Introduction

In this blog post, we will explore how to solve the LeetCode problem "1870" 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 are given a floating-point number hour, representing the amount of time you have to reach the office. To commute to the office, you must take n trains in sequential order. You are also given an integer array dist of length n, where dist[i] describes the distance (in kilometers) of the ith train ride. Each train can only depart at an integer hour, so you may need to wait in between each train ride. For example, if the 1st train ride takes 1.5 hours, you must wait for an additional 0.5 hours before you can depart on the 2nd train ride at the 2 hour mark. Return the minimum positive integer speed (in kilometers per hour) that all the trains must travel at for you to reach the office on time, or -1 if it is impossible to be on time. Tests are generated such that the answer will not exceed 107 and hour will have at most two digits after the decimal point. Example 1: Input: dist = [1,3,2], hour = 6 Output: 1 Explanation: At speed 1: - The first train ride takes 1/1 = 1 hour. - Since we are already at an integer hour, we depart immediately at the 1 hour mark. The second train takes 3/1 = 3 hours. - Since we are already at an integer hour, we depart immediately at the 4 hour mark. The third train takes 2/1 = 2 hours. - You will arrive at exactly the 6 hour mark. Example 2: Input: dist = [1,3,2], hour = 2.7 Output: 3 Explanation: At speed 3: - The first train ride takes 1/3 = 0.33333 hours. - Since we are not at an integer hour, we wait until the 1 hour mark to depart. The second train ride takes 3/3 = 1 hour. - Since we are already at an integer hour, we depart immediately at the 2 hour mark. The third train takes 2/3 = 0.66667 hours. - You will arrive at the 2.66667 hour mark. Example 3: Input: dist = [1,3,2], hour = 1.9 Output: -1 Explanation: It is impossible because the earliest the third train can depart is at the 2 hour mark. Constraints: n == dist.length 1 <= n <= 105 1 <= dist[i] <= 105 1 <= hour <= 109 There will be at most two digits after the decimal point in hour.

Explanation

• Binary Search for Optimal Speed: The problem can be solved efficiently using binary search. We search for the minimum speed within a possible range (1 to 10\^7 as specified in the constraints).
  • Check if a Given Speed is Feasible: For each speed considered in the binary search, we check if it's possible to reach the office on time. This involves calculating the time taken for each train ride and adding any necessary waiting time.
  • Adjust Search Range: Based on whether the current speed is feasible, we adjust the binary search range to find a lower or higher speed.

• Runtime Complexity: O(N log M), where N is the number of trains (length of dist) and M is the maximum possible speed (10\^7). Storage Complexity: O(1).

Code

    def min_speed_to_reach_office(dist, hour):
    """
    Finds the minimum positive integer speed needed to reach the office on time.

    Args:
        dist: A list of integers representing the distance of each train ride.
        hour: A float representing the total time available to reach the office.

    Returns:
        The minimum speed as an integer, or -1 if it's impossible to reach on time.
    """

    def is_possible(speed):
        """
        Checks if it's possible to reach the office on time with the given speed.
        """
        time = 0
        for i in range(len(dist) - 1):
            time += (dist[i] + speed - 1) // speed  # Ceil division
        time += dist[-1] / speed
        return time <= hour

    left, right = 1, 10**7
    ans = -1

    while left <= right:
        mid = (left + right) // 2
        if is_possible(mid):
            ans = mid
            right = mid - 1
        else:
            left = mid + 1

    return ans