通过添加或减去至多 K 使数组的所有元素相等

给定一个包含大小为N 的正整数和一个整数K的数组arr[] ，任务是使数组中的所有元素等于某个值D (D > 0)使得|arr[i] – D| ≤ K 。如果无法使数组相等，则打印D或-1的值。
例子：

Input: arr[] = {1, 2, 3, 4, 5}, K = 2 
Output: 3 
Explanation: 
All the elements in the array can be made equal to 3 as: 
|arr[0] – 3| = 2 ≤ 2 
|arr[1] – 3| = 1 ≤ 2 
|arr[2] – 3| = 0 ≤ 2 
|arr[3] – 3| = 1 ≤ 2 
|arr[4] – 3| = 2 ≤ 2 
Input: arr[] = {1, 6, 20}, K = 1 
Output: -1 
Explanation: 
It is not possible to equalize the array 
 

方法：思路是先找到数组的最小元素。

• 如果M是数组的最小元素，则M + K是该最小元素为满足条件arr[i] – D ≤ K可以采用的最大可能值。
• 然后， D = M + K ，如果对于数组中的所有元素， (M + K) 位于[arr[i] – K, arr[i] + K] 范围内。
• 因此，我们只需遍历数组中的每个元素并检查这种情况。

下面是上述方法的实现：

C++

// C++ program to make all elements
// of an Array equal by adding or
// subtracting at most K
 
#include 
using namespace std;
 
// Function to equalize the array by
// adding or subtracting at most K
// value from each element
int equalize(int arr[], int n, int k)
{
 
    // Finding the minimum element
    // from the array
    int min_ele
        = *min_element(arr, arr + n);
 
    // Boolean variable to check if the
    // array can be equalized or not
    bool flag = true;
 
    // Traversing the array
    for (int i = 0; i < n; i++) {
 
        // Checking if the values lie
        // within the possible range
        // for each element
        if (!((arr[i] + k) >= min_ele + k
              && min_ele + k >= (arr[i] - k))) {
 
            // If any value doesn't lie in
            // the range then exit the loop
            flag = false;
            break;
        }
    }
 
    if (flag) {
 
        // Value after equalizing the array
        return min_ele + k;
    }
 
    // Array cannot be equalized
    else
        return -1;
}
 
// Driver code
int main()
{
    int K = 2;
    int arr[] = { 1, 2, 3, 4, 5 };
    int N = sizeof(arr) / sizeof(arr[0]);
 
    cout << equalize(arr, N, K);
}

Java

// Java program to make all elements
// of an Array equal by adding or
// subtracting at most K
import java.util.*;
 
class GFG{
  
// Function to equalize the array by
// adding or subtracting at most K
// value from each element
static int equalize(int arr[], int n, int k)
{
  
    // Finding the minimum element
    // from the array
    int min_ele
        = Arrays.stream(arr).min().getAsInt();
  
    // Boolean variable to check if the
    // array can be equalized or not
    boolean flag = true;
  
    // Traversing the array
    for (int i = 0; i < n; i++) {
  
        // Checking if the values lie
        // within the possible range
        // for each element
        if (!((arr[i] + k) >= min_ele + k
              && min_ele + k >= (arr[i] - k))) {
  
            // If any value doesn't lie in
            // the range then exit the loop
            flag = false;
            break;
        }
    }
  
    if (flag) {
  
        // Value after equalizing the array
        return min_ele + k;
    }
  
    // Array cannot be equalized
    else
        return -1;
}
  
// Driver code
public static void main(String[] args)
{
    int K = 2;
    int arr[] = { 1, 2, 3, 4, 5 };
    int N = arr.length;
  
    System.out.print(equalize(arr, N, K));
}
}
 
// This code is contributed by Princi Singh

Python3

# Python program to make all elements
# of an Array equal by adding or
# subtracting at most K
 
# Function to equalize the array by
# adding or subtracting at most K
# value from each element
def equalize(arr, n, k):
 
    # Finding the minimum element
    # from the array
    min_ele = min(arr);
 
    # Boolean variable to check if the
    # array can be equalized or not
    flag = True;
 
    # Traversing the array
    for i in range(n):
 
        # Checking if the values lie
        # within the possible range
        # for each element
        if (not((arr[i] + k) >= (min_ele + k) and
            (min_ele + k) >= (arr[i] - k))) :
 
            # If any value doesn't lie in
            # the range then exit the loop
            flag = False;
            break;
 
    if (flag):
 
        # Value after equalizing the array
        return min_ele + k;
     
    # Array cannot be equalized
    else:
        return -1;
 
# Driver code
if __name__=='__main__':
 
    K = 2;
    arr = [ 1, 2, 3, 4, 5] ;
    N = len(arr)
 
    print(equalize(arr, N, K))
 
# This code is contributed by Princi Singh

C#

// C# program to make all elements
// of an Array equal by adding or
// subtracting at most K
using System;
using System.Linq;
 
class GFG{
   
// Function to equalize the array by
// adding or subtracting at most K
// value from each element
static int equalize(int []arr, int n, int k)
{
   
    // Finding the minimum element
    // from the array
    int min_ele = arr.Min();
   
    // Boolean variable to check if the
    // array can be equalized or not
    bool flag = true;
   
    // Traversing the array
    for (int i = 0; i < n; i++) {
   
        // Checking if the values lie
        // within the possible range
        // for each element
        if (!((arr[i] + k) >= min_ele + k
              && min_ele + k >= (arr[i] - k))) {
   
            // If any value doesn't lie in
            // the range then exit the loop
            flag = false;
            break;
        }
    }
   
    if (flag) {
   
        // Value after equalizing the array
        return min_ele + k;
    }
   
    // Array cannot be equalized
    else
        return -1;
}
   
// Driver code
public static void Main(String[] args)
{
    int K = 2;
    int []arr = { 1, 2, 3, 4, 5 };
    int N = arr.Length;
   
    Console.Write(equalize(arr, N, K));
}
}
 
// This code is contributed by Princi Singh

Javascript

// Javascript program to make all elements
// of an Array equal by adding or
// subtracting at most K
 
 
// Function to equalize the array by
// adding or subtracting at most K
// value from each element
function equalize(arr, n, k)
{
 
    // Finding the minimum element
    // from the array
    let min_ele
        = arr.sort((a, b) => a - b)[0];
 
    // Boolean variable to check if the
    // array can be equalized or not
    let flag = true;
 
    // Traversing the array
    for (let i = 0; i < n; i++) {
 
        // Checking if the values lie
        // within the possible range
        // for each element
        if (!((arr[i] + k) >= min_ele + k
            && min_ele + k >= (arr[i] - k))) {
 
            // If any value doesn't lie in
            // the range then exit the loop
            flag = false;
            break;
        }
    }
 
    if (flag) {
 
        // Value after equalizing the array
        return min_ele + k;
    }
 
    // Array cannot be equalized
    else
        return -1;
}
 
// Driver code
 
let K = 2;
let arr = [ 1, 2, 3, 4, 5 ];
let N = arr.length;
 
document.write(equalize(arr, N, K));
 
// This code is contributed by _saurabh_jaiswal

输出：

3

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