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Minimum Jumps With Fee

Explore how to solve the minimum jumps with fee problem by applying recursive and dynamic programming methods. Understand how to optimize the naive recursive solution using memoization and tabulation to efficiently calculate the least cost to reach beyond the top step.

Statement

You are given n steps of stairs and a list fee because each step has a fee associated with it. Your task is to calculate the minimum fee required to reach the top of the stairs (beyond the top step), assuming you start with the first step. At every step, you can take 1 step, 2 steps, or 3 steps.

Let’s say you have a staircase of six steps. The fee for each step is [1,2,3,2,3,1][1,2,3,2,3,1]. The minimum cost to reach the top will be 33. This cost is calculated as follows:

  • Starting from the first step, totalfee=1total fee = 1
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