Introduction

In this blog post, we will explore how to solve the LeetCode problem "983" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

You have planned some train traveling one year in advance. The days of the year in which you will travel are given as an integer array days. Each day is an integer from 1 to 365. Train tickets are sold in three different ways: a 1-day pass is sold for costs[0] dollars, a 7-day pass is sold for costs[1] dollars, and a 30-day pass is sold for costs[2] dollars. The passes allow that many days of consecutive travel. For example, if we get a 7-day pass on day 2, then we can travel for 7 days: 2, 3, 4, 5, 6, 7, and 8. Return the minimum number of dollars you need to travel every day in the given list of days. Example 1: Input: days = [1,4,6,7,8,20], costs = [2,7,15] Output: 11 Explanation: For example, here is one way to buy passes that lets you travel your travel plan: On day 1, you bought a 1-day pass for costs[0] = $2, which covered day 1. On day 3, you bought a 7-day pass for costs[1] = $7, which covered days 3, 4, ..., 9. On day 20, you bought a 1-day pass for costs[0] = $2, which covered day 20. In total, you spent $11 and covered all the days of your travel. Example 2: Input: days = [1,2,3,4,5,6,7,8,9,10,30,31], costs = [2,7,15] Output: 17 Explanation: For example, here is one way to buy passes that lets you travel your travel plan: On day 1, you bought a 30-day pass for costs[2] = $15 which covered days 1, 2, ..., 30. On day 31, you bought a 1-day pass for costs[0] = $2 which covered day 31. In total, you spent $17 and covered all the days of your travel. Constraints: 1 <= days.length <= 365 1 <= days[i] <= 365 days is in strictly increasing order. costs.length == 3 1 <= costs[i] <= 1000

Explanation

Here's the solution to the problem:

• Dynamic Programming: Use dynamic programming to calculate the minimum cost to travel up to each day of the year. The DP array dp[i] stores the minimum cost to travel up to day i.
• Iteration and Optimization: Iterate through each day from 1 to 365. If the day is not a travel day, the cost is the same as the previous day. If the day is a travel day, consider the three pass options (1-day, 7-day, 30-day) and choose the one that results in the minimum cost.

• Base Case: The initial cost for day 0 is 0.

• Runtime Complexity: O(N), where N is 365 (number of days in a year). Storage Complexity: O(N).

Code

    def mincostTickets(days, costs):
    """
    Calculates the minimum cost to travel every day in the given list of days.

    Args:
        days (list[int]): The days of the year in which you will travel.
        costs (list[int]): The costs of the 1-day, 7-day, and 30-day passes.

    Returns:
        int: The minimum number of dollars you need to travel every day in the given list of days.
    """
    n = len(days)
    dp = [0] * 366
    dayset = set(days)

    for i in range(1, 366):
        if i not in dayset:
            dp[i] = dp[i - 1]
        else:
            dp[i] = min(
                dp[i - 1] + costs[0],
                dp[max(0, i - 7)] + costs[1],
                dp[max(0, i - 30)] + costs[2]
            )

    return dp[365]