Why to Use Pre-Computation?

What is the Pre-Computation Technique?

Precomputation refers to the process of pre-calculating and storing the results of certain computations or data structures in advance, in order to speed up the execution time of a program. This can be useful in situations where the same calculations or data structures are needed multiple times, as it avoids the need to recalculate them every time. Time-Space Trade-Off during Pre-Computation: In order to reduce the amount of time, pre-computation relies on quickly accessing the pre-existing data. We need to store that data in some sort of data structure, hence the Auxiliary space requirement increases....

Why to Use Pre-Computation?

A variety of questions in competitive programming requires printing solution for each Query. Test cases are designed in such a way that if a programmer computes solution again and again for each query then it may result in TLE (Time Limit Exceed).Pre-Computation allows to store a part of solution before processing the queries and then for each query instead of calculating the solution we just need to retrieve that solution. For example, let’s say you have Q queries and each query requires to traverse an array of size N, this will result in a time complexity of O(Q*N), imagine if we can precompute and store the data in O(N) time and then process each query in O(1) time, then we can clearly see that the complexity drastically drops to O(max(Q,N))....

Use-Cases of Pre-Computation in Competitive Programming:

1. Prefix/Suffix Arrays:...

Real World Application of Pre-Computation:

Precomputation in DatabasesPrecomputation in Data AnalyticsMachine Learning and AIPathfindingRecommendation Systems...

Key Takeaways:

Precomputation is a common technique that uses fast information retrieval rather than computing again and again.It’s a trade-off between time and space.Different question requires different pre-computation techniques hence to tackle those problem the best we can do is to practice a lot of problems....

Practice problems on Precomputation Techniques:

Problem Difficulty Queries for the product of first N factorials Easy Range sum queries without updates Easy Range Queries for Frequencies of array elements Easy Count Primes in Ranges Easy Check in binary array the number represented by a subarray is odd or even Easy GCDs of given index ranges in an array Easy Mean of range in array Medium Difference Array | Range update query in O(1) Medium Range sum query using Sparse Table Medium Number whose sum of XOR with given array range is maximum Medium Number of primes in a subarray (with updates) Medium Sum of Interval and Update with Number of Divisors Medium Print modified array after multiple array range increment operations Medium Sparse Table Hard Range Minimum Query (Square Root Decomposition and Sparse Table) Hard Range Query on array whose each element is XOR of index value and previous element Hard Queries for GCD of all numbers of an array except elements in a given range Hard Queries of nCr%p in O(1) time complexity Hard...