Greedy Algorithms: Techniques for Optimization and Activity Scheduling, Huffman Codes, Study notes of Algorithms and Programming

Download Greedy Algorithms: Techniques for Optimization and Activity Scheduling, Huffman Codes and more Study notes Algorithms and Programming in PDF only on Docsity! 1 Greedy Algorithms Greedy algorithms is a technique for solving some optimization problems. A greedy algorithm solution to a problem usu- ally involves: 1. Repeatedly identify a decision to be made. 2. Make a locally optimal choice for each deci- sion. To reach a globally optimal solution, the prob- lem must have an appropriate recursive struc- ture, i.e., an optimal solution equals a locally optimal choice plus an optimal solution for the remainder of the problem. 2 Activity Selection A set of activities are to be scheduled in a room. An activity a has start time start[a] and a finish time finish[a]. Maximize the number of sched- uled activities. Locally optimal choice: Among activities with no conflicts with previously scheduled activities, choose the activity with the earliest finish time. Recursive structure: This choice maximizes the amount of time afterwards, so no other choice can allow more activities to be scheduled. A is an array of activities. S is a schedule. Greedy-Activity-Selector(A) sort A by finish[A] n ← length[A] S ← {A[1]} j ← 1 for i ← 2 to n do if start[A[i]] ≥ finish[A[j]] then S ← S ∪ {A[i]} j ← i return S