Given an unsigned number, find the minimum number that could be formed by using the bits of the given unsigned number.
Examples :
Input : 6
Output : 3
Binary representation of 6 is 0000….0110. Smallest number with same number of set bits 0000….0011.
Input : 11
Output : 7
Simple Approach:
1. Find binary representation of the number using simple decimal to binary representation technique.
2. Count number of set bits in the binary representation equal to ‘n’.
3. Create a binary representation with it’s ‘n’ least significant bits set to 1.
4. Convert the binary representation back to the number.
Efficient Approach:
1. Just measure the number of 1’s present in the bit representation of the number.
2. (Number of set bits raised to the power of 2) – 1 represents the minimized number.
C++
// An efficient C++ program to find// minimum number formed by bits of a given number.#include <bits/stdc++.h>#define ll unsigned intusing namespace std;// Returns minimum number formed by// bits of a given number.ll minimize(ll a){ // _popcnt32(a) gives number of 1's // present in binary representation // of a. ll n = _popcnt32(a); return (pow(2, n) - 1);}// Driver function.int main(){ ll a = 11; cout << minimize(a) << endl; return 0;} |
Java
// An efficient Java program to // find minimum number formed// by bits of a given number.import java.io.*;class GFG{ public static int _popcnt32(long number) { int count = 0; while (number > 0) { count += number & 1L; number >>= 1L; } return count; } // Returns minimum number formed // by bits of a given number. static long minimize(long a) { // _popcnt32(a) gives number // of 1's present in binary // representation of a. int n = _popcnt32(a); return ((long)Math.pow(2, n) - 1); } // Driver Code. public static void main(String args[]) { long a = 11; System.out.print(minimize(a)); }}// This code is contributed by // Manish Shaw(manishshaw1) |
Python3
# An efficient Python3 program # to find minimum number formed# by bits of a given number.# Returns minimum number formed by# bits of a given number.def minimize(a): # _popcnt32(a) gives number of 1's # present in binary representation # of a. n = bin(a).count("1") return (pow(2, n) - 1)# Driver Codea = 11print(minimize(a))# This code is contributed by Mohit Kumar |
C#
// An efficient C# program to // find minimum number formed// by bits of a given number.using System;using System.Linq;using System.Collections.Generic;class GFG{ // Returns minimum number formed // by bits of a given number. static long minimize(long a) { // _popcnt32(a) gives number // of 1's present in binary // representation of a. string binaryString = Convert.ToString(a, 2); int n = binaryString.Split(new [] {'0'}, StringSplitOptions.RemoveEmptyEntries).Length + 1; return ((long)Math.Pow(2, n) - 1); } // Driver Code. static void Main() { long a = 11; Console.Write(minimize(a)); }}// This code is contributed by // Manish Shaw(manishshaw1) |
Javascript
<script>// An efficient Javascript program to // find minimum number formed// by bits of a given number. function _popcnt32(number) { let count = 0; while (number > 0) { count += number & 1; number >>= 1; } return count; } // Returns minimum number formed // by bits of a given number. function minimize(a) { // _popcnt32(a) gives number // of 1's present in binary // representation of a. let n = _popcnt32(a); return (Math.pow(2, n) - 1); } // Driver Code. let a = 11; document.write(minimize(a)); // This code is contributed by unknown2108</script> |
Time Complexity: O(log N), as the _popcnt32 has a time complexity O(logN), however, _popcnt32 has a maximum value of O(log32), so it can be interpreted as O(1) as well.
Auxiliary Space: O(1)
Note : The above code uses GCC specific functions. If we wish to write code for other compilers, we may use Count set bits in an integer.
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