通过每次删除一对总和至多 K 来清空数组的最小步骤

给定一个数组arr[]和一个目标值K 。任务是找到从数组中取出所有元素所需的最少步骤数。在每一步中，最多可以从数组中选择两个元素，使得它们的总和不能超过目标值K 。
注意：数组的所有元素都小于或等于K 。

Input: arr[] = [5, 1, 5, 4], K = 8 
Output: 3 
Explanation: 
We can pick {1, 4}, {5}, {5} in 3 steps: 
Other possible arrangement can be {1, 5}, {4}, {5} in three steps. 
So, the minimum number of steps are required is 3
Input: [1, 2, 1, 1, 3], n = 9 
Output: 3 
Explanation: 
We can pick {1, 1}, {2, 3} and {1} in three steps. 
Other possible choices {1, 3}, {1, 2}, {1} or {1, 1}, {1, 3}, {2} 
So, the minimum number of steps are required is 3 
 

方法：上述问题可以使用贪心方法和两个指针技术来解决。这个想法是从数组中挑选最小和最大的元素并检查总和是否不超过N然后删除这些元素并计算这一步，否则删除最大的元素，然后重复上述步骤直到删除所有元素。以下是步骤：

1. 对给定的数组arr[] 进行排序。
2. 初始化两个索引i = 0和j = N – 1 。
3. 如果元素arr[i]和arr[j]的总和不超过N，则增加i并减少j 。
4. 否则递减j 。
5. 重复上述步骤直到i <= j并计算每一步。

下面是上述方法的实现：

C++

// C++ program for the above approach
#include 
using namespace std;
 
// Function to count minimum steps
int countMinSteps(int arr[], int target,
                int n)
{
 
    // Function to sort the array
    sort(arr, arr + n);
    int minimumSteps = 0;
    int i = 0, j = n - 1;
 
    // Run while loop
    while (i <= j) {
 
        // Condition to check whether
        // sum exceed the target or not
        if (arr[i] + arr[j] <= target) {
            i++;
            j--;
        }
        else {
            j--;
        }
 
        // Increment the step
        // by 1
        minimumSteps++;
    }
 
    // Return minimum steps
    return minimumSteps;
}
 
// Driver Code
int main()
{
    // Given array arr[]
    int arr[] = { 4, 6, 2, 9, 6, 5, 8, 10 };
 
    // Given target value
    int target = 11;
 
    int size = sizeof(arr) / sizeof(arr[0]);
 
    // Function call
    cout << countMinSteps(arr, target, size);
 
    return 0;
}

Java

// Java program implementation
// of the above approach
import java.util.*;
import java.io.*;
 
class GFG{
 
// Function to count minimum steps    
static int countMinSteps(int arr[],
                         int target,
                         int n)
{
     
    // Function to sort the array
    Arrays.sort(arr);
 
    int minimumSteps = 0;
    int i = 0;
    int j = n - 1;
 
    // Run while loop
    while (i <= j)
    {
         
        // Condition to check whether
        // sum exceed the target or not
        if (arr[i] + arr[j] <= target)
        {
            i += 1;
            j -= 1;
        }
        else
        {
            j -= 1;
        }
     
        // Increment the step by 1
        minimumSteps += 1;
    }
 
    // Return minimum steps
    return minimumSteps;
}
 
// Driver code
public static void main(String[] args)
{
    int arr[] = { 4, 6, 2, 9, 6, 5, 8, 10 };
 
    // Given target value
    int target = 11;
 
    int size = arr.length;
         
    // Print the minimum flip
    System.out.print(countMinSteps(arr, target,
                                        size));
}
}
 
// This code is contributed by code_hunt

Python3

# Python3 program for the above approach
 
# Function to count minimum steps
def countMinSteps(arr, target, n):
     
    # Function to sort the array
    arr.sort()
 
    minimumSteps = 0
    i, j = 0, n - 1
     
    # Run while loop
    while i <= j:
         
        # Condition to check whether
        # sum exceed the target or not
        if arr[i] + arr[j] <= target:
            i += 1
            j -= 1
        else:
            j -= 1
             
        # Increment the step
        # by 1
        minimumSteps += 1
         
    # Return minimum steps
    return minimumSteps
 
# Driver code
     
# Given array arr[]
arr = [ 4, 6, 2, 9, 6, 5, 8, 10 ]
     
# Given target value
target = 11
 
size = len(arr)
     
# Function call
print(countMinSteps(arr, target, size))
 
# This code is contributed by Stuti Pathak

C#

// C# program implementation
// of the above approach
using System;
 
class GFG{
 
// Function to count minimum steps    
static int countMinSteps(int[] arr,
                         int target,
                         int n)
{
     
    // Function to sort the array
    Array.Sort(arr);
 
    int minimumSteps = 0;
    int i = 0;
    int j = n - 1;
 
    // Run while loop
    while (i <= j)
    {
         
        // Condition to check whether
        // sum exceed the target or not
        if (arr[i] + arr[j] <= target)
        {
            i += 1;
            j -= 1;
        }
        else
        {
            j -= 1;
        }
 
        // Increment the step by 1
        minimumSteps += 1;
    }
 
    // Return minimum steps
    return minimumSteps;
}
 
// Driver code
public static void Main()
{
    int[] arr = new int[]{ 4, 6, 2, 9,
                           6, 5, 8, 10 };
 
    // Given target value
    int target = 11;
 
    int size = arr.Length;
     
    // Print the minimum flip
    Console.Write(countMinSteps(
                  arr, target, size));
}
}
 
// This code is contributed by sanjoy_62

Javascript

 
// javascript program for the above approach
 
// Function to count minimum steps
function countMinSteps(arr, target, n)
{
 
    // Function to sort the array
    arr = arr.sort(function(a, b) {
  return a - b;
});
    var minimumSteps = 0;
    var i = 0, j = n - 1;
 
    // Run while loop
    while (i <= j) {
 
        // Condition to check whether
        // sum exceed the target or not
        if (arr[i] + arr[j] <= target) {
            i++;
            j--;
        }
        else {
            j--;
        }
 
        // Increment the step
        // by 1
        minimumSteps++;
    }
 
    // Return minimum steps
    return minimumSteps;
}
 
// Driver Code
 
    // Given array arr[]
    var arr = [4, 6, 2, 9, 6, 5, 8, 10];
 
    // Given target value
    var target = 11;
 
    var size = arr.length;
 
    // Function call
    document.write(countMinSteps(arr, target, size));
 
// This code is contributed by ipg2016107.

输出：

5

时间复杂度： O(N*log N)
辅助空间： O(1)