Given an unsorted sequence A={a0,a1,a2,......an-1} of n integers. How do I find the longest increasing sub-sequence of the given sequence. Is there any dynamic programming solution.
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Codeforces (c) Copyright 2010-2026 Михаил Мирзаянов
Соревнования по программированию 2.0
Время на сервере: 14.05.2026 09:49:40 (i1).
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Do you need this solution?
A[i] - our sequence
DP[i] = the length of the LIS ending with element numbered i.
We'll keep track of vector V as follows:
V[j] = A[k], such that dp[k] = j and k is the largest number < i, satisfying this condition.
Suppose, we have found out all the dp[1..i-1], and V is up to date. How to find dp[i]? It's easy to find by binary search on V, isn't it? OK, find it, and don't forget to update V.
Start with dp[1] = 1 and V[1] = A[1] (1-based sequence)
I mean that when saying "By sorting all values we had before and binary search on them?".
1) override elements in V and
2) append elements to V.
You can try to solve it here: http://acm.tju.edu.cn/toj/showp2400.html