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.
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.length1 <= n <= 1051 <= dist[i] <= 1051 <= hour <= 109hour.Idea: To find the minimum positive integer speed that allows you to reach the office in the given time, you can use binary search on the speed. Initialize the left boundary to 1 (minimum speed) and right boundary to a large number (e.g., 10^7, as specified in the problem statement), then narrow down the possible speed by simulating the commute.
Steps:
If you narrow down to a result, it is the minimum speed required. If search is exhausted without finding a valid speed, return -1.
The solution involves performing a binary search over possible speeds. The minSpeedOnTime function iterates over each train's distance at a given mid speed, calculating the time taken accounting for waiting until the next hour if necessary. The result is a narrowed-down speed that allows for reaching within the specified hour, making use of ceiling round-ups for all train rides except for the last one.
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Time Complexity: O(n log k), where n is the number of train distances and k is the maximum speed (10^7).
Space Complexity: O(1), as the solution does not require any extra space beyond a fixed set of variables.
1870. Minimum Speed to Arrive on Time | LEETCODE WEEKLY CONTEST 242 | LEETCODE • code Explainer • 6,064 views views
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