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← Explore all topicsEvery time you Google something, scroll through Instagram, or watch a movie on Netflix, you’re interacting with algorithms. These invisible…
In many situations we are faced with a problem of pairing elements of two sets. The traditional example is boys…
We have already encountered linear programming (see Section 6.6)—the general problem of optimizing a linear function of several variables subject…
The greedy strategy, considered in the preceding chapter, constructs a solution to an optimization problem piece by piece, always adding…
Suppose we have to encode a text that comprises symbols from some n-symbol alphabet by assigning to each of the text’s…
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…
In the previous section, we considered the greedy algorithm that “grows” a mini-mum spanning tree through a greedy inclusion of…
The following problem arises naturally in many practical situations: given n points, connect them in the cheapest possible way so that there…
Let us revisit the change-making problem faced, at least subconsciously, by millions of cashiers all over the world: give change for a…
We start this section with designing a dynamic programming algorithm for the knapsack problem: given n items of known weights w1, . .…
In this section, we look at two well-known algorithms: Warshall’s algorithm for computing the transitive closure of a directed graph…
A Greedy algorithm is an algorithmic paradigm that builds up a solution piece by piece, always choosing the next piece that offers…