Find Duplicate in Range 0 and n-1

Code

#include <stdio.h>

int find_duplicate(int arr[], int n) {
    int freq[100] = {0};  // assuming max value < 100

    for (int i = 0; i < n; i++) {
        if (freq[arr[i]] == 1)
            return arr[i];  // found duplicate
        freq[arr[i]]++;
    }

    return -1;  // no duplicate found
}

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\n", result);
    return 0;
}

Solving Approach

Here’s a clean algorithm-style breakdown to find a repeated element in an array of size n, where elements are in the range [0, n-1] and exactly one number is repeated once:

🔁 Algorithm: Find Duplicate in Array

Input: Array arr[] of size n
Output: The repeated number

✅ Step 1: Initialize two pointers

Let slow = arr[0]
Let fast = arr[0]

✅ Step 2: Detect cycle (Floyd’s Tortoise and Hare)

Repeat:
    slow = arr[slow]
    fast = arr[arr[fast]]
Until slow == fast

✅ Step 3: Find entry point of cycle (duplicate)

Set slow = arr[0]
Repeat:
    slow = arr[slow]
    fast = arr[fast]
Until slow == fast

Return slow as the duplicate