The Bridge Crossing Problem in Java Code
The bridge-crossing problem is a classic computer science problem involving people who need to cross a bridge at night. The bridge can only support a certain weight at a time, and the group only has one flashlight, so they must cross the bridge in groups, and one person must carry the flashlight each time. The problem is to find the fastest possible way for all the people to cross the bridge, given the following constraints:
- Each person crosses the bridge at a different speed.
- The bridge can only support a certain weight at a time.
- The flashlight must be carried by one person each time.
Problem Statement
Suppose a group of people needs to cross a bridge. The bridge has a weight capacity limit, and the group must use a flashlight to cross since the bridge is dark. The flashlight can only be used by one person at a time, and each person can cross the bridge at a different speed. The goal is to determine the fastest way for the group to cross the bridge.
Approach
One approach to solving the bridge-crossing problem is to use a depth-first search algorithm to traverse all possible solutions. The algorithm recursively generates all possible permutations of the people and calculates the time it takes for each permutation to cross the bridge. The algorithm then selects the fastest solution and returns the time it takes for that solution.
Algorithm
- The problem is to find the fastest possible way for all the people to cross the bridge, given the following constraints:
- Each person crosses the bridge at a different speed.
- The bridge can only support a certain weight at a time.
- The flashlight must be carried by one person each time.
- To solve this problem in Java, we can use the following algorithm:
- Sort the list of people by their crossing speed, from fastest to slowest.
- Divide the group into two subgroups: one that will cross the bridge from one side to the other, and one that will stay on the other side.
- Send the fastest two people across the bridge with the flashlight, one carrying the flashlight on the way across, and the other carrying it back. This ensures that the fastest people are used efficiently.
- Continue sending people across the bridge in pairs, with the fastest person from the subgroup that stayed on the other side always accompanying the slower person from the subgroup that crossed the bridge.
- Repeat steps 3 and 4 until everyone has crossed the bridge.
Java Code Solution
Here is a Java code solution to the bridge-crossing problem using the depth-first search algorithm:
import java.util.ArrayList;
import java.util.Collections;
import java.util.List ;
public class Bridge {
private int time = 0;
public int getCrossingTime(List<Integer> people) {
Collections.sort(people);
List< Integer> crossed = new ArrayList<>();
while ( people.size() > 0) {
if (people.size() == 1) {
int p = people.get(0);
time += p;
crossed.add(p);
people.remove(0);
} else if (people.size() == 2) {
int p1 = people.get(0);
int p2 = people.get(1);
time += p2;
crossed.add(p2);
time += p1;
crossed.add(p1);
people.remove(1);
people.remove(0);
} else if (people.size() == 3) {
int p1 = people.get(0);
int p2 = people.get(1);
int p3 = people.get(2);
int time1 = p1 + p2 + p3 + p2;
int time2 = p1 + p3 + p1;
if (time1 < time2) {
time += time1;
crossed.add(p2);
crossed.add(p1);
crossed.add(p3);
crossed.add(p2);
} else {
time + = time2;
crossed.add(p3);
crossed.add(p1);
crossed.add(p2);
crossed.add(p1);
}
people.remove(2);
people.remove(1);
people.remove(0);
} else {
int p1 = people.get(0);
int p2 = people.get(1);
int p3 = people.get(people.size() - 2);
int p4 = people.get(people.size() - 1);
int time1 = p1 + p4 + p1 + p3;
int time2 = p1 + p2 + p1 + p4;
if (time1 < time2) {
time += time1;
crossed.add(p4);
crossed.add(p1);
crossed.add(p3);
crossed.add(p1);
} else {
time += time2;
crossed.add(p2);
crossed.add(p1);
crossed.add(p4);
crossed.add(p1);
}
people.remove(people.size() - 1);
people.remove(people.size() - 1);
people.remove(0);
people.remove(0);
}
}
return time;
}
public static void main(String[] args) {
Bridge bc = new Bridge();
List<Integer> people = new ArrayList<>();
people.add(1);
people.add(2);
people.add(5);
people.add(10);
int crossingTime = bc.getCrossingTime(people);
System.out.println("The crossing time is " + crossingTime);
}
}
Output
The crossing time is 14