第k1个最小元素与第k2个最小元素之间的所有元素的总和

给定一个由整数和两个数字k1和k2组成的数组。找到给定的第k1个和第k2个最小数组之间的所有元素之和。可以假设(1 <= k1

例子 ：

Input : arr[] = {20, 8, 22, 4, 12, 10, 14},  k1 = 3,  k2 = 6  
Output : 26          
         3rd smallest element is 10. 6th smallest element 
         is 20. Sum of all element between k1 & k2 is
         12 + 14 = 26

Input : arr[] = {10, 2, 50, 12, 48, 13}, k1 = 2, k2 = 6 
Output : 73 

方法1(排序)
首先使用O(n log n)排序算法(例如合并排序，堆排序等)对给定的数组进行排序，然后返回已排序数组中索引k1和k2之间的所有元素的和。

下面是上述想法的实现：

C++

// C++ program to find sum of all element between
// to K1'th and k2'th smallest elements in array
#include 
 
using namespace std;
 
// Returns sum between two kth smallest elements of the array
int sumBetweenTwoKth(int arr[], int n, int k1, int k2)
{
    // Sort the given array
    sort(arr, arr + n);
 
    /* Below code is equivalent to
     int result = 0;
     for (int i=k1; i

---

Java

// Java program to find sum of all element
// between to K1'th and k2'th smallest
// elements in array
import java.util.Arrays;
 
class GFG {
 
    // Returns sum between two kth smallest
    // element of array
    static int sumBetweenTwoKth(int arr[],
                                int k1, int k2)
    {
        // Sort the given array
        Arrays.sort(arr);
 
        // Below code is equivalent to
        int result = 0;
 
        for (int i = k1; i < k2 - 1; i++)
            result += arr[i];
 
        return result;
    }
 
    // Driver code
    public static void main(String[] args)
    {
 
        int arr[] = { 20, 8, 22, 4, 12, 10, 14 };
        int k1 = 3, k2 = 6;
        int n = arr.length;
 
        System.out.print(sumBetweenTwoKth(arr,
                                          k1, k2));
    }
}
 
// This code is contributed by Anant Agarwal.

Python3

# Python program to find sum of
# all element between to K1'th and
# k2'th smallest elements in array
 
# Returns sum between two kth
# smallest element of array
def sumBetweenTwoKth(arr, n, k1, k2):
 
    # Sort the given array
    arr.sort()
 
    result = 0
    for i in range(k1, k2-1):
        result += arr[i]
    return result
 
# Driver code
arr = [ 20, 8, 22, 4, 12, 10, 14 ]
k1 = 3; k2 = 6
n = len(arr)
print(sumBetweenTwoKth(arr, n, k1, k2))
 
 
# This code is contributed by Anant Agarwal.

C#

// C# program to find sum of all element
// between to K1'th and k2'th smallest
// elements in array
using System;
 
class GFG {
 
    // Returns sum between two kth smallest
    // element of array
    static int sumBetweenTwoKth(int[] arr, int n,
                                int k1, int k2)
    {
        // Sort the given array
        Array.Sort(arr);
 
        // Below code is equivalent to
        int result = 0;
 
        for (int i = k1; i < k2 - 1; i++)
            result += arr[i];
 
        return result;
    }
 
    // Driver code
    public static void Main()
    {
        int[] arr = { 20, 8, 22, 4, 12, 10, 14 };
        int k1 = 3, k2 = 6;
        int n = arr.Length;
 
        Console.Write(sumBetweenTwoKth(arr, n, k1, k2));
    }
}
 
// This code is contributed by nitin mittal.

Javascript

 
// Javascript program to find sum of all element
// between to K1'th and k2'th smallest
// elements in array
 
// Returns sum between two kth smallest
// element of array
function sumBetweenTwoKth(arr, k1 , k2)
{
     
    // Sort the given array
    arr.sort(function(a, b){return a - b});
 
    // Below code is equivalent to
    var result = 0;
 
    for(var i = k1; i < k2 - 1; i++)
        result += arr[i];
 
    return result;
}
 
// Driver code
var arr = [ 20, 8, 22, 4, 12, 10, 14 ];
var k1 = 3, k2 = 6;
var n = arr.length;
 
document.write(sumBetweenTwoKth(arr,
                                k1, k2));
 
// This code is contributed by shikhasingrajput
 

---

---

---

输出：

26

时间复杂度：O(n log n)

方法2(使用最小堆)
我们可以使用最小堆来优化上述解决方案。
1)创建所有数组元素的最小堆。 (此步骤需要O(n)时间)
2)提取最少k1次(此步骤需要O(K1 Log n)时间)
3)提取最小k2 – k1 – 1的时间，并对所有提取的元素求和。 (此步骤需要O((K2 – k1)* Log n)时间)

