The interpretation of expected time bound for searches in a hash table
As CLRS book,page 260 stated,
I wouldn't have any problem if the author says the bound is eventually
or even
What kind of theories shall we apply to simplify the original result, i.e, cancelling the factor 1/n of a. Since n is one of inputs of the function, is it necessary to cancel it by treating it as a constant? What i've missed? is anyone got the same confusion T_T?
Solution
alpha/n is asimptotically smaller (has lower order) being compared with alpha, so it might be ignored. When n (hashtable size, AFAIU) becomes larger, 1/n value tends to zero.
Note - wiki table does not contain 1/n function because it is evaluated as having zero impact
Alike situation - if time is Theta(n^2 + 100*n + 10000), dominating summand is quadratic, and
Theta(n^2 + 100*n + 10000)` = Theta(n^2)
- Change one pair of vertices to create a cycle in an oriented graph
- Finding a small image in a bigger one
- Efficient calculation of Fibonacci series
- Find the Smallest Integer Not in a List
- Best way to find a point on a circle closest to a given point
- Word Prediction algorithm
- Double cone model of HSI Color Space to RGB
- how to split an iterable in constant-size chunks
- Time complexity in Divide and Conquer algorithms
- How to decrypt a string with unknown encryption algorithm?
- Your Rank Is Pure Google Code Jam Assistance
- Algorithms for string processing
- Splitting up a list into parts of balanced lengths
- Implementing token bucket algorithm
- Bitwise Interval Arithmetic
- Combination between two lists using cartesian product with a small twist
- Performing calculation over huge dataset in mongoDB with nodejs express.js in backend code | Optimising time and memory
- Find k-th smallest element data structure
- The simplest algorithm for poker hand evaluation
- How to get an ordered list of vertices defining an island/region in a heightmap array
- Travelling salesman problem for a tree graph (no hamiltonian path)
- Find maximum of all minimum sum
- Finding all possible bijections between two sets
- Exact hitting set for keywords in text
- Ray-triangle intersection
- Rank of Partition with specific length
- Does greedily removing intervals with most conflicts solve interval scheduling?
- How to show that union and intersection of min cuts in flow network is also a min cut
- Randomly assign a flag with specific percentage rate requirement
- What algorithms do popular C++ compilers use for std::sort and std::stable_sort?