# Questions tagged [subsequences]

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### Test if there exists an integer k to add to one sequence to make it a subsequence of another sequence

Suppose that sequence $A$ contains $n$ integers $a_1,a_2,a_3,\ldots,a_n$ and sequence $B$ contains $m$ integers $b_1,b_2,b_3,\ldots,b_m$. We know that $m \geq n$. We assume without loss of generality ...
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### How to build a set of closed chains with a sequence of different vertices?

I have a set of many bi-directional links like A-B, A-C, B-C, A-D, C-D, D-E, etc. I need to find a set of many closed chains with a sequence of different vertices (...
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### Forbidden Sequence Dynamic Programming

Given a finite set $\Omega$, I have the following problem. Say there is a list of forbidden subsequences $F \subset \Omega \cup \Omega^2 \cup \Omega^3 \dots \Omega^\infty$, while we do not know the ...
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### Sequential subsequence removal with arbitrary predicate

I want to extract sub-sequences from a sequence of float values. The "scale" and range of these values is arbitrary (as I can manipulate it at will) but the "shape" is consistent. For a visual ...
29 views

### Minimize sequence storage by overlapping prefixes

I bumped into this problem today, and after a bit of pondering, I think I have a solution in $O(n^3)$, which is better than no solution or an $O(n!)$ solution, but my answer still isn't great. Can ...
81 views

### Time complexity of finding subsequences of a string segmented into parts

Let $S$ be a string of length $N$, consisting of digits 0 to 9. For convenience, we assume $N$ to be a multiple of 3. Then, we split $S$ into $N/3$ equal parts, each of length 3. For each equal part,...
56 views

### ILP representation of the number of maximal 1 sequences in a row

I am currently using an ILP to model events which occur on some input sequence from $1...n$. These events modify the input sequence in order to obtain a desired sequence. Each event can happen on some ...
189 views

### Interleave two arrays such that collisions are minimised (dynamic programming) [closed]

This is a fascinating bioinformatics dynamic programming that I am solving. I am not looking for an answer to the problem, but rather any algorithms, research papers, or other pointers that could be ...
459 views

### Use dynamic programming to merge two arrays such that the number of repetitions of the same element is minimised

Let's say we have two arrays m and n containing the characters from the set a, b, c , d, e. ...
255 views

### Maximum product of contiguous subsequence over $\mathbb{R}$

For the problem of a subsequence of maximum product with negative, zero and positive integers, I have the following working solution (inspiration from here). Let us first show how to solve the ...
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### How can I efficiently find the largest positive interval in an unsorted array? [duplicate]

Given a set of values like [4, 8, 1, 5, 2, 6, 9, 2, 3, 5, 11, 9], how can I find the largest positive interval between any two of them? For example in the one I just listed, index 0 to index 1 has an ...
302 views

### Shortest Uncommon Subsequence

Here is another GeeksforGeeks problem that asks how to find the shortest Uncommon Subsequence of 2 strings? For example, Input : S = “babab” T = “babba” Output : 3The subsequence “aab” of ...
191 views

### Maximize interleaving subsequences two digit arrays/strings

Suppose I have two digit arrays, A and B as follows A = [3,4,5,6] B = [9,8,3] Now, I have ...
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### How can I optimise a 8b10b encoding for maximum alignment?

Imagine you encode an 8 bit symbol as a 10 bit symbol that is sent sequentially over a wire. The goal at the receiver is to detect the byte boundary. Since there are 4 times more encoded symbols than ...
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### Number of contiguous subsequences summing to a given target

I could not figure out an efficient way (better than $O(n^2)$) to count the number of contiguous subsequences of an array of both positive and negative integers summing up to a given number $k$. For ...
236 views

### How is the Longest Common Sub-sequence of two sequences is a special case of the Sequence Alignment problem?

Could anyone briefly show me how the Longest Common Sub-sequence of two sequences is a special case of the Sequence Alignment problem? I cannot wrap my head around this. Thank you.
48 views

### longest sub-sequence in both directions

Given a character array A of size n, compute the length of a longest sub-sequence S of A such that, S read backward is also a sub-sequence of A. Example: A = cabca the sub-sequence S = abc is the ...
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### Activity planning problem

Given a sequence of N activity durations, the time P of pause between activities, and D, the length of a day (there are no breaks between days, only between activities in a day), what is the minimum ...
426 views

### Number of possible sequence partitioning

Given a sequence of 1 and 0 elements, what is the number of possible partitioning of the sequence in sub-sequences (not necessarily consecutive elements, and any number of sub-sequences are allowed) ...