Question

Design an algorithm that, given the location of m cuts in a string length of n, outputs the miniμm cost.

a) It can't be done efficiently
b) Dynamic programming might help
c) A greedy algorithm solves it
d) This is an NP-complete problem

Answer 1

Dynamic programming is the ideal approach to solve the algorithmic problem of finding the minimum cost of making cuts in a string, as it considers all possible configurations of cuts efficiently and ensures finding the optimal solution.

Step-by-step explanation:

The question pertains to an algorithmic problem related to finding the minimum cost of making cuts in a string of given length. This is a classic problem that is best approached using dynamic programming. Dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems. It is applicable here as it can help in finding the minimum cost by considering the cost of each possible combination of cuts, which can be built up from solving smaller subproblems. This approach ensures that every possible configuration of cuts is considered efficiently, without redundancy. Greedy algorithms, on the other hand, do not guarantee the minimum cost for this problem, as making locally optimal choices at each step may not lead to a globally optimal solution.