算法题：查找第N个谐波数的程序

本文概述

• C ++
• Java
• Python 3
• C#
• 的PHP

给定数字N，任务是找到第N个谐波数。

设n次谐波数为Hn.

谐波序列如下：

H1 = 1
H2 = H1 + 1/2
H3 = H2 + 1/3
H4 = H3 + 1/4
。 。 。
Hn = Hn-1 + 1/n

例子:

Input : N = 5
Output : 2.45

Input : N = 9
Output : 2.71786

这个想法是从H1遍历, 然后连续从H1寻找H2, 从H2寻找H3 .....依此类推。

下面是查找第N个谐波数的程序：

C ++

//CPP program to find N-th Harmonic Number
  
#include <iostream>
using namespace std;
  
//Function to find N-th Harmonic Number
double nthHarmonic( int N)
{
     //H1 = 1
     float harmonic = 1.00;
  
     //loop to apply the forumula 
     //Hn = H1 + H2 + H3 ... + Hn-1 + Hn-1 + 1/n
     for ( int i = 2; i <= N; i++) {
         harmonic += ( float )1 /i;
     }
  
     return harmonic;
}
  
//Driver Code
int main()
{
     int N = 8;
      
     cout<<nthHarmonic(N);
      
     return 0;
}

Java

//Java program to find N-th Harmonic Number
  
import java.io.*;
  
class GFG {
      
//Function to find N-th Harmonic Number
static double nthHarmonic( int N)
{
     //H1 = 1
     float harmonic = 1 ;
  
     //loop to apply the forumula 
     //Hn = H1 + H2 + H3 ... + Hn-1 + Hn-1 + 1/n
     for ( int i = 2 ; i <= N; i++) {
         harmonic += ( float ) 1 /i;
     }
  
     return harmonic;
}
  
//Driver Code
  
     public static void main (String[] args) {
             int N = 8 ;
      
     System.out.print(nthHarmonic(N));
      
     }
}
//This code is contributed 
//by ajit

Python 3

# Python3 program to find 
# N-th Harmonic Number
  
# Function to find N-th Harmonic Number 
def nthHarmonic(N) :
  
     # H1 = 1 
     harmonic = 1.00
  
     # loop to apply the forumula 
     # Hn = H1 + H2 + H3 ... + 
     # Hn-1 + Hn-1 + 1/n 
     for i in range ( 2 , N + 1 ) :
         harmonic + = 1 /i
  
     return harmonic
      
# Driver code     
if __name__ = = "__main__" :
  
     N = 8
     print ( round (nthHarmonic(N), 5 ))
  
# This code is contributed by ANKITRAI1

C#

//C# program to find N-th Harmonic Number
using System;
  
class GFG 
{
      
//Function to find N-th Harmonic Number
static double nthHarmonic( int N)
{
     //H1 = 1
     float harmonic = 1;
  
     //loop to apply the forumula 
     //Hn = H1 + H2 + H3 ... + 
     //Hn-1 + Hn-1 + 1/n
     for ( int i = 2; i <= N; i++)
     {
         harmonic += ( float )1 /i;
     }
  
     return harmonic;
}
  
//Driver Code
static public void Main ()
{
     int N = 8;
      
     Console.Write(nthHarmonic(N));
}
}
  
//This code is contributed 
//by Raj

的PHP

<?php
//PHP program to find 
//N-th Harmonic Number
  
//Function to find N-th
//Harmonic Number
function nthHarmonic( $N )
{
     //H1 = 1
     $harmonic = 1.00;
  
     //loop to apply the forumula 
     //Hn = H1 + H2 + H3 ... + 
     //Hn-1 + Hn-1 + 1/n
     for ( $i = 2; $i <= $N ; $i ++) 
     {
         $harmonic += (float)1 /$i ;
     }
  
     return $harmonic ;
}
  
//Driver Code
$N = 8;
echo nthHarmonic( $N );
      
//This code is contributed 
//by Shivi_Aggarwal
?>

输出如下：

2.71786

时间复杂度： O(N)

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