" "` `;` ` ` `}` `}` ` ` `// Driver Code` `int` `main()` `{` ` ` `// Given Number` ` ` `int` `N = 63;` ` ` ` ` `// Function Call` ` ` `all_powers(N);` ` ` `return` `0;` `}` |

**Output:**

32 16 8 4 2 1

**Time Complexity:** *O(log N)***Auxiliary Space:** *O(1)*