# Tagged Questions

Mathematical questions about Algorithms, including the analysis of algorithms, combinatorial algorithms, proofs of correctness, invariants, and semantic analyses. See also (computational-mathematics) and (computational-complexity).

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### self teach algorithms [closed]

What are some good resources to self teach the subject of Algorithms for someone with background in mathematics? That is, does there exists a more theoretical and abstract approach versus practical ...
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### First Intersection Of Periodically Repeating Intervals

I have a set of coupled tasks, let's say $M$ of them. The $ith$ coupled task is represented as the following 3-tuple $\{A_i,D_i,B_i\}$ where $A_i$ represents the time it takes to perform the first ...
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### What would be the formula to get the position of a combination, instead of a permutation ,given an index in this example

Let be an array A = {a,b,c,d,e,f} of six elements and we want three elements at the time, so the total number of permutations with repetitions will be: 6^3. Now to get the position of those ...
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### Number of integer solutions of an equation $x^3 + y^2 = k$ [closed]

Given equation $$x^3 + y^2 = k$$ How can one count efficiently a number of integer solutions?
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### Is there a minimum spanning tree including $e$ after removing at most $k$ edges?

Let an undirected, connected graph $G=(V,E)$ with the weight funciton $w:E\to \mathbb{R}$, an edge $e$, and $0<k\in\mathbb{N}$. Describe an algorithm determines if there are at most $k$ edges could ...
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### Maximum number of non-intersecting lines

Given a polygon with $n$ vertices as $P_1,P_2,\ldots,P_n$ and a point $A$ in 2D space, what algorithm can I use to determine how many of the segments $\overline{AP_i}$ do not intersect an edge of the ...
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### Red-black tree insert

I'm currently trying to figure out this exercise (sorry for link to image, it's for the red-black trees): http://i.imgur.com/IKMCkVf.png And I do know that the correct one is number three from the ...
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### Algorithm to order and partition a set of of (n,m) pairs with constraints.

I ran into this problem while looking at Google API distance matrix service. Say you have a collection of a few million (origins, destinations) unique pairs/2 column table like (address, zip) for ...
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### Max Flow Min Cut - Prove that $e$ crosses some minimal cut

I already asked about the opposite direction but I'm really confused about it, so I'd like to get some help please: Let's assume we have a flow network $G$ and some edge $e$. Now, Let's assume ...
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### Computing unknown matrix norm

Suppose that we have a unknown vector norm but there is a machine that get a vector and correctly tell us the norm of the vector. Is there any algorithm to compute the matrix norm corresponding to ...
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### Variation of TSP - Revisit Nodes

I have a problem where I have an symmetric graph and I want to find that shortest path that visits every node at least once (not exactly once). In order to solve this problem, I have found that we ...