Design & Analysis of Algorithms 11 min read
Dijkstra’s Algorithm
In this section, we consider the single-source shortest-paths problem: for a given vertex called the source in a weighted connected graph, find shortest…
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Design & Analysis of Algorithms 14 min read
Kruskal’s Algorithm
In the previous section, we considered the greedy algorithm that “grows” a mini-mum spanning tree through a greedy inclusion of…
Design & Analysis of Algorithms 13 min read
Prim’s Algorithm
The following problem arises naturally in many practical situations: given n points, connect them in the cheapest possible way so that there…
Design & Analysis of Algorithms 6 min read
Greedy Technique
Let us revisit the change-making problem faced, at least subconsciously, by millions of cashiers all over the world: give change for a…
Design & Analysis of Algorithms 11 min read
The Knapsack Problem and Memory Functions
We start this section with designing a dynamic programming algorithm for the knapsack problem: given n items of known weights w1, . .…
Design & Analysis of Algorithms 17 min read
Warshall’s and Floyd’s Algorithms
In this section, we look at two well-known algorithms: Warshall’s algorithm for computing the transitive closure of a directed graph…
Design & Analysis of Algorithms 2 min read
Greedy approach vs Dynamic programming
A Greedy algorithm is an algorithmic paradigm that builds up a solution piece by piece, always choosing the next piece that offers…
Design & Analysis of Algorithms 9 min read
Knapsack Problem
Here is another well-known problem in algorithmics. Given n items of known weights w1, w2, . . . , wn and values v1, v2, .…
Design & Analysis of Algorithms 3 min read
Exhaustive Search
Exhaustive Search: 1. Traveling Salesman Problem 2. Knapsack Problem 3. Assignment Problem 4. Exercises Many important problems require finding an…
Design & Analysis of Algorithms 16 min read
Closest-Pair and Convex-Hull Problems by Brute Force
In this section, we consider a straightforward approach to two well-known prob-lems dealing with a finite set of points in…