给定一个由N 个正整数组成的数组arr[] ，任务是找到数组元素除以2的最小除法数(整数除法)，以使所有数组元素相同。
例子：
Input: arr[] = {3, 1, 1, 3}
Output: 2
Explanation:
Operation 1: Divide arr[0] ( = 3) by 2. The array arr[] modifies to {1, 1, 1, 3}.
Operation 2: Divide arr[3] ( = 3) by 2. The array arr[] modifies to {1, 1, 1, 1}.
Therefore, the count of division operations required is 2.
Input: arr[] = {2, 2, 2}
Output: 0
方法：解决给定问题的想法是找到数组中所有元素可以减少到的最大数量。请按照以下步骤解决问题：
- 初始化一个变量，比如ans ，以存储所需的除法运算的最小计数。
- 初始化一个 HashMap，比如M ，以存储数组元素的频率。
- 遍历数组arr[]直到发现任何数组元素arr[i]大于0 。继续将arr[i]除以2并同时更新 Map M 中获得的元素的频率。
- 遍历 HashMap 并找到频率为N的最大元素。将其存储在maxNumber 中。
- 同样，遍历数组arr[]并通过将arr[i]除以2并将操作计数添加到变量ans 中，找到将arr[i]减少到maxNumber所需的操作数。
- 完成以上步骤后，打印ans的值作为结果。
下面是上述方法的实现：
C++
// C++ program for the above approach
#include
using namespace std;
// Function to count minimum number of
// division by 2 operations required to
// make all array elements equal
void makeArrayEqual(int A[], int n)
{
// Stores the frequencies of elements
map mp;
// Stores the maximum number to
// which every array element
// can be reduced to
int max_number = 0;
// Stores the minimum number
// of operations required
int ans = 0;
// Traverse the array and store
// the frequencies in the map
for (int i = 0; i < n; i++) {
int b = A[i];
// Iterate while b > 0
while (b) {
mp[b]++;
// Keep dividing b by 2
b /= 2;
}
}
// Iterate over the map to find
// the required maximum number
for (auto x : mp) {
// Check if the frequency
// is equal to n
if (x.second == n) {
// If true, store it in
// max_number
max_number = x.first;
}
}
// Iterate over the array, A[]
for (int i = 0; i < n; i++) {
int b = A[i];
// Find the number of operations
// required to reduce A[i] to
// max_number
while (b != max_number) {
// Increment the number of
// operations by 1
ans++;
b /= 2;
}
}
// Print the answer
cout << ans;
}
// Driver Code
int main()
{
int arr[] = { 3, 1, 1, 3 };
int N = sizeof(arr) / sizeof(arr[0]);
makeArrayEqual(arr, N);
return 0;
} Java
/*package whatever //do not write package name here */
import java.io.*;
import java.util.Map;
import java.util.HashMap;
class GFG
{
// Function to count minimum number of
// division by 2 operations required to
// make all array elements equal
public static void makeArrayEqual(int A[], int n)
{
// Stores the frequencies of elements
HashMap map = new HashMap<>();
// Stores the maximum number to
// which every array element
// can be reduced to
int max_number = 0;
// Stores the minimum number
// of operations required
int ans = 0;
// Traverse the array and store
// the frequencies in the map
for (int i = 0; i < n; i++) {
int b = A[i];
// Iterate while b > 0
while (b>0) {
Integer k = map.get(b);
map.put(b, (k == null) ? 1 : k + 1);
// Keep dividing b by 2
b /= 2;
}
}
// Iterate over the map to find
// the required maximum number
for (Map.Entry e :
map.entrySet()) {
// Check if the frequency
// is equal to n
if (e.getValue() == n) {
// If true, store it in
// max_number
max_number = e.getKey();
}
}
// Iterate over the array, A[]
for (int i = 0; i < n; i++) {
int b = A[i];
// Find the number of operations
// required to reduce A[i] to
// max_number
while (b != max_number) {
// Increment the number of
// operations by 1
ans++;
b /= 2;
}
}
// Print the answer
System.out.println(ans + " ");
}
// Driver Code
public static void main(String[] args)
{
int arr[] = { 3, 1, 1, 3 };
int N = arr.length;
makeArrayEqual(arr, N);
}
}
// This code is contributed by aditya7409. Python3
# Python 3 program for the above approach
# Function to count minimum number of
# division by 2 operations required to
# make all array elements equal
def makeArrayEqual(A, n):
# Stores the frequencies of elements
mp = dict()
# Stores the maximum number to
# which every array element
# can be reduced to
max_number = 0
# Stores the minimum number
# of operations required
ans = 0
# Traverse the array and store
# the frequencies in the map
for i in range(n):
b = A[i]
# Iterate while b > 0
while (b>0):
if (b in mp):
mp[b] += 1
else:
mp[b] = mp.get(b,0)+1
# Keep dividing b by 2
b //= 2
# Iterate over the map to find
# the required maximum number
for key,value in mp.items():
# Check if the frequency
# is equal to n
if (value == n):
# If true, store it in
# max_number
max_number = key
# Iterate over the array, A[]
for i in range(n):
b = A[i]
# Find the number of operations
# required to reduce A[i] to
# max_number
while (b != max_number):
# Increment the number of
# operations by 1
ans += 1
b //= 2
# Print the answer
print(ans)
# Driver Code
if __name__ == '__main__':
arr = [3, 1, 1, 3]
N = len(arr)
makeArrayEqual(arr, N)
# This code is contributed by bgangwar59.C#
using System;
using System.Collections.Generic;
class GFG
{
// Function to count minimum number of
// division by 2 operations required to
// make all array elements equal
public static void makeArrayEqual(int[] A, int n)
{
// Stores the frequencies of elements
Dictionary map = new Dictionary();
// Stores the maximum number to
// which every array element
// can be reduced to
int max_number = 0;
// Stores the minimum number
// of operations required
int ans = 0;
// Traverse the array and store
// the frequencies in the map
for (int i = 0; i < n; i++) {
int b = A[i];
// Iterate while b > 0
while (b > 0)
{
if (map.ContainsKey(b))
map[b] ++;
else
map[b]= 1;
// Keep dividing b by 2
b /= 2;
}
}
// Iterate over the map to find
// the required maximum number
foreach(KeyValuePair e in map)
{
// Check if the frequency
// is equal to n
if (e.Value == n) {
// If true, store it in
// max_number
max_number = e.Key;
}
}
// Iterate over the array, A[]
for (int i = 0; i < n; i++) {
int b = A[i];
// Find the number of operations
// required to reduce A[i] to
// max_number
while (b != max_number) {
// Increment the number of
// operations by 1
ans++;
b /= 2;
}
}
// Print the answer
Console.Write(ans + " ");
}
// Driver Code
public static void Main(String[] args)
{
int[] arr = { 3, 1, 1, 3 };
int N = arr.Length;
makeArrayEqual(arr, N);
}
}
// This code is contributed by shubhamsingh10. 输出：
2时间复杂度： O(N*log N)
辅助空间： O(N)
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