Minimum number N such that total set bits of all numbers from 1 to N is at-least X
Given a number X, the task is to find the minimum number N such that total set bits of all numbers from 1 to n is atleast X.
Examples:
Input: x = 5 Output: 4 Set bits in 1-> 1 Set bits in 2-> 1 Set bits in 3-> 2 Set bits in 4-> 1 Hence first four numbers add upto 5 Input: x = 20 Output: 11
Approach: Use binary search to get the minimum most number whose sum of bits till N is atleast X. At start, low is 0 and high is initialized according to the constraint. Check if count of set bits is atleast X, every time it is, change high to mid-1, else change it to mid+1. Everytime we do high = mid-1, store the minimal of answer.
Below is the implementation of the above approach:
C++
// C++ implementation of the above approach #include <bits/stdc++.h> using namespace std; #define INF 99999 #define size 10 // Function to count sum of set bits // of all numbers till N int getSetBitsFromOneToN(int N) { int two = 2, ans = 0; int n = N; while (n) { ans += (N / two) * (two >> 1); if ((N & (two - 1)) > (two >> 1) - 1) ans += (N & (two - 1)) - (two >> 1) + 1; two <<= 1; n >>= 1; } return ans; } // Function to find the minimum number int findMinimum(int x) { int low = 0, high = 100000; int ans = high; // Binary search for the lowest number while (low <= high) { // Find mid number int mid = (low + high) >> 1; // Check if it is atleast x if (getSetBitsFromOneToN(mid) >= x) { ans = min(ans, mid); high = mid - 1; } else low = mid + 1; } return ans; } // Driver Code int main() { int x = 20; cout << findMinimum(x); return 0; } |
Java
// Java implementation of the above approach import java.util.*; class solution { static int INF = 99999; static int size = 10; // Function to count sum of set bits // of all numbers till N static int getSetBitsFromOneToN(int N) { int two = 2, ans = 0; int n = N; while (n!=0) { ans += (N / two) * (two >> 1); if ((N & (two - 1)) > (two >> 1) - 1) ans += (N & (two - 1)) - (two >> 1) + 1; two <<= 1; n >>= 1; } return ans; } // Function to find the minimum number static int findMinimum(int x) { int low = 0, high = 100000; int ans = high; // Binary search for the lowest number while (low <= high) { // Find mid number int mid = (low + high) >> 1; // Check if it is atleast x if (getSetBitsFromOneToN(mid) >= x) { ans = Math.min(ans, mid); high = mid - 1; } else low = mid + 1; } return ans; } // Driver Code public static void main(String args[]) { int x = 20; System.out.println(findMinimum(x)); } } //This code is contributed by // Shashank_Sharma |
Python3
# Python3 implementation of the # above approach INF = 99999size = 10 # Function to count sum of set bits # of all numbers till N def getSetBitsFromOneToN(N): two, ans = 2, 0 n = N while (n > 0): ans += (N // two) * (two >> 1) if ((N & (two - 1)) > (two >> 1) - 1): ans += (N & (two - 1)) - (two >> 1) + 1 two <<= 1 n >>= 1 return ans # Function to find the minimum number def findMinimum(x): low = 0 high = 100000 ans = high # Binary search for the lowest number while (low <= high): # Find mid number mid = (low + high) >> 1 # Check if it is atleast x if (getSetBitsFromOneToN(mid) >= x): ans = min(ans, mid) high = mid - 1 else: low = mid + 1 return ans # Driver Code x = 20print(findMinimum(x)) # This code is contributed by # Mohit kumar 29 |
C#
// Csharp implementation of the above approach using System ; class solution { static int INF = 99999; static int size = 10; // Function to count sum of set bits // of all numbers till N static int getSetBitsFromOneToN(int N) { int two = 2, ans = 0; int n = N; while (n!=0) { ans += (N / two) * (two >> 1); if ((N & (two - 1)) > (two >> 1) - 1) ans += (N & (two - 1)) - (two >> 1) + 1; two <<= 1; n >>= 1; } return ans; } // Function to find the minimum number static int findMinimum(int x) { int low = 0, high = 100000; int ans = high; // Binary search for the lowest number while (low <= high) { // Find mid number int mid = (low + high) >> 1; // Check if it is atleast x if (getSetBitsFromOneToN(mid) >= x) { ans = Math.Min(ans, mid); high = mid - 1; } else low = mid + 1; } return ans; } // Driver Code public static void Main() { int x = 20; Console.WriteLine(findMinimum(x)); } // This code is contributed by Ryuga } |
PHP
<?php // PHP implementation of the above approach // Function to count sum of set bits // of all numbers till N function getSetBitsFromOneToN($N) { $two = 2; $ans = 0; $n = $N; while ($n) { $ans += (int)($N / $two) * ($two >> 1); if (($N & ($two - 1)) > ($two >> 1) - 1) $ans += ($N & ($two - 1)) - ($two >> 1) + 1; $two <<= 1; $n >>= 1; } return $ans; } // Function to find the minimum number function findMinimum($x) { $low = 0; $high = 100000; $ans = $high; // Binary search for the lowest number while ($low <= $high) { // Find mid number $mid = ($low + $high) >> 1; // Check if it is atleast x if (getSetBitsFromOneToN($mid) >= $x) { $ans = min($ans, $mid); $high = $mid - 1; } else $low = $mid + 1; } return $ans; } // Driver Code $x = 20; echo findMinimum($x); // This code is contributed // by Sach_Code ?> |
Output:
11
Time Complexity: O(log N * log N)
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