Minimum Jumps With Fee
Explore how to solve the minimum jumps with fee problem using dynamic programming techniques. Understand the naive recursive method and optimize it with top-down memoization and bottom-up tabulation to reduce time complexity from exponential to linear. Gain skills to efficiently handle large inputs and apply recursive number patterns in C++.
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 . The minimum cost to reach the top will be . This cost is calculated as follows:
- Starting from the first step, .
- Taking 3 steps would get us to the fourth floor. The fee for the fourth floor is 2, so the