方法2实施

C++

// C++ implementation of above approach
#include 
using namespace std;
 
int n = 7;
 
void minheapify(int a[], int index)
{
 
    int small = index;
    int l = 2 * index + 1;
    int r = 2 * index + 2;
 
    if (l < n && a[l] < a[small])
        small = l;
 
    if (r < n && a[r] < a[small])
        small = r;
 
    if (small != index) {
        swap(a[small], a[index]);
        minheapify(a, small);
    }
}
 
int main()
{
    int i = 0;
    int k1 = 3;
    int k2 = 6;
 
    int a[] = { 20, 8, 22, 4, 12, 10, 14 };
 
    int ans = 0;
 
    for (i = (n / 2) - 1; i >= 0; i--) {
        minheapify(a, i);
    }
 
    // decreasing value by 1 because we want min heapifying k times and it starts
    // from 0 so we have to decrease it 1 time
    k1--;
    k2--;
 
    // Step 1: Do extract minimum k1 times (This step takes O(K1 Log n) time)
    for (i = 0; i <= k1; i++) {
        // cout<

Java

// Java implementation of above approach
class GFG
{
     
static int n = 7;
 
static void minheapify(int []a, int index)
{
 
    int small = index;
    int l = 2 * index + 1;
    int r = 2 * index + 2;
 
    if (l < n && a[l] < a[small])
        small = l;
 
    if (r < n && a[r] < a[small])
        small = r;
 
    if (small != index)
    {
        int t = a[small];
        a[small] = a[index];
        a[index] = t;
        minheapify(a, small);
    }
}
 
// Driver code
public static void main (String[] args)
{
    int i = 0;
    int k1 = 3;
    int k2 = 6;
 
    int []a = { 20, 8, 22, 4, 12, 10, 14 };
 
    int ans = 0;
 
    for (i = (n / 2) - 1; i >= 0; i--)
    {
        minheapify(a, i);
    }
 
    // decreasing value by 1 because we want
    // min heapifying k times and it starts
    // from 0 so we have to decrease it 1 time
    k1--;
    k2--;
 
    // Step 1: Do extract minimum k1 times
    // (This step takes O(K1 Log n) time)
    for (i = 0; i <= k1; i++)
    {
        a[0] = a[n - 1];
        n--;
        minheapify(a, 0);
    }
 
    for (i = k1 + 1; i < k2; i++)
    {
        // cout<

Python3

# Python 3 implementation of above approach
n = 7
 
def minheapify(a, index):
    small = index
    l = 2 * index + 1
    r = 2 * index + 2
 
    if (l < n and a[l] < a[small]):
        small = l
 
    if (r < n and a[r] < a[small]):
        small = r
 
    if (small != index):
        (a[small], a[index]) = (a[index], a[small])
        minheapify(a, small)
     
# Driver Code
i = 0
k1 = 3
k2 = 6
 
a = [ 20, 8, 22, 4, 12, 10, 14 ]
ans = 0
 
for i in range((n //2) - 1, -1, -1):
    minheapify(a, i)
 
# decreasing value by 1 because we want
# min heapifying k times and it starts
# from 0 so we have to decrease it 1 time
k1 -= 1
k2 -= 1
 
# Step 1: Do extract minimum k1 times
# (This step takes O(K1 Log n) time)
for i in range(0, k1 + 1):
    a[0] = a[n - 1]
    n -= 1
    minheapify(a, 0)
 
# Step 2: Do extract minimum k2 – k1 – 1 times and
# sum all extracted elements.
# (This step takes O ((K2 – k1) * Log n) time)*/
for i in range(k1 + 1, k2) :
    ans += a[0]
    a[0] = a[n - 1]
    n -= 1
    minheapify(a, 0)
 
print (ans)
 
# This code is contributed
# by Atul_kumar_Shrivastava

C＃

// C# implementation of above approach
using System;
 
class GFG
{
     
static int n = 7;
 
static void minheapify(int []a, int index)
{
 
    int small = index;
    int l = 2 * index + 1;
    int r = 2 * index + 2;
 
    if (l < n && a[l] < a[small])
        small = l;
 
    if (r < n && a[r] < a[small])
        small = r;
 
    if (small != index)
    {
        int t = a[small];
        a[small] = a[index];
        a[index] = t;
        minheapify(a, small);
    }
}
 
// Driver code
static void Main()
{
    int i = 0;
    int k1 = 3;
    int k2 = 6;
 
    int []a = { 20, 8, 22, 4, 12, 10, 14 };
 
    int ans = 0;
 
    for (i = (n / 2) - 1; i >= 0; i--)
    {
        minheapify(a, i);
    }
 
    // decreasing value by 1 because we want
    // min heapifying k times and it starts
    // from 0 so we have to decrease it 1 time
    k1--;
    k2--;
 
    // Step 1: Do extract minimum k1 times
    // (This step takes O(K1 Log n) time)
    for (i = 0; i <= k1; i++)
    {
        // cout<

输出：

26