Longest Increasing Subsequence问题及解法

问题描述：

Given an unsorted array of integers, find the length of longest increasing subsequence.

For example,
Given [10, 9, 2, 5, 3, 7, 101, 18],
The longest increasing subsequence is [2, 3, 7, 101], therefore the length is 4. Note that there may be more than one LIS combination, it is only necessary for you to return the length.

Your algorithm should run in O(n2) complexity.

问题分析：

记录每个元素为递增子序列最后一个元素时子序列的长度，通过比较该长度即可获得答案。

过程详见代码：

class Solution {
public:
    int lengthOfLIS(vector<int>& nums) {
        int n = nums.size();
		int res = 0;
		vector<int> dp(n, 1);
		for (int i = 0; i < n; i++)
		{
			for (int j = 0; j < i; j++)
			{
				if (nums[i] > nums[j])
					dp[i] = max(dp[j] + 1, dp[i]);
			}
			res = max(dp[i], res);
		}
		return res;
    }
};