# Questions tagged [algorithm-design]

Questions related to general, high level, techniques for the design of algorithms.

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### Algorithm design: Model redundancy in tests

I've run across an interesting problem at work that I'm not quite sure how to grapple. Broadly, there is a suite of of $n$ tests to ensure the quality of a product. However, the tests are both time-...
61 views

### The awkward status of Mersenne Twister

Random number generators generally fit into 3 categories IMO: ad-hoc designs serving as stub to be replaced by something else if this ever happens, considerate designs aiming at achieving statistical ...
129 views

### How can I find 2 median values of an array which is an union of 2 arrays in O(log n)?

So I have 2 sorted arrays which will have the same length and what I need to do is sort the union array (the union of the two sorted arrays) and then find two median values, I need to do this in O(log ...
1 vote
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### Algorithm for sorting within windows

I am writing an app which displays speeches on various topics, with each speech having a number of attributes. I want to give the user the choice to sort a list of speeches by an attribute, even ...
34 views

### Suggestions for a source of algorithm design problems?

I’m finishing up Roughgarden’s two-part algorithms course on edx, and it was good, but I didn’t actually ‘design and analyze’ many algorithms, the questions mostly tested whether you understood the ...
1 vote
44 views

### Abstract algebra algorithms

Let’s make a big list of algorithms relying on abstract algebra. This will help us see how ubiquitous algebra is in algorithm design. I’ll start with two: one is the General Number Field Sieve, the ...
1k views

### How to Match Socks

When I do my laundry I tend to make a pile of unmatched socks, putting new socks on the top of the pile and matching off pairs if two of the same sock are near the top of the stack. Since eventually ...
1 vote
120 views

### Intersection of line segments induced by point sets from fixed geometry

I am reading up on algorithms and at the moment looking at the below problem from Jeff Erickson's book Algorithms. I solved (a) by seeing a relationship to the previous problem on computing the ...
1 vote
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60 views

### Finding max value algorithm with subset comparison

I have a set of $N$ different values, and my goal is to find the biggest one in the least number of comparisons. Comparing subsets (using the sum of each) is also allowed, and counts as one comparison....
19k views

### Implementation of QuickSort to handle duplicates

I have this past year question based on the following scenario: When the list of items to be sorted contains a lot of duplicate values, we can improve QuickSort by grouping all the values that are ...
296 views

### Longest substrings of common length with the same parity

Given two sequences $a$ and $b$, find largest $x$ such that in $a$ there is substring $A$ and substring $B$ in $b$ meeting those conditions: length of both $A$ and $B$ is equal to $x$; sum of ...
1 vote
434 views

### Algorithm to organize a tournament where the team componentes change each round

So, I was tasked with creating an app that generates the schedule of a doubles tennis tournament (i.e., teams of two) in a way that, by the end of it, everyone would have played against the rest of ...
42 views

### Trouble Convincing Myself Algorithm Correctness

I'm having a tough time convincing myself right when coming up for some solutions to medium/hard leetcode.com problems. Take the following question for example. ...
156 views

### Avoiding correlated values and reduced collision resistance in multiple hash states

I need to design a hash function that fits this criteria: Limited to 32-bit integer operations (for compatibility with JavaScript bitwise operations, my target system) Produces an n-bit hash digest, ...
161 views

### Arrange objects in space so that the outline takes the least surface/volume

Imagine you have a number of 2-dimensional objects. The question is how to fit them all in a rectangular space in such a way that this rectangle takes the smallest area possible. On the below image ...
1 vote
I am given the following invariant: Invariant The greatest $i$ keys of an Array are always in sorted order on the last $i$ indices of the Array. I am supposed to ...