找到修改后的数组的最小值的最大值

给定大小数组$N$还有一个数字$S$ 。任务是修改给定的数组，以便：

• 修改前后的数组元素之和之差恰好等于S。
• 修改后的数组元素应为非负数。
• 修改后的数组中的最小值必须最大化。
• 要修改给定的数组，可以增加或减少该数组的任何元素。

任务是找到修改后的数组的最小数量。如果不可能，则打印-1。最小数量应尽可能大。

例子：

Input : a[] = {2, 2, 3}, S = 1
Output : 2
Explanation : Modified array is {2, 2, 2}

Input : a[] = {1, 3, 5}, S = 10
Output : -1

一种有效的方法是在修改后的数组中的最小数的最小值和最大值之间进行二进制搜索。最小可能值为零，最大可能数组为给定数组中的最小数量。如果给定的数组元素的总和小于S，则不可能回答。因此，打印-1。如果给定的数组元素之和等于S，则答案将为零。

下面是上述方法的实现：

C++

// CPP program to find the maximum possible
// value of the minimum value of
// modified array
  
#include 
using namespace std;
  
// Function to find the maximum possible value
// of the minimum value of the modified array
int maxOfMin(int a[], int n, int S)
{
    // To store minimum value of array
    int mi = INT_MAX;
  
    // To store sum of elements of array
    int s1 = 0;
  
    for (int i = 0; i < n; i++) {
        s1 += a[i];
        mi = min(a[i], mi);
    }
  
    // Solution is not possible
    if (s1 < S)
        return -1;
  
    // zero is the possible value
    if (s1 == S)
        return 0;
  
    // minimum possible value
    int low = 0;
  
    // maximum possible value
    int high = mi;
  
    // to store a required answer
    int ans;
  
    // Binary Search
    while (low <= high) {
  
        int mid = (low + high) / 2;
  
        // If mid is possible then try to increase
        // required answer
        if (s1 - (mid * n) >= S) {
            ans = mid;
            low = mid + 1;
        }
  
        // If mid is not possible then decrease
        // required answer
        else
            high = mid - 1;
    }
  
    // Return required answer
    return ans;
}
  
// Driver Code
int main()
{
    int a[] = { 10, 10, 10, 10, 10 };
  
    int S = 10;
  
    int n = sizeof(a) / sizeof(a[0]);
  
    cout << maxOfMin(a, n, S);
  
    return 0;
}

Java

// Java  program to find the maximum possible
// value of the minimum value of
// modified array
  
import java.io.*;
  
class GFG {
      
// Function to find the maximum possible value
// of the minimum value of the modified array
static int maxOfMin(int a[], int n, int S)
{
    // To store minimum value of array
    int mi = Integer.MAX_VALUE;
  
    // To store sum of elements of array
    int s1 = 0;
  
    for (int i = 0; i < n; i++) {
        s1 += a[i];
        mi = Math.min(a[i], mi);
    }
  
    // Solution is not possible
    if (s1 < S)
        return -1;
  
    // zero is the possible value
    if (s1 == S)
        return 0;
  
    // minimum possible value
    int low = 0;
  
    // maximum possible value
    int high = mi;
  
    // to store a required answer
    int ans=0;
  
    // Binary Search
    while (low <= high) {
  
        int mid = (low + high) / 2;
  
        // If mid is possible then try to increase
        // required answer
        if (s1 - (mid * n) >= S) {
            ans = mid;
            low = mid + 1;
        }
  
        // If mid is not possible then decrease
        // required answer
        else
            high = mid - 1;
    }
  
    // Return required answer
    return ans;
}
  
// Driver Code
    public static void main (String[] args) {
  
    int a[] = { 10, 10, 10, 10, 10 };
  
    int S = 10;
  
    int n = a.length;
  
    System.out.println( maxOfMin(a, n, S));
    }
//This code is contributed by ajit.    
}

Python

# Python program to find the maximum possible
# value of the minimum value of
# modified array
  
  
# Function to find the maximum possible value
# of the minimum value of the modified array
def maxOfMin(a, n, S):
  
    # To store minimum value of array
    mi = 10**9
  
    # To store sum of elements of array
    s1 = 0
  
    for i in range(n):
        s1 += a[i]
        mi = min(a[i], mi)
      
  
    # Solution is not possible
    if (s1 < S):
        return -1
  
    # zero is the possible value
    if (s1 == S):
        return 0
  
    # minimum possible value
    low = 0
  
    # maximum possible value
    high = mi
  
    # to store a required answer
    ans=0
  
    # Binary Search
    while (low <= high):
  
        mid = (low + high) // 2
  
        # If mid is possible then try to increase
        # required answer
        if (s1 - (mid * n) >= S):
            ans = mid
            low = mid + 1
          
  
        # If mid is not possible then decrease
        # required answer
        else:
            high = mid - 1
      
  
    # Return required answer
    return ans
  
  
# Driver Code
  
a=[10, 10, 10, 10, 10] 
  
S = 10
  
n =len(a)
  
print(maxOfMin(a, n, S))
#This code is contributed by Mohit kumar 29

C#

// C# program to find the maximum possible 
// value of the minimum value of 
// modified array 
  
using System;
  
class GFG { 
      
    // Function to find the maximum possible value 
    // of the minimum value of the modified array 
    static int maxOfMin(int []a, int n, int S) 
    { 
        // To store minimum value of array 
        int mi = int.MaxValue; 
      
        // To store sum of elements of array 
        int s1 = 0; 
      
        for (int i = 0; i < n; i++) { 
            s1 += a[i]; 
            mi = Math.Min(a[i], mi); 
        } 
      
        // Solution is not possible 
        if (s1 < S) 
            return -1; 
      
        // zero is the possible value 
        if (s1 == S) 
            return 0; 
      
        // minimum possible value 
        int low = 0; 
      
        // maximum possible value 
        int high = mi; 
      
        // to store a required answer 
        int ans=0; 
      
        // Binary Search 
        while (low <= high) { 
      
            int mid = (low + high) / 2; 
      
            // If mid is possible then try to increase 
            // required answer 
            if (s1 - (mid * n) >= S) { 
                ans = mid; 
                low = mid + 1; 
            } 
      
            // If mid is not possible then decrease 
            // required answer 
            else
                high = mid - 1; 
        } 
      
        // Return required answer 
        return ans; 
    } 
  
    // Driver Code 
    public static void Main () { 
  
    int []a = { 10, 10, 10, 10, 10 }; 
  
    int S = 10; 
  
    int n = a.Length; 
  
    Console.WriteLine(maxOfMin(a, n, S)); 
    } 
    //This code is contributed by Ryuga 
}

PHP

= $S) 
        {
            $ans = $mid;
            $low = $mid + 1;
        }
  
        // If mid is not possible then
        // decrease required answer
        else
            $high = $mid - 1;
    }
  
    // Return required answer
    return $ans;
}
  
// Driver Code
$a = array( 10, 10, 10, 10, 10 );
$S = 10;
$n = sizeof($a);
echo maxOfMin($a, $n, $S);
  
// This code is contributed by akt_mit
?>

输出：

8