Given an array arr[] consisting of even integers. At each move, you can select any even number X from the array and divide all the occurrences of X by 2. The task is to find the minimum number of moves needed so that all the elements in the array become odd.
Examples:
Input: arr[] = {40, 6, 40, 20}
Output: 4
Move 1: Select 40 and divide all the occurrences
of 40 by 2 to get {20, 6, 20, 20}
Move 2: Select 20 and divide all the occurrences
of 20 by 2 to get {10, 6, 10, 10}
Move 3: Select 10 and divide all the occurrences
of 10 by 2 to get {5, 6, 5, 5}.
Move 4: Select 6 and divide it by 2 to get {5, 3, 5, 5}.Input: arr[] = {2, 4, 16, 8}
Output: 4
Approach: This problem can be solved using greedy approach. At every move, take the largest remaining even number in the array and divide it by 2. The largest is taken because there is a chance that it can become equal to some other element in the array after it is divided by 2 which minimizes the total operations.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std;// Function to return the count of// minimum operations requiredint minOperations(int arr[], int n){ // Insert all the elements in a set set<int> s; for (int i = 0; i < n; i++) { s.insert(arr[i]); } // To store the number of moves int moves = 0; // While the set is not empty while (s.empty() == 0) { // The last element of the set int z = *(s.rbegin()); // If the number is even if (z % 2 == 0) { moves++; s.insert(z / 2); } // Remove the element from the set s.erase(z); } return moves;}// Driver codeint main(){ int arr[] = { 40, 6, 40, 20 }; int n = sizeof(arr) / sizeof(int); cout << minOperations(arr, n); return 0;} |
Java
// Java implementation of the approachimport java.io.*;import java.util.*;class GFG { // Function to return the count of // minimum operations required static int minOperations(int arr[], int n) { // Insert all the elements in a set TreeSet<Integer> s = new TreeSet<Integer>(); for (int i = 0; i < n; i++) { s.add(arr[i]); } // To store the number of moves int moves = 0; // While the set is not empty while (s.size() != 0) { // The last element of the set Integer z = s.last(); // If the number is even if (z % 2 == 0) { moves++; s.add(z / 2); } // Remove the element from the set s.remove(z); } return moves; } // Driver code public static void main (String[] args) { int arr[] = { 40, 6, 40, 20 }; int n = arr.length; System.out.println(minOperations(arr, n)); }}// This code is contributed by ApurvaRaj |
Python3
# Python3 implementation of the approachfrom collections import OrderedDict as mpp# Function to return the count of# minimum operations requireddef minOperations(arr, n): # Insert all the elements in a set s = mpp() for i in range(n): s[arr[i]] = 1 # To store the number of moves moves = 0 # While the set is not empty while (len(s) > 0): # The last element of the set z = sorted(list(s.keys()))[-1] # If the number is even if (z % 2 == 0): moves += 1 s[z / 2] = 1 # Remove the element from the set del s[z] return moves# Driver codearr = [40, 6, 40, 20]n = len(arr)print(minOperations(arr, n))# This code is contributed by mohit kumar 29 |
C#
// C# implementation of the approach using System;using System.Collections.Generic;class GFG { // Function to return the count of // minimum operations required static int minOperations(int []arr, int n) { // Insert all the elements in a set SortedSet<int> s = new SortedSet<int>(); for (int i = 0; i < n; i++) { s.Add(arr[i]); } // To store the number of moves int moves = 0; // While the set is not empty while (s.Count != 0) { // The last element of the set int z = s.Max; // If the number is even if (z % 2 == 0) { moves++; s.Add(z / 2); } // Remove the element from the set s.Remove(z); } return moves; } // Driver code public static void Main(String[] args) { int []arr = { 40, 6, 40, 20 }; int n = arr.Length; Console.WriteLine(minOperations(arr, n)); } } // This code is contributed by 29AjayKumar |
Javascript
<script>// Javascript implementation of the approach// Function to find all the distinct// remainders when n is divided by// all the elements from// the range [1, n + 1]function findRemainders(n){ // Set will be used to store // the remainders in order // to eliminate duplicates var vc = new Set(); // Find the remainders for(var i = 1; i <= Math.ceil(Math.sqrt(n)); i++) vc.add(parseInt(n / i)); for(var i = parseInt(n / Math.ceil(Math.sqrt(n))) - 1; i >= 0; i--) vc.add(i); // Print the contents of the set [...vc].sort((a, b) => a - b).forEach(it => { document.write(it + " "); });}// Driver codevar n = 5;findRemainders(n);// This code is contributed by famously</script> |
4
Time Complexity: O(n*log(n))
Auxiliary Space: O(n)
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