You are running a physics experiment with n complicated steps that you must do in order, and students sign-up for some steps to help. Your experiment requires n steps, and each of the m students gives you a list of which steps they can help out with (steps require special skills). From experience, you know things run most smoothly when you have as little switching of shifts as possible.
For example, if your experiment has <1, 2, 3, 4, 5, 6> steps
Another example if your experiment has 8 steps <1, 2, 3, 4, 5, 6, 7, 8>
Given: n number of steps, m number of students that give you a list of steps (sorted) they can participate in. Assume there's a lookup table where you can find if student X signed up for step Y in O(1), so no need to factor that into your runtime.
Find: An optimal way to schedule students to steps such that there is the least amount of switching as possible.
- Describe the optimal substructure of this problem
- Describe the greedy algorithm that could find an optimal way to schedule the students
- What is the runtime complexity of your greedy algorithm? Again, you don't need to factor in the setup of the lookup table, just your scheduling algorithm.
public class PhysicsExperiment1 {
/**
* The actual greedy scheduler you will be implementing!
* @param numStudents The number of students who can participate, m
* @param numSteps The number of steps in the experiment, n
* @param signUpTable An easy lookup tool, signUpTable[x][Y] = student X signed up or did not sign up for step Y.
* Example:
signUpTable[1][3] = 1 if Student 1 signed up for Step 3
signUpTable[1][3] = 0 if Student 1 didn't sign up for Step 3
* @return scheduleTable: a table similar to the signUpTable where scheduleTable[X][Y] = 1 means
* student X is assigned to step Y in an optimal schedule
*/
public int[][] scheduleExperiments(
int numStudents,
int numSteps,
int[][] signUpTable
) {
// Your scheduleTable is initialized as all 0's so far. Your code will put 1's
// in the table in the right places based on the return description
int[][] scheduleTable = new int[numStudents + 1][numSteps + 1];
// Your code goes here
return scheduleTable;
}
/**
* Makes the convenient lookup table based on the steps each student says they can do
* @param numSteps the number of steps in the experiment
* @param studentSignUps student sign ups ex: {{1, 2, 4}, {3, 5}, {6, 7}}
* @return a lookup table so if we want to know if student x can do step y,
lookupTable[x][y] = 1 if student x can do step y
lookupTable[x][y] = 0 if student x cannot do step y
*/
public int[][] makeSignUpLookup(int numSteps, int[][] studentSignUps) {
int numStudents = studentSignUps.length;
int[][] lookupTable = new int[numStudents+1][numSteps + 1];
for (int student = 1; student <= numStudents; student++) {
int[] signedUpSteps = studentSignUps[student-1];
for (int i = 0; i < signedUpSteps.length; i++) {
lookupTable[student][signedUpSteps[i]] = 1;
}
}
return lookupTable;
}
/**
* Prints the optimal schedule by listing which steps each student will do
* Example output is Student 1: 1, 3, 4
* @param schedule The table of 0's and 1's of the optimal schedule, where
* schedule[x][y] means whether in the optimal schedule student x is doing step y
*/
public void printResults(int[][] schedule) {
for (int student = 1; student < schedule.length; student++) {
int[] curStudentSchedule = schedule[student];
System.out.print("Student " + student + ": ");
for (int step = 1; step < curStudentSchedule.length; step++) {
if (curStudentSchedule[step] == 1) {
System.out.print(step + " ");
}
}
System.out.println("");
}
}
/**
* This validates the input data about the experiment step sign-ups.
* @param numStudents the number of students
* @param numSteps the number of steps
* @param signUps the data given about which steps each student can do
* @return true or false whether the input sign-ups match the given number of
* students and steps, and whether all the steps are guaranteed at least
* one student.
*/
public boolean inputsValid(int numStudents, int numSteps, int signUps[][]) {
int studentSignUps = signUps.length;
// Check if there are any students or signups
if (numStudents < 1 || studentSignUps < 1) {
System.out.println("You either did not put in any student or any signups");
return false;
}
// Check if the number of students and sign-up rows matches
if (numStudents != studentSignUps) {
System.out.println("You input " + numStudents + " students but your signup suggests " + signUps.length);
return false;
}
// Check that all steps are guaranteed in the signups
int[] stepsGuaranteed = new int[numSteps + 1];
for (int i = 0; i < studentSignUps; i++) {
for (int j = 0; j < signUps[i].length; j++) {
stepsGuaranteed[signUps[i][j]] = 1;
}
}
for (int step = 1; step <= numSteps; step++) {
if (stepsGuaranteed[step] != 1) {
System.out.println("Your signup is incomplete because not all steps are guaranteed.");
return false;
}
}
return true;
}
/**
* This sets up the scheduling test case and calls the scheduling method.
* @param numStudents the number of students
* @param numSteps the number of steps
* @param signUps which steps each student can do, in order of students and steps
*/
public void makeExperimentAndSchedule(int experimentNum, int numStudents, int numSteps, int[][] signUps) {
System.out.println("----Experiment " + experimentNum + "----");
if (!inputsValid(numStudents, numSteps, signUps)) {
System.out.println("Experiment signup info is invalid");
return;
}
int[][] signUpsLookup = makeSignUpLookup(numSteps, signUps);
int[][] schedule = scheduleExperiments(numStudents, numSteps, signUpsLookup);
printResults(schedule);
System.out.println("");
}
/**
* You can make additional test cases using the same format. In fact the helper functions
* I've provided will even check your test case is set up correctly. Do not touch any of
* of the existing lines. Just make sure to comment out or delete any of your own test cases
* when you submit. The three experiment test cases existing in this main method should be
* the only output when running this file.
