Longest Consecutive Sequence

描述

Given an unsorted array of integers, find the length of the longest consecutive elements sequence.

For example,Given [100, 4, 200, 1, 3, 2],The longest consecutive elements sequence is [1, 2, 3, 4]. Return its length: 4.

Your algorithm should run in O(n) complexity.

分析

如果允许$O(n \log n)$的复杂度，那么可以先排序，可是本题要求O(n)。

由于序列里的元素是无序的，又要求O(n)，首先要想到用哈希表。

用一个哈希表存储所有出现过的元素，对每个元素，以该元素为中心，往左右扩张，直到不连续为止，记录下最长的长度。

代码

// Longest Consecutive Sequence
// Time Complexity: O(n)，Space Complexity: O(n)
public class Solution {
    public int longestConsecutive(int[] nums) {
        final HashSet<Integer> mySet = new HashSet<Integer>();
        for (int i : nums) mySet.add(i);
        int longest = 0;
        for (int i : nums) {
            int length = 1;
            for (int j = i - 1; mySet.contains(j); --j) {
                mySet.remove(j);
                ++length;
            }
            for (int j = i + 1; mySet.contains(j); ++j) {
                mySet.remove(j);
                ++length;
            }
            longest = Math.max(longest, length);
        }
        return longest;
    }
}

原文: https://soulmachine.gitbooks.io/algorithm-essentials/content/java/linear-list/array/longest-consecutive-sequence.html