Last Moment Before All Ants Fall Out of a Plank

class Solution {
public:
    int finalMoment(int length, vector<int>& leftAnts, vector<int>& rightAnts) {
        int maxTime = 0;
        for (int lAnt : leftAnts) {
            maxTime = max(maxTime, lAnt);
        }
        
        for (int rAnt : rightAnts) {
            maxTime = max(maxTime, length - rAnt);
        }
        
        return maxTime;
    }
};

This solution is implemented in C++ for the problem where ants walk on a plank and we need to determine the last moment before all ants fall off. The plank is of a specified length, and the positions of ants moving to the left and right are given in two separate vectors leftAnts and rightAnts.

The function finalMoment takes these inputs and calculates the maximum time it will take for the last ant to fall off the plank. Here's what happens in the code:

• Initialize maxTime to 0. This variable will track the maximum amount of time taken by any ant to fall off.
• Loop through each ant in leftAnts. Update maxTime to the greater value between its current value and the position lAnt of the current ant. This represents the time at which an ant that started on position lAnt on the left side will fall off the right end of the plank.
• Similarly, loop through each ant in rightAnts, but this time calculate the time it takes for each right-moving ant to reach the left end. Update maxTime to the greater value between its current value and length - rAnt. This gives the time it would take the ant to fall from its starting position to the left end of the plank.
• Return maxTime, which by the end of the function will be the time it takes for the last ant to fall off the plank.

The solution efficiently calculates the required time by considering the maximum time needed for any single ant to leave the plank, ensuring it covers all scenarios by taking the straightforward paths of left-moving and right-moving ants into account.

class Solution {
    public int calculateLastMoment(int length, int[] leftAnts, int[] rightAnts) {
        int lastMomentTime = 0;
        for (int position : leftAnts) {
            lastMomentTime = Math.max(lastMomentTime, position);
        }
        
        for (int position : rightAnts) {
            lastMomentTime = Math.max(lastMomentTime, length - position);
        }
        
        return lastMomentTime;
    }
}

The provided Java program solves the problem of determining the last moment before all ants fall off a plank. The plank is given a specific length, and ants are falling from both the left and right sides. The function calculateLastMoment accepts the length of the plank and two arrays representing the positions of ants starting from the left and the right.

• Initialize lastMomentTime to 0, which will store the maximum time taken for any ant to fall off the plank.
• Loop through all positions in leftAnts, and update lastMomentTime to be the maximum value between the current lastMomentTime and the position of the current ant from the left end.
• Similarly, loop through all positions in rightAnts. Here, the time for an ant to fall off from the right side is calculated as the difference between the plank length and the ant's position (length - position). Update lastMomentTime accordingly to ensure it holds the maximum fall time.

This approach leverages the fact that an ant's maximum fall time is simply the maximum distance it has to travel to fall off the plank, irrespective of other ants' positions or directions. The algorithm efficiently calculates this value using simple iterations and comparisons and returns the result, ensuring an optimal and direct solution to the problem.

class Solution:
    def findLastTime(self, length: int, leftCrickets: List[int], rightCrickets: List[int]) -> int:
        lastTime = 0
        for leftPosition in leftCrickets:
            lastTime = max(lastTime, leftPosition)

        for rightPosition in rightCrickets:
            lastTime = max(lastTime, length - rightPosition)

        return lastTime

The Python3 solution provided for the problem titled "Last Moment Before All Ants Fall Out of a Plank" calculates the time just before all ants fall off from both ends of a given plank.

• length: the total length of the plank
• leftCrickets: a list of start positions for ants moving to the left
• rightCrickets: a list of start positions for ants moving to the right

The function findLastTime uses the following approach:

1. Initialize a variable lastTime to zero to store the maximum time taken for an ant to fall off the plank.
2. Iterate through each ant's position in leftCrickets:
   • Update lastTime to be the maximum of lastTime and the ant's position leftPosition, which directly indicates the time taken by the ant to fall if moving leftward.
3. Iterate through each ant's position in rightCrickets:
   • Calculate the time for the ant to fall off from the right end by subtracting its position from length and update lastTime accordingly.

The function finally returns lastTime, which is the maximum time needed for all ants to fall off the plank either from the left or right end.