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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.
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.
1function minSpeedOnTime(dist, hour) {
2 let left = 1, right = 10000000;
3 while (left < right) {
4
JavaScript implementation makes use of binary search technique to determine the minimum possible speed. By testing mid-values as potential speeds, it iteratively narrows down possible speeds based on whether they allow reaching within available hours.