[LeetCode] 382. Linked List Random Node

Given a singly linked list, return a random node's value from the linked list. Each node must have the same probability of being chosen.

Follow up:
What if the linked list is extremely large and its length is unknown to you? Could you solve this efficiently without using extra space?

Example:

// Init a singly linked list [1,2,3].
ListNode head = new ListNode(1);
head.next = new ListNode(2);
head.next.next = new ListNode(3);
Solution solution = new Solution(head);

// getRandom() should return either 1, 2, or 3 randomly. Each element should have equal probability of returning.
solution.getRandom();

链表随机节点。

题意是给一个单链表，请随机返回一个node.val。followup是如果链表太大或者size未知怎么处理，需要确保每个元素被返回的几率相同。

思路是水塘抽样。我参考了这个帖子。水塘抽样的思路我举例说明。比如你需要从 [111, 222, 333, 444] 中随机选取3个数字，此时每个数字被选到的几率是3/4。一开始你选了[111, 222, 333]，然后你选取444的几率是3/4；对于111来说，他依然留在水塘里的几率 = P(444没有被选到的几率) + P(444被选到但是replace了222或333的几率) = 1/4 + 3/4 * 2/3 = 3/4。对于这道题而言，水塘的size就是1。

时间O(n)

空间O(1)

Java实现

/**
 * Definition for singly-linked list.
 * public class ListNode {
 *     int val;
 *     ListNode next;
 *     ListNode() {}
 *     ListNode(int val) { this.val = val; }
 *     ListNode(int val, ListNode next) { this.val = val; this.next = next; }
 * }
 */
class Solution {
    private ListNode head;
    private Random rmd;

    /** @param head The linked list's head.
        Note that the head is guaranteed to be not null, so it contains at least one node. */
    public Solution(ListNode head) {
        this.head = head;
        rmd = new Random();
    }

    /** Returns a random node's value. */
    public int getRandom() {
        ListNode temp = head;
        int res = temp.val;
        int i = 1;
        while (temp.next != null) {
            temp = temp.next;
            i++;
            if (rmd.nextInt(i) == 0) {
                res = temp.val;
            }
        }
        return res;
    }
}

/**
 * Your Solution object will be instantiated and called as such:
 * Solution obj = new Solution(head);
 * int param_1 = obj.getRandom();
 */

LeetCode 题目总结