最小化分配给数组中存在的不同元素的点总和

给定一个大小为N的数组arr[] ，任务是将点分配给每个不同的数组元素，以便分配的点总和尽可能最小。

分配积分需要满足以下条件：

• 可以赋予数字的最小点数是 1。
• 每个不同的元素都应该分配一个唯一的值。
• 应根据数字的值分配分数，即与较大的数字相比，较小的数字应分配较低的分数。

例子：

Input: N = 5, arr[] = {10, 20, 10, 25}
Output: 7
Explanation: Assign 1 point to 10, 2 points to 20, 3 points to 25. Sum of points = 1 + 2 + 1 + 3 = 7, which is the minimum possible.

Input: N = 4, arr[] = {7, 7, 7, 7}
Output: 4
Explanation: Assign 1 point to 7. Sum of points = 1 + 1 + 1 + 1 = 4, which is the minimum possible.

方法：可以通过将较低的点分配给较小的元素来贪婪地解决该问题。请按照以下步骤解决问题：

• 将变量ans初始化为1以存储所需的结果。
• 按递增顺序对给定数组进行排序。
• 初始化一个变量point为1来存储当前元素的点数。
• 使用变量i在范围[0, N-1] 中迭代
  • 如果arr[i]等于arr[i+1] ，则按point递增ans 。
  • 否则将point的值增加1 ，然后将point添加到ans 。
• 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 assign points to each
// number in an array such that the
// sum of points assigned is minimized
void findMinimumSum(int arr[], int n)
{
    // Sort the array in increasing order
    sort(arr, arr + n);
 
    // Assign point_value to 1
    int point_value = 1;
 
    // Store the required result
    int total_points = 1;
 
    // Traverse the array, arr[]
    for (int i = 0; i < n - 1; i++) {
 
        // If adjacent elements are same add
        // current point_value to total_point
        if (arr[i] == arr[i + 1])
            total_points += point_value;
 
        // Otherwise, assign a new point_value
        // and add it to total_points
        else {
            point_value = point_value + 1;
            total_points += point_value;
        }
    }
 
    // Print the result
    cout << total_points;
}
 
// Driver Code
int main()
{
    // Given Input
    int arr[] = { 10, 20, 10, 25 };
    int n = 4;
 
    // Function Call
    findMinimumSum(arr, n);
 
    return 0;
}

Java

// Java program for the above approach
import java.util.*;
class GFG{
     
// Function to assign points to each
// number in an array such that the
// sum of points assigned is minimized
static void findMinimumSum(int []arr, int n)
{
     
    // Sort the array in increasing order
    Arrays.sort(arr);
 
    // Assign point_value to 1
    int point_value = 1;
 
    // Store the required result
    int total_points = 1;
 
    // Traverse the array, arr[]
    for(int i = 0; i < n - 1; i++)
    {
         
        // If adjacent elements are same add
        // current point_value to total_point
        if (arr[i] == arr[i + 1])
            total_points += point_value;
 
        // Otherwise, assign a new point_value
        // and add it to total_points
        else
        {
            point_value = point_value + 1;
            total_points += point_value;
        }
    }
 
    // Print the result
    System.out.print(total_points);
}
 
// Driver Code
public static void main(String[] args)
{
    // Given Input
    int []arr = { 10, 20, 10, 25 };
    int n = 4;
 
    // Function Call
    findMinimumSum(arr, n);
}
}
 
// This code is contributed by sanjoy_62.

Python3

# Python3 program for the above approach
 
# Function to assign points to each
# number in an array such that the
# sum of points assigned is minimized
def findMinimumSum(arr, n):
     
    # Sort the array in increasing order
    arr = sorted(arr)
 
    # Assign point_value to 1
    point_value = 1
 
    # Store the required result
    total_points = 1
 
    # Traverse the array, arr[]
    for i in range(n - 1):
 
        # If adjacent elements are same add
        # current point_value to total_point
        if (arr[i] == arr[i + 1]):
            total_points += point_value
 
        # Otherwise, assign a new point_value
        # and add it to total_points
        else:
            point_value = point_value + 1
            total_points += point_value
 
    # Print the result
    print(total_points)
 
# Driver Code
if __name__ == '__main__':
     
    # Given Input
    arr = [ 10, 20, 10, 25 ]
    n = 4
 
    # Function Call
    findMinimumSum(arr, n)
 
# This code is contributed by mohit kumar 29

C#

// C# program for the above approach
using System;
using System.Collections.Generic;
 
class GFG{
 
// Function to assign points to each
// number in an array such that the
// sum of points assigned is minimized
static void findMinimumSum(int []arr, int n)
{
     
    // Sort the array in increasing order
    Array.Sort(arr);
 
    // Assign point_value to 1
    int point_value = 1;
 
    // Store the required result
    int total_points = 1;
 
    // Traverse the array, arr[]
    for(int i = 0; i < n - 1; i++)
    {
         
        // If adjacent elements are same add
        // current point_value to total_point
        if (arr[i] == arr[i + 1])
            total_points += point_value;
 
        // Otherwise, assign a new point_value
        // and add it to total_points
        else
        {
            point_value = point_value + 1;
            total_points += point_value;
        }
    }
 
    // Print the result
    Console.Write(total_points);
}
 
// Driver Code
public static void Main()
{
     
    // Given Input
    int []arr = { 10, 20, 10, 25 };
    int n = 4;
 
    // Function Call
    findMinimumSum(arr, n);
}
}
 
// This code is contributed by SURENDRA_GANGWAR

Javascript

// Javascript program for the above approach
 
// Function to assign points to each
// number in an array such that the
// sum of points assigned is minimized
function findMinimumSum(arr, n) {
    // Sort the array in increasing order
    arr.sort((a, b) => a - b);
 
    // Assign point_value to 1
    let point_value = 1;
 
    // Store the required result
    let total_points = 1;
 
    // Traverse the array, arr[]
    for (let i = 0; i < n - 1; i++) {
 
        // If adjacent elements are same add
        // current point_value to total_point
        if (arr[i] == arr[i + 1])
            total_points += point_value;
 
        // Otherwise, assign a new point_value
        // and add it to total_points
        else {
            point_value = point_value + 1;
            total_points += point_value;
        }
    }
 
    // Print the result
    document.write(total_points);
}
 
// Driver Code
 
// Given Input
let arr = [10, 20, 10, 25];
let n = 4;
 
// Function Call
findMinimumSum(arr, n);
 
// This code is contributed by gfgking.

输出：

7

时间复杂度： O(N*logN)  
辅助空间： O(1)

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