Time To Cross A Bridge - Leetcode Solution

The Time To Cross A Bridge problem on leetcode is a classic puzzle problem that involves finding the shortest time taken for a group of people to cross a bridge with some constraints.

Problem Statement:

A group of n people want to cross a bridge in the shortest possible time, but they can only cross the bridge in groups of at most two people at a time. Each person in the group has a specific crossing time and the total time is the sum of the times of the people crossing the bridge.

For example, if there are 4 people with crossing times [2, 1, 5, 10], the shortest time for them to cross would be 17, as shown below:

• The first and second person cross in 2 minutes (total time is 2)
• The first person returns back with a flashlight in 1 minute (total time is 3)
• The third and fourth person cross in 10 minutes (total time is 13)
• The second person returns back with the flashlight in 2 minutes (total time is 15)
• The first and second person cross again in 2 minutes (total time is 17)

Solution:

To solve this problem, we can use the following approach:

1. Sort the list of crossing times in ascending order.

2. Create two pointers, one at the start of the list and one at the end of the list.

3. Iterate through the list, pairing the person at the start of the list with the person at the end of the list and keeping track of the total time for each pair.

4. If there are more than two people remaining, choose the faster of the two people at the front of the list and pair them with the slowest person remaining.

5. Continue pairing until there are no more people remaining.

6. Return the total time taken for all the people to cross the bridge.

Here is the python code for the solution:

def calculate_time(crossing_times): crossing_times.sort() total_time = 0 i = 0 j = len(crossing_times) - 1

while i < j:
    total_time += max(crossing_times[i], crossing_times[j])
    i += 1
    j -= 1
    
    if j - i > 0:
        total_time += crossing_times[i]
        i += 1
        
return total_time

Input: [2, 1, 5, 10]

Output: 17

Time Complexity:

The time complexity of this solution is O(nlogn), where n is the number of people crossing the bridge. The sorting operation takes O(nlogn) time, and the iteration through the list takes O(n) time.

Space Complexity:

The space complexity of this solution is O(1), as we are not using any extra data structures to store the input or output.

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