Find the Duplicate Number

Question

Given an array nums containing n + 1 integers where each integer is between 1 and n (inclusive), prove that at least one duplicate number must exist. Assume that there is only one duplicate number, find the duplicate one.

Note: You must not modify the array (assume the array is read only). You must use only constant, O(1) extra space. Your runtime complexity should be less than O(n2). There is only one duplicate number in the array, but it could be repeated more than once.

Solution

只能說如果沒辦法把這題轉換成找環起點的問題，那基本上應該是想不出來。這題核心思路跟 Linked List Cycle II 一樣，那要如何在 array 裡面使用快慢指針的方法呢？

slow = nums[0]; fast = nums[nums[0]];

    public int findDuplicate(int[] nums) {
        if (nums.length > 1) {
            int slow = nums[0];
            int fast = nums[nums[0]];
            while (slow != fast) {
                slow = nums[slow];
                fast = nums[nums[fast]];
            }

            fast = 0;
            while (fast != slow) {
                fast = nums[fast];
                slow = nums[slow];
            }
            return fast;
        }
        return -1;
    }