Harmonic Sum - Problem

Calculate the harmonic sum for a given positive integer N.

The harmonic sum is defined as: 1 + 1/2 + 1/3 + 1/4 + ... + 1/N

Display the result rounded to 6 decimal places.

Input & Output

Example 1 — Small Case

$ Input: n = 3

› Output: 1.833333

💡 Note: Harmonic sum = 1/1 + 1/2 + 1/3 = 1.000000 + 0.500000 + 0.333333 = 1.833333

Example 2 — Single Term

$ Input: n = 1

› Output: 1.000000

💡 Note: Harmonic sum = 1/1 = 1.000000

Example 3 — Larger Case

$ Input: n = 5

› Output: 2.283333

💡 Note: 1/1 + 1/2 + 1/3 + 1/4 + 1/5 = 1 + 0.5 + 0.333333 + 0.25 + 0.2 = 2.283333

Constraints

1 ≤ n ≤ 10⁶
Result must be displayed to exactly 6 decimal places

Visualization

Tap to expand

Asked in

A Accenture 15 T TCS 12 I Infosys 8

The harmonic sum problem requires computing 1 + 1/2 + 1/3 + ... + 1/N. The key insight is that a simple for-loop accumulating each term 1/i gives us the exact result. Best approach is single loop accumulation with Time: O(n), Space: O(1).

Common Approaches

✓ Optimized Single Pass

⏱️ Time: O(n) Space: O(1)

Uses the same loop approach but with small optimizations like pre-computing constants and avoiding unnecessary function calls. The mathematical complexity remains the same since harmonic series has no closed form.

Simple Loop Accumulation

⏱️ Time: O(n) Space: O(1)

Iterate through numbers 1 to N, compute the reciprocal of each number (1/i), and add it to a running sum. Format the final result to 6 decimal places.

Optimized Single Pass — Algorithm Steps

Initialize sum = 0.0
Use optimized loop structure
Minimize function call overhead
Direct formatting

Visualization

Tap to expand

Step-by-Step Walkthrough

Initialize

Set sum = 0.0, i = 1

While Loop

Continue while i <= N

Add Term

Add 1/i to sum, increment i

Result

Format final sum to 6 decimals

Code -

solution.c — C

#include <stdio.h>

double solution(int n) {
    double harmonicSum = 0.0;
    int i = 1;
    while (i <= n) {
        harmonicSum += 1.0 / i;
        i++;
    }
    return harmonicSum;
}

int main() {
    int n;
    scanf("%d", &n);
    
    double result = solution(n);
    printf("%.6f\n", result);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Still requires iterating through all N terms, no mathematical shortcut exists

✓ Linear Growth

Space Complexity

O(1)

Only uses a single variable to store the running sum

✓ Linear Space

12.5K Views

Medium Frequency

~5 min Avg. Time

450 Likes

Ln 1, Col 1

Smart Actions

💡 Explanation

AI Ready

💡 Suggestion Tab to accept Esc to dismiss

// Output will appear here after running code

Code Editor Closed

Click the red button to reopen

Harmonic Sum - Problem

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Optimized Single Pass — Algorithm Steps

Visualization

Code -

Time & Space Complexity

Select Compiler