最小化最小元素和最大元素之间的差异

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

推荐：在继续解决方案之前，请先在{IDE}上尝试您的方法。

方法：

1. 查找数组中存在的最大和最小元素。
2. 检查max和min元素的差值是否小于等于k ：
   • 如果是，则返回 max 和 min 元素之间的差异。
   • 否则，转到步骤 3。
3. 计算数组的最大和最小元素的平均值。
4. 遍历数组并做如下操作：
   • 如果数组元素大于平均值，则将其减少 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最大和最小元素之间的差异。

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
?>

Javascript

 
// Javascript program to minimize
// the difference between
// minimum and maximum elements
     
    // Function to minimize the difference between
    // minimum and maximum elements
    function minimizeDiff(arr,n,k)
    {
        // Find max and min elements of the array
        let max = Math.max(...arr);
        let min = Math.min(...arr);
   
        // 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
           let avg = Math.floor((max + min) / 2);
   
        for (let 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 = Math.max(...arr);
        min = Math.min(...arr);
   
        // return the new difference
        return (max - min);
    }
     
    // Driver code
    let arr=[3, 16, 12, 9, 20];
    let n = 5;
    let k = 3;
    document.write("Max height difference = "
                + minimizeDiff(arr, n, k));
     
     
     
// This code is contributed by avanitrachhadiya2155
 

输出：

Max height difference = 11

时间复杂度：O(N)

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