Find the first duplicate number in the list where the range is 1:n+1 and the size of the array is n that implies there should be at least one duplicate in the list

find_repeat_big.js

'use strict'

var num_list_1 = [3, 4, 2, 3, 1, 5];
var num_list_2 = [3, 1, 2, 2];
var num_list_3 = [4, 3, 1, 1, 4];

function find_duplicate(num_list) {
    // initializing
    var slowIndex = num_list.length - 1;
    var fastIndex = num_list.length - 1;

    var slow = num_list[slowIndex];
    var fast = num_list[fastIndex];

    while(true) {
        // move next
        slowIndex = slow - 1;
        slow = num_list[slowIndex];

        fastIndex = fast - 1;
        fast = num_list[fastIndex];
        fastIndex = fast - 1;
        fast = num_list[fastIndex];

        // if the values are the same and indices are different this is the duplicate
        if (slow === fast) {
            if (slowIndex !== fastIndex) {
                return slow;
            }

            slowIndex = num_list.length - 1;
            slow = num_list[slowIndex];

            while (true) {
                // move slow point one by one until the values are the same
                slowIndex = slow - 1;
                slow = num_list[slowIndex];

                fastIndex = fast - 1;
                fast = num_list[fastIndex];

                if (slow === fast) {
                    if (slowIndex !== fastIndex) {
                        return slow;
                    } else {
                        return slowIndex + 1;
                    }
                }
            }
        }
    }
}

console.log(find_duplicate(num_list_1));
console.log(find_duplicate(num_list_2));
console.log(find_duplicate(num_list_3));