# Questions tagged [algorithms]

An algorithm is a sequence of well-defined steps that defines an abstract solution to a problem. Use this tag when your issue is related to design and analysis of algorithms.

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### Algorithm to detect if word belongs to pushdown automaton

I am creating a simple program to detect if the given pushdown automaton accepts the given word, and I have a problem in finding an algorithm that does that. My thought at first would be to go ...
724 views

### Generalized data structure

Data structures are seen as important, equal to algorithms. This view is especially encouraged in situations, where appropriate data structure is the main factor that allows an algorithm to exist and ...
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### Why does using unary in subset sum problem result polynomial time complexity?

From my understanding, the complexity of the algorithm is O(number of inputs * number of bits for input). The number of bits in binary notation is obviously less ...
541 views

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### Minimal Spanning tree and Prim's Algorithm

Is there any example that anybody could come up with that shows Prim's algorithm does not always give the correct result when it comes knowing the minimal spanning tree.
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### Graph searching: Breadth-first vs. depth-first

When searching graphs, there are two easy algorithms: breadth-first and depth-first (Usually done by adding all adjactent graph nodes to a queue (breadth-first) or stack (depth-first)). Now, are ...
53k views

### What is tail recursion?

I know the general concept of recursion. I came across the concept of tail recursion while studying the quicksort algorithm. In this video of quick sort algorithm from MIT at 18:30 seconds the ...
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### Factorial algorithm more efficient than naive multiplication

I know how to code for factorials using both iterative and recursive (e.g. n * factorial(n-1) for e.g.). I read in a textbook (without been given any further ...
71k views

### Find median of unsorted array in $O(n)$ time

To find the median of an unsorted array, we can make a min-heap in $O(n\log n)$ time for $n$ elements, and then we can extract one by one $n/2$ elements to get the median. But this approach would take ...
34k views

### Floyd's Cycle detection algorithm | Determining the starting point of cycle

I am seeking help understanding Floyd's cycle detection algorithm. I have gone through the explanation on wikipedia (http://en.wikipedia.org/wiki/Cycle_detection#Tortoise_and_hare) I can see how the ...
Searching an array of $N$ elements using binary search takes, in the worst case $\log_2 N$ iterations because, at each step we trim half of our search space. If, instead, we used 'ternary search', we'...