最小化最大和最小元素之间的差异

给定一个数组$N$整数和整数$k$ 。允许通过将元素增加或减少k(仅一次)来修改元素。

任务是最小化和打印最短和最长塔之间的最大差异。

例子：

Input: arr[] = {1, 10, 8, 5}, k = 2
Output : Max height difference = 5
Explanation:
modified arr[]={3, 8, 6, 7}
max difference: 5

Input: arr[] = {3, 16, 12, 9, 20}, k = 3
Output : Max height difference: 11

建议：在继续解决方案之前，请先在{IDE}上尝试使用您的方法。

方法：

1. 查找数组中存在的最大和最小元素。
2. 检查max和min元素之间的差是否小于或等于k ：
   • 如果是，则返回max和min元素之间的差。
   • 否则，请转到步骤3。
3. 计算数组的最大和最小元素的平均值。
4. 遍历数组并执行以下操作：
   • 如果数组元素大于平均值，则将其减小k。
   • 如果数组元素小于平均值，则将其增加k。
5. 返回修改后的数组的max和min元素之间的差。

下面是上述方法的实现：

C++

// C++ program to minimize the difference between
// minimum and maximum elements
  
#include 
using namespace std;
  
// Function to minimize the difference between
// minimum and maximum elements
int minimizeDiff(int* arr, int n, int k)
{
    // Find max and min elements of the array
    int max = *(max_element(arr, arr + n));
    int min = *(min_element(arr, arr + n));
  
    // Check whether the difference between
    // the max and min element is less than
    // or equal to k or not
    if ((max - min) <= k) {
        return (max - min);
    }
  
    // Calculate average of max and min
    int avg = (max + min) / 2;
  
    for (int i = 0; i < n; i++) {
        // If the array element is greater than the
        // average then decrease it by k
        if (arr[i] > avg)
            arr[i] -= k;
        // If the array element is smaller than the
        // average then increase it by k
        else
            arr[i] += k;
    }
  
    // Find max and min of the modified array
    max = *(max_element(arr, arr + n));
    min = *(min_element(arr, arr + n));
  
    // return the new difference
    return (max - min);
}
  
// Driver code
int main()
{
    int arr[] = { 3, 16, 12, 9, 20 };
    int n = 5;
    int k = 3;
  
    cout << "Max height difference = "
         << minimizeDiff(arr, n, k) << endl;
  
    return 0;
}

Java

// Java program to minimize the difference between 
// minimum and maximum elements 
import java.util.*;
  
class GFG 
{
  
    // Function to minimize the difference between 
    // minimum and maximum elements 
    static int minimizeDiff(int[] arr, int n, int k)
    {
        // Find max and min elements of the array 
        int max = Arrays.stream(arr).max().getAsInt();
        int min = Arrays.stream(arr).min().getAsInt();
  
        // Check whether the difference between 
        // the max and min element is less than 
        // or equal to k or not 
        if ((max - min) <= k)
        {
            return (max - min);
        }
  
        // Calculate average of max and min 
        int avg = (max + min) / 2;
  
        for (int i = 0; i < n; i++) 
        {
            // If the array element is greater than the 
            // average then decrease it by k 
            if (arr[i] > avg) 
            {
                arr[i] -= k;
            } 
              
            // If the array element is smaller than the 
            // average then increase it by k 
            else 
            {
                arr[i] += k;
            }
        }
  
        // Find max and min of the modified array 
        max = Arrays.stream(arr).max().getAsInt();
        min = Arrays.stream(arr).min().getAsInt();
  
        // return the new difference 
        return (max - min);
    }
  
    // Driver code
    public static void main(String[] args) 
    {
        int arr[] = {3, 16, 12, 9, 20};
        int n = 5;
        int k = 3;
  
        System.out.println("Max height difference = "
                + minimizeDiff(arr, n, k));
    }
}
  
// This code has been contributed by 29AjayKumar

Python3

# Python 3 program to minimize the 
# difference between minimum and
# maximum elements 
  
# Function to minimize the difference 
# between minimum and maximum elements 
def minimizeDiff(arr, n, k) :
  
    # Find max and min elements 
    # of the array 
    max_element = max(arr)
    min_element = min(arr)
  
    # Check whether the difference between 
    # the max and min element is less than 
    # or equal to k or not 
    if ((max_element - min_element) <= k) : 
        return (max_element - min_element) 
      
    # Calculate average of max and min 
    avg = (max_element + min_element) // 2
  
    for i in range(n): 
          
        # If the array element is greater than 
        # the average then decrease it by k 
        if (arr[i] > avg) :
            arr[i] -= k 
              
        # If the array element is smaller than  
        # the average then increase it by k 
        else :
            arr[i] += k 
  
    # Find max and min of the 
    # modified array 
    max_element = max(arr) 
    min_element = min(arr) 
  
    # return the new difference 
    return (max_element - min_element); 
  
# Driver code 
if __name__ == "__main__" :
      
    arr = [ 3, 16, 12, 9, 20 ]
    n = 5
    k = 3
      
    print("Max height difference =", 
            minimizeDiff(arr, n, k))
  
# This code is contributed by Ryuga

C#

// C# program to minimize the difference between 
// minimum and maximum elements 
using System;
using System.Linq;
  
class GFG 
{
  
    // Function to minimize the difference between 
    // minimum and maximum elements 
    static int minimizeDiff(int[] arr, int n, int k)
    {
        // Find max and min elements of the array 
        int max = arr.Max();
        int min = arr.Min();
  
        // Check whether the difference between 
        // the max and min element is less than 
        // or equal to k or not 
        if ((max - min) <= k)
        {
            return (max - min);
        }
  
        // Calculate average of max and min 
        int avg = (max + min) / 2;
  
        for (int i = 0; i < n; i++) 
        {
            // If the array element is greater than the 
            // average then decrease it by k 
            if (arr[i] > avg) 
            {
                arr[i] -= k;
            } 
              
            // If the array element is smaller than the 
            // average then increase it by k 
            else
            {
                arr[i] += k;
            }
        }
  
        // Find max and min of the modified array 
        max = arr.Max();
        min = arr.Min();
  
        // return the new difference 
        return (max - min);
    }
  
    // Driver code
    public static void Main() 
    {
        int []arr = {3, 16, 12, 9, 20};
        int n = 5;
        int k = 3;
  
        Console.WriteLine("Max height difference = "
                + minimizeDiff(arr, n, k));
    }
}
  
/* This code contributed by PrinciRaj1992 */

PHP

 $avg)
            $arr[$i] -= $k;
              
        // If the array element is smaller than 
        // the average then increase it by k
        else
            $arr[$i] += $k;
    }
  
    // Find max and min of the 
    // modified array
    $max = max($arr);
    $min = min($arr);
  
    // return the new difference
    return ($max - $min);
}
  
// Driver code
$arr = array( 3, 16, 12, 9, 20 );
$n = 5;
$k = 3;
  
echo "Max height difference = " . 
      minimizeDiff($arr, $n, $k). "\n";
  
// This code is contributed by ita_c
?>

输出：

Max height difference = 11

时间复杂度：O(N)