最长递增子序列（Longest increasing subsequences）

the input is a sequence of numbers a1, a2, ……, an. A subsequence is any subset of these numbers taken in order, of the form ai1, ai2, ……, aik where 1 <= i1 <= i2 <= … ik <= n, and an increasing subsequence is one in which the numbers are getting strictly larger.（标蓝的数字均为下标）

The task is to find the increasing subsequence of greatest length. For instance, the longest increasing subsequence of 5, 2, 8, 6, 3, 6, 9, 7 is 2, 3, 6, 9.

#include <iostream>
#include <vector>

using namespace std;

int main()
{
	vector<int> seq;

	//输入序列
	while (1)
	{
		int temp;
		cin >> temp;
		seq.push_back(temp);

		char tmp = getchar();
		if (tmp == '\n')
		{
			break;
		}
	}

	int length = int(seq.size());

	vector<int> lis(length);				//lis[i]存储以seq[i]为终点时最长递增子序列的大小
	vector<int> path(length);				//path[i]存储以seq[i]为终点时最长递增子序列的上一个数字

	int Lis[2] = {1, 0};					//Lis[0]存储最长递增子序列的长度，Lis[1]存储最长递增子序列终点数的下标

	for (int i = 0; i < length; ++i)
	{
		//将lis数组初始化为1
		lis[i] = 1;
		//将path数组初始化为下标值
		path[i] = i;
		
		for (int j = 0; j < i; ++j)
		{
			if (seq[i] > seq[j])
			{
				if (lis[j] + 1 > lis[i])
				{
					lis[i] = lis[j] + 1;
					path[i] = j;
				}
			}
		}
		if (lis[i] > Lis[0])
		{
			Lis[0] = lis[i];
			Lis[1] = i;
		}
	}

	//输出最长递增子序列(这是倒序输出的！)
	int i = Lis[1];
	cout << seq[i] << ' ';
	while (path[i] != i)
	{
		cout << seq[path[i]] << ' ';
		i = path[i];
	}

	return 0;
}