382. Linked List Random Node

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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:

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// 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();

解法1： Reservoir Sampling

是reservoir sampling的直接应用。从discussion上看来的比较好懂的解释：

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Start...
When we read the first node head, if the stream ListNode stops here, we can just return the head.val. The possibility is 1/1.
When we read the second node, we can decide if we replace the result r or not. The possibility is 1/2. So we just generate a random number between 0 and 1, and check if it is equal to 1. If it is 1, replace r as the value of the current node, otherwise we don't touch r, so its value is still the value of head.
When we read the third node, now the result r is one of value in the head or second node. We just decide if we replace the value of r as the value of current node(third node). The possibility of replacing it is 1/3, namely the possibility of we don't touch r is 2/3. So we just generate a random number between 0 ~ 2, and if the result is 2 we replace r.
We can continue to do like this until the end of stream ListNode.

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/**
 * Definition for singly-linked list.
 * public class ListNode {
 *     int val;
 *     ListNode next;
 *     ListNode(int x) { val = x; }
 * }
 */
class Solution {
    /** @param head The linked list's head.
        Note that the head is guaranteed to be not null, so it contains at least one node. */
    ListNode head = null;
    Random random = null;
    public Solution(ListNode head) {
        this.head = head;
        random = new Random(System.currentTimeMillis());
    }
    /** Returns a random node's value. */
    public int getRandom() {
        // k = 1
        int res = head.val;
        ListNode ptr = head.next;
        for (int i = 1; ptr != null; i++) {
            if (random.nextInt(i + 1) == i) {
                res = ptr.val;
            }
            ptr = ptr.next;
        }
        return res;
    }
}
/**
 * Your Solution object will be instantiated and called as such:
 * Solution obj = new Solution(head);
 * int param_1 = obj.getRandom();
 */