Find Duplicate in Range 0 and n-1

Code

#include <stdio.h>
// S = sum(arr) − sum(0..n-1) = dup − miss.

// Q = sum(arr^2) − sum(i^2 for i=0..n-1) = dup^2 − miss^2.

//  dup + miss = Q/S;

// dup = (Q/S + S)/2;

int find_duplicate(int arr[], int n) {
    // Your logic here
    long long sum = 0;
    long long sum_of_squares = 0;
 
    for(int i=0;i<n;i++){
        sum += arr[i];
        sum_of_squares += arr[i]*arr[i];
    }
    long long S = sum - n*(n-1)/2;
    long long Q = sum_of_squares - (n-1)*(n)*(2*n-1)/6;;
    int dup = (Q/S+S)/2;

    return dup;
}

int main() {
    int n;
    scanf("%d", &n);

    int arr[100];
    for (int i = 0; i < n; i++) scanf("%d", &arr[i]);

    int result = find_duplicate(arr, n);
    printf("%d", result);
    return 0;
}

Solving Approach