How do you solve Minimum Speed to Arrive on Time on LeetCode?

Minimum Speed to Arrive on Time (LeetCode #1870) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log m) time complexity and O(1) space complexity. Key insight: Binary search helps efficiently narrow down the minimum speed.

What is the brute force solution for Minimum Speed to Arrive on Time?

The brute force approach for Minimum Speed to Arrive on Time is Brute Force, with O(n²) time complexity and O(1) space complexity. We can try every possible speed starting from 1 km/h and calculate the total time taken for each speed until we find one that allows us to arrive on time. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n log m).

What algorithm or data structure is used to solve Minimum Speed to Arrive on Time?

Minimum Speed to Arrive on Time uses the following concepts: Array, Binary Search. The recommended patterns to study are: Binary Search, Greedy.

What are the interview tips for Minimum Speed to Arrive on Time?

Explain your thought process clearly, especially when transitioning from brute force to optimal. Be prepared to discuss the time complexity of your solutions. Practice binary search problems to become comfortable with the technique.

What are common mistakes when solving Minimum Speed to Arrive on Time?

Not considering the need to wait for the next train at integer hours. Overlooking the constraints of speed limits.

#1870

Minimum Speed to Arrive on Time

Medium

ArrayBinary SearchBinary SearchGreedy

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log m)
Space	O(1)	O(1)

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Intuition

Time O(n log m)Space O(1)

Instead of checking every speed, we can use binary search to efficiently find the minimum speed that allows us to arrive on time. This reduces the number of checks significantly.

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Algorithm

6 steps

1Step 1: Set low to 1 and high to 10^7.
2Step 2: While low is less than or equal to high, calculate mid as the average of low and high.
3Step 3: Calculate the total time taken for the current mid speed.
4Step 4: If the total time is less than or equal to hour, update the answer and reduce high to mid - 1.
5Step 5: If total time is greater than hour, increase low to mid + 1.
6Step 6: Return the answer.

solution.py16 lines

1def minSpeedOnTime(dist, hour):
2    low, high = 1, 10**7
3    answer = -1
4    while low <= high:
5        mid = (low + high) // 2
6        total_time = 0
7        for i in range(len(dist)):
8            total_time += dist[i] / mid
9            if i < len(dist) - 1:
10                total_time = int(total_time) + (total_time % 1 > 0)
11        if total_time <= hour:
12            answer = mid
13            high = mid - 1
14        else:
15            low = mid + 1
16    return answer

ℹ

Complexity note: The binary search runs in log m time (where m is the maximum speed), and for each speed, we traverse the distances array, leading to O(n log m) complexity.

1Binary search helps efficiently narrow down the minimum speed.
2Calculating total time correctly is crucial to determine if we arrive on time.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.