Find Duplicate in Range 0 and n-1

Code

#include <stdio.h>

int find_duplicate(int arr[], int n) {
   long long sum = 0, sum_sq = 0;
    long long expected_sum = (long long)(n - 1) * (n) / 2;
    long long expected_sq = (long long)(n - 1) * n * (2 * n - 1) / 6;

    for (int i = 0; i < n; i++) {
        sum += arr[i];
        sum_sq += (long long)arr[i] * arr[i];
    }

    long long diff = sum - expected_sum;            // (d - m)
    long long sq_diff = sum_sq - expected_sq;       // (d^2 - m^2) = (d - m)(d + m)

    long long sum_dm = sq_diff / diff;              // (d + m)

    long long duplicate = (diff + sum_dm) / 2;      // d = (diff + sum_dm)/2

    return (int)duplicate;
}



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