# Questions tagged [efficiency]

Using as few resources (e.g. time, space) as possible while solving a problem. Use this tag if your question is specifically about resource usage, not for generic algorithm questions that happen to mention running times.

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### Generating number of possibilites of popping two stacks to two other stacks

Context: I'm working on this problem: There are two stacks here: A: 1,2,3,4 <- Stack Top B: 5,6,7,8 A and B will pop out to other two stacks: C and D....
2answers
4k views

### Efficient map data structure supporting approximate lookup

I'm looking for a data structure that supports efficient approximate lookups of keys (e.g., Levenshtein distance for strings), returning the closest possible match for the input key. The best suited ...
2answers
14k views

### When can I use dynamic programming to reduce the time complexity of my recursive algorithm?

Dynamic programming can reduce the time needed to perform a recursive algorithm. I know that dynamic programming can help reduce the time complexity of algorithms. Are the general conditions such that ...
1answer
9k views

### Removing Left Recursion from Context-Free Grammars - Ordering of nonterminals

I have recently implemented the Paull's algorithm for removing left-recursion from context-free grammars: Assign an ordering $A_1, \dots, A_n$ to the nonterminals of the grammar. for $i := 1$ to $n$ ...
3answers
11k views

### What is the most efficient way to compute factorials modulo a prime?

Do you know any algorithm that calculates the factorial after modulus efficiently? For example, I want to program: ...
6answers
5k views

### Dealing with intractability: NP-complete problems

Assume that I am a programmer and I have an NP-complete problem that I need to solve it. What methods are available to deal with NPC problems? Is there a survey or something similar on this topic?
5answers
59k views

### Adding elements to a sorted array

What would be the fastest way of doing this (from an algorithmic perspective, as well as a practical matter)? I was thinking something along the following lines. I could add to the end of an array ...
3answers
442 views

### Notions of efficient computation

A polynomial-time Turing machine algorithm is considered efficient if its run-time, in the worst-case, is bounded by a polynomial function in the input size. I'm aware of the strong Church-Turing ...
2answers
11k views

### Are all context-free and regular languages efficiently decidable?

I came across this figure which shows that context-free and regular languages are (proper) subsets of efficient problems (supposedly $\mathrm{P}$). I perfectly understand that efficient problems are a ...
4answers
7k views

### Why polynomial time is called “efficient”?

Why in computer science any complexity which is at most polynomial is considered efficient? For any practical application(a), algorithms with complexity $n^{\log n}$ are way faster than algorithms ...