What’s the mathematical intuition behind amortized analysis?
I understand the basic idea of amortized complexity, but I'm looking for a clearer theoretical intuition. How can an operation that is occasionally very expensive still have a…
algorithm analysis
Why do we usually give the tightest Big O bound?
If an algorithm runs in O(n), then O(n²), O(n³), and even O(n!) are technically valid upper bounds too. So when someone asks for an algorithm's Big O complexity,…
Why do we use the tightest Big O bound?
If an algorithm runs in O(n), then O(n²), O(n³), and even O(n!) are technically valid upper bounds too. So why do people expect the smallest or tightest bound…
How can I combine the even and odd cases into one recurrence?
I'm new to data structures and algorithms and am analyzing the running time of this exponentiation function. When n is even, it makes one recursive call with n/2;…
Why Is My Python Solution Timing Out Despite O(N² + U) Complexity?
I'm confused about why this solution exceeds the two-second limit. The grid size N is at most 2000, and there can be up to 100,000 updates. I estimated…
How Can I Quickly Determine an Algorithm’s Time Complexity?
I have trouble understanding what an algorithm is doing just by reading its code, especially when trying to estimate its time complexity. Are there any reliable techniques or…
How Can I Quickly Figure Out an Algorithm’s Time Complexity?
I have trouble understanding what an algorithm is doing just by reading the code, especially when I need to estimate its time complexity. Are there any reliable shortcuts…
Is this function O(n) or O(1)?
I have a debate going on with my professor about the time complexity of a function I've written. The code is as follows: ```cpp int f(int m, int…
What is the Purpose of Uniform Hashing and Why Does It Matter?
I'm trying to grasp the concept of uniform hashing and what its practical implications are. The slides I have state that uniform hashing means each key has an…
Is O(c^(k+1)) the same as O(c^k)?
I'm working on a project related to the Hitting Set problem, which involves exponential algorithms, and I stumbled upon a question: Are O(c^(k+1)) and O(c^k) equivalent? Just like…