检查数字是否可以表示为K个不同的正整数之和

给定两个整数N和K ，任务是检查N是否可以表示为K个不同的正整数之和。

例子：

Input: N = 12, K = 4 
Output: Yes 
N = 1 + 2 + 4 + 5 = 12 (12 as sum of 4 distinct integers)

Input: N = 8, K = 4 
Output: No 
 

方法：考虑序列1 + 2 + 3 +…+ K ，它具有恰好K个不同的整数，且具有最小可能的和，即Sum =(K *(K – 1))/ 2 。现在，如果N <萨姆那么它不可能表示N为K不同的正整数的和，但如果N≥萨姆然后任意整数发言权X≥0可以被添加到求和，以产生等于N，即1 + 2的总和+ 3 +…+(K – 1)+(K + X)确保存在正好K个不同的正整数。

下面是上述方法的实现：

C++

// C++ implementation of the approach
#include 
using namespace std;
 
// Function that returns true if n
// can be represented as the sum of
// exactly k distinct positive integers
bool solve(int n, int k)
{
    // If n can be represented as
    // 1 + 2 + 3 + ... + (k - 1) + (k + x)
    if (n >= (k * (k + 1)) / 2) {
        return true;
    }
 
    return false;
}
 
// Driver code
int main()
{
    int n = 12, k = 4;
 
    if (solve(n, k))
        cout << "Yes";
    else
        cout << "No";
 
    return 0;
}

Java

// Java implementation of the approach
import java.io.*;
 
class GFG {
 
    // Function that returns true if n
    // can be represented as the sum of
    // exactly k distinct positive integers
    static boolean solve(int n, int k)
    {
        // If n can be represented as
        // 1 + 2 + 3 + ... + (k - 1) + (k + x)
        if (n >= (k * (k + 1)) / 2) {
            return true;
        }
 
        return false;
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int n = 12, k = 4;
 
        if (solve(n, k))
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}
 
// This code is contributed by anuj_67..

Python3

# Python 3 implementation of the approach
 
# Function that returns true if n
# can be represented as the sum of
# exactly k distinct positive integers
def solve(n,k):
    # If n can be represented as
    # 1 + 2 + 3 + ... + (k - 1) + (k + x)
    if (n >= (k * (k + 1)) // 2):
        return True
 
    return False
 
# Driver code
if __name__ == '__main__':
    n = 12
    k = 4
 
    if (solve(n, k)):
        print("Yes")
    else:
        print("No")
 
# This code is contributed by
# Surendra_Gangwar

C#

// C# implementation of the approach
using System;
 
class GFG
{
    // Function that returns true if n
    // can be represented as the sum of
    // exactly k distinct positive integers
    static bool solve(int n, int k)
    {
        // If n can be represented as
        // 1 + 2 + 3 + ... + (k - 1) + (k + x)
        if (n >= (k * (k + 1)) / 2) {
            return true;
        }
 
        return false;
    }
 
    // Driver code
    static public void Main ()
    {
        int n = 12, k = 4;
 
        if (solve(n, k))
            Console.WriteLine("Yes");
        else
            Console.WriteLine("No");
    }
}
 
// This code is contributed by ajit.

PHP

= ($k * ($k + 1)) / 2) {
        return true;
    }
 
    return false;
}
 
// Driver code
 
$n = 12;
$k = 4;
 
if (solve($n, $k))
    echo  "Yes";
else
    echo  "No";
 
// This code is contributed by ihritik
 
?>

Javascript

 
// Javascript implementation of the approach
 
// Function that returns true if n
// can be represented as the sum of
// exactly k distinct positive integers
function solve(n, k)
{
     
    // If n can be represented as
    // 1 + 2 + 3 + ... + (k - 1) + (k + x)
    if (n >= (k * (k + 1)) / 2)
    {
        return true;
    }
    return false;
}
 
// Driver code
var n = 12, k = 4;
 
if (solve(n, k))
    document.write("Yes");
else
    document.write("No");
 
// This code is contributed by todaysgaurav
 

输出：

Yes