Sum of First N Natural Numbers in C

Formula: n(n+1)/2 (Gauss, O(1))

Loop method: Learning/interviews (O(n))

1. Mathematical Formula (Production)

              
            
C

          O(1) time - Overflow safe
        
#include<stdio.h>

long long sumNatural(int n) {
    return (long long)n * (n + 1) / 2;
}

int main() {
    int n;
    printf("Enter N: ");
    scanf("%d", &n);
    
    printf("Sum = %lld\n", sumNatural(n));
    return 0;
}

N=100 → 5050 (Instant)

2. For Loop (Interview Demo)

              
            
C

          Traditional O(N) approach
        
#include<stdio.h>
int main() {
    int n, sum = 0;
    printf("Enter N: ");
    scanf("%d", &n);
    
    for(int i = 1; i <= n; i++) {
        sum += i;
    }
    
    printf("Sum = %d\n", sum);
    return 0;
}

3. While Loop Alternative

              
            
C

          Same logic, different syntax
        
#include<stdio.h>
int main() {
    int n, i = 1, sum = 0;
    printf("Enter N: ");
    scanf("%d", &n);
    
    while(i <= n) {
        sum += i;
        i++;
    }
    
    printf("Sum = %d\n", sum);
    return 0;
}

4. Production-Ready (Validation + Verification)

              
            
C

          Input validation + dual verification
        
#include<stdio.h>

long long formulaSum(int n) {
    if(n < 1) return 0;
    return (long long)n * (n + 1) / 2;
}

long long loopSum(int n) {
    long long sum = 0;
    for(int i = 1; i <= n; i++) sum += i;
    return sum;
}

int main() {
    int n;
    printf("Enter positive integer N: ");
    scanf("%d", &n);
    
    if(n < 1) {
        printf("Error: N must be >= 1\n");
        return 1;
    }
    
    long long formula = formulaSum(n);
    long long verify = loopSum(n);
    
    printf("Formula: %lld ✓\n", formula);
    printf("Loop:    %lld ✓\n", verify);
    printf("Match: %s\n", formula == verify ? "PASS" : "FAIL");
    
    return 0;
}

5. Test Cases

              
            
TEXT

          Expected outputs
        
N | Formula     | Result
--+-------------+-------
 1 | 1(2)/2     | 1
 5 | 5(6)/2     | 15
10 |10(11)/2    | 55
50 |50(51)/2    | 1275
100|100(101)/2  | 5050

6. Performance Comparison

              
            
TEXT

          Time complexity
        
Method     | Time   | Space | Use Case
-----------|--------|-------|----------
Formula    | O(1)   | O(1)  | Production
For Loop   | O(N)   | O(1)  | Learning
While Loop | O(N)   | O(1)  | Interviews

7. Overflow Protection

              
TEXT

          int vs long long limits
        
int (32-bit): Max N = 46,340
long long (64-bit): Max N = 9.2e18

Use: (long long)n * (n + 1) / 2

8. Interview Tips

Quick Copy-Paste

              
C

          One-liner formula
        
long long sum = (long long)n * (n + 1) / 2;

Production: Formula method.
Learning: Loop method.