【LeetCode】287. Find the Duplicate Number

Difficulty:medium

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Description

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.

Example 1:

Input: [1,3,4,2,2]
Output: 2

Example 2:

Input: [3,1,3,4,2]
Output: 3

Note:

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

Intuition

we can regard the array as a linked list: treat the index as a node, treat the value as a next pointer. For example: (array =>linked List)

↓↓

So we can transform this problem into a Linked List Cycle problem, refer to Linked List Cycle II for more details.

Solution

    public int findDuplicate(int[] nums) {
        if(nums==null)
            return -1; //invalid
        int fast=0;
        int slow=0;
        do{
            fast=nums[nums[fast]];
            slow=nums[slow];
        }while(fast!=slow);
        int entry=0;
        while(entry!=slow){
            entry=nums[entry];
            slow=nums[slow];
        }
        return entry;
    }

　　

Complexity

Time complexity : O(n)

Space complexity : O(1)

What I've learned

there is a cycle in the list, becasue:

1. Two different indexes have the same value, which means two different nodes point to the same node.

2. node0 (index=0) will absolutely point to another node.

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