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Aug 1, 2015 · Find the longest increasing subsequence in nlogn time. https://github.com/mission-peace/interview/blob/master/src/com/interview/array/LongestIncreasingSubSeq...
- 12 min
- 217.8K
- Tushar Roy - Coding Made Simple
Jun 15, 2020 · The Longest Increasing Subsequence (LIS) problem is to find the length of the longest subsequence of a given sequence such that all elements of the subsequence are sorted in increasing order. For example, the length of LIS for {10, 12, 9, 13, 21, 50, 41, 65, 85} is 7 and LIS is {10, 12, 13, 21, 50, 65, 85}. This Problem can be solved in O (n² ...
Apr 13, 2010 · Process the input elements in order and maintain a list of tuples for each element. Each tuple (A,B), for the element i will denotes, A = length of longest increasing sub-sequence ending at i and B = index of predecessor of list[i] in the longest increasing sub-sequence ending at list[i].
Longest Increasing Subsequence problem can be solved with the help of 3 different Approach: Brute Force; Dynamic Programming; Binary Search; Time Complexity. Time Complexity of LIS: Brute force: O(N^2) Dynamic Programming: O(n^2) Binary Search: O(nlogn) Using Binary Search is a efficient Method
Nov 22, 2019 · This subsequence is not necessarily contiguous, or unique. In this tutorial we illus... Given an array of random numbers, find a longest increasing subsequence.
- 5 min
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- Stable Sort
the trick for the nlogn solution is to maintain, in addition to your dp table, an auxiliary table A so that A[ i ] holds the information "what is the minimum number in the array, such that an increasing subsequence of length i terminates at", it is easy to see that this array will be strictly increasing.
Lemma (Easy): The minimum number of increasing subsequences required to cover A A A is at least the size of longest non-increasing subsequence of A A A. Proof: No two elements of any non-increasing subsequence can be part of the same increasing subsequence.
