General Steps to Find an Augmenting Path in a Residual Network $G_f = (V, E_f)$ Goal: Find a path from the source s to the sink t such that all edges on the path have positive residual capacity. Once found, you can push the bottleneck capacity along this path into the flow. Forward residual capacity … Read more
A hash table is an efficient data structure used to implement associative arrays or sets. Its core idea is to use a hash function to map keys to indices in an array, enabling fast lookup, insertion, and deletion operations. However, different languages and standard libraries have variations in their specific implementations, particularly in handling hash … Read more
Activity Selection Problem Proof of Optimality for the Greedy Algorithm in the Activity Selection Problem We prove that the greedy strategy of always selecting the activity with the earliest finish time yields an optimal solution to the activity selection problem. The proof relies on two key properties: 1. Greedy-Choice Property Claim: There exists an optimal … Read more
In its simplest form, binary search works on a contiguous sequence with specified left and right indices, also known as the search space. It continuously narrows down the search range to eventually locate the target value or determine that it does not exist. Basic Concept Binary search maintains three pointers: left, right, and mid At … Read more