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Surely, it is not about correctness. It is only a slightly general version of linear search. This technique is not uncommon. Obviously the more general the procedure is, the more applicable it is. Li …

Yes, you can perform this operation in $O(n)$ using a stack $\mathbb{S}$. Before presenting the algorithm directly, I would like to give you an illustration using your example. It is not difficult f …

Which algorithm does "Eulers technique to find an Eulerian cycle" refer to? It probably refers to the Hierholzer algorithm (wiki) which takes linear time. The algorithm below is from the wiki a …

Although the final result is correct, your solution is not. The recurrences of the form $T(n) = T(n-1) + 2/n$ is often called "decrease and conquer"; while the ones of the form $T(n) = T(n/2) + O(1)$ …

Below I try to prove that the greedy algorithm ($\mathcal{A}$) given by @norbertpy (and @Bergi) is correct. Please check it. Problem Definition: The algorithm $\mathcal{A}$ of @norbertpy is for a …

[1] Efficient Algorithms for the One-Dimensional $k$-Center Problem. arXiv, 2014. …

You are right about "independence" between subproblems. Therefore, you use the new subproblems (wiki) by introducing another variable $i$, meaning using the items up to $i$: Define $V[i,s]$ to be …

I assume that $k = 2^m$ ($m \in \mathbb{N}$) and $k \le n$. Here is a recursive (divide-and-conquer) algorithm: Select the median of the array $A$ and use it to partition the array into $A_l$ and $ …

The following problem is exercise 4.3 of the book "Algorithms" by S. Dasgupta, C. Papadimitriou, and U. Vazirani. Squares. …

What about log files described in AWStats logfile analyzer 7.5 Documentation? An error log file is not always completely sorted but only "nearly" sorted because of cache and writing log engines us …

Becuase $5$ is a constant, you can use (almost) any naive method to find the median of $5$ elements in constant time. However, it is known that $6$ comparisons are sufficient (and necessary) to find …

The algorithm with $n + \lceil \lg n \rceil -2$ comparisons uses "tournament" (lecture note from utdallas). To form a tournament tree: Compare $A[2i−1]$ with $A[2i]$ for $i = 1$ to $n$. We compare t …

The proofs of these two theorems contain the algorithms you are looking for. …

I am seeking for some popular science videos on computer algorithms for my last lecture delivered in this term. … The topic of the videos includes but are limited to algorithm design, algorithm analysis, computational complexity, the application of algorithms, the history of algorithms (even computer science), the …

Do you know the Harmonic series (wiki)? $$1 + \frac{1}{2} + \cdots + \frac{1}{n} = 1 + \sum_{i=2}^{n} \frac{1}{i} \le 1 + \int_{1}^{n} \frac{1}{x} \text{d}x = 1 + \ln n = \Theta(\log n).$$ Similarly …