*/
public static void main(String args[]){
PhysicsExperiment pe = new PhysicsExperiment();
// Experiment 1: Example 1 from README, 3 students, 6 steps:
int[][] signUpsExperiment1 = {{1, 2, 3, 5}, {2, 3, 4}, {1, 4, 5, 6}};
pe.makeExperimentAndSchedule(1, 3, 6, signUpsExperiment1);
// Experiment 2: Example 2 from README, 4 students, 8 steps
int[][] signUpsExperiment2 = {{5, 7, 8}, {2, 3, 4, 5, 6}, {1, 5, 7, 8}, {1, 3, 4, 8}};
pe.makeExperimentAndSchedule(2, 4, 8, signUpsExperiment2);
// Experiment 3: Another test case, 5 students, 11 steps
int[][] signUpsExperiment3 = {{7, 10, 11}, {8, 9, 10}, {2, 3, 4, 5, 7}, {1, 5, 6, 7, 8}, {1, 3, 4, 8}};
pe.makeExperimentAndSchedule(3, 5, 11, signUpsExperiment3);
}
}
Final Output
----Experiment 1----
Student 1: 1 2 3
Student 2:
Student 3: 4 5 6
----Experiment 2----
Student 1: 7 8
Student 2: 2 3 4 5 6
Student 3: 1
Student 4:
----Experiment 3----
Student 1: 11
Student 2: 9 10
Student 3: 2 3 4 5
Student 4: 1 6 7 8
Student 5:
Thankyou in advance.
public class Main {
/**
* The actual greedy scheduler you will be implementing!
* @param numStudents The number of students who can participate, m
* @param numSteps The number of steps in the experiment, n
* @param signUpTable An easy lookup tool, signUpTable[x][Y] = student X signed up or did not sign up for step Y.
* Example:
signUpTable[1][3] = 1 if Student 1 signed up for Step 3
signUpTable[1][3] = 0 if Student 1 didn't sign up for Step 3
* @return scheduleTable: a table similar to the signUpTable where scheduleTable[X][Y] = 1 means
* student X is assigned to step Y in an optimal schedule
*/
public int[][] scheduleExperiments(
int numStudents,
int numSteps,
int[][] signUpTable
) {
// Your scheduleTable is initialized as all 0's so far. Your code will put 1's
// in the table in the right places based on the return description
int[][] scheduleTable = new int[numStudents + 1][numSteps + 1];
// Your code goes here
return scheduleTable;
}
/**
* Makes the convenient lookup table based on the steps each student says they can do
* @param numSteps the number of steps in the experiment
* @param studentSignUps student sign ups ex: {{1, 2, 4}, {3, 5}, {6, 7}}
* @return a lookup table so if we want to know if student x can do step y,
lookupTable[x][y] = 1 if student x can do step y
lookupTable[x][y] = 0 if student x cannot do step y
*/
public int[][] makeSignUpLookup(int numSteps, int[][] studentSignUps) {
int numStudents = studentSignUps.length;
int[][] lookupTable = new int[numStudents+1][numSteps + 1];
for (int student = 1; student <= numStudents; student++) {
int[] signedUpSteps = studentSignUps[student-1];
for (int i = 0; i < signedUpSteps.length; i++) {
lookupTable[student][signedUpSteps[i]] = 1;
}
}
return lookupTable;
}
/**
* Prints the optimal schedule by listing which steps each student will do
* Example output is Student 1: 1, 3, 4
* @param schedule The table of 0's and 1's of the optimal schedule, where
* schedule[x][y] means whether in the optimal schedule student x is doing step y
*/
public void printResults(int[][] schedule) {
for (int student = 1; student < schedule.length; student++) {
int[] curStudentSchedule =
schedule[student];
System.out.print(curStudentSchedule);
System.out.print("Student " + student + ": ");
for (int step = 1; step < curStudentSchedule.length; step++) {
if (curStudentSchedule[step] == 1) {
System.out.print(step + " ");
}
}
System.out.println("");
}
}
/**
* This validates the input data about the experiment step sign-ups.
* @param numStudents the number of students
* @param numSteps the number of steps
* @param signUps the data given about which steps each student can do
* @return true or false whether the input sign-ups match the given number of
* students and steps, and whether all the steps are guaranteed at least
* one student.
*/
public boolean inputsValid(int numStudents, int numSteps, int signUps[][]) {
int studentSignUps = signUps.length;
// Check if there are any students or signups
if (numStudents < 1 || studentSignUps < 1) {
System.out.println("You either did not put in any student or any signups");
return false;
}
// Check if the number of students and sign-up rows matches
if (numStudents != studentSignUps) {
System.out.println("You input " + numStudents + " students but your signup suggests " + signUps.length);
return false;
}
// Check that all steps are guaranteed in the signups
int[] stepsGuaranteed = new int[numSteps + 1];
for (int i = 0; i < studentSignUps; i++) {
for (int j = 0; j < signUps[i].length; j++) {
stepsGuaranteed[signUps[i][j]] = 1;
}
}
for (int step = 1; step <= numSteps; step++) {
if (stepsGuaranteed[step] != 1) {
System.out.println("Your signup is incomplete because not all steps are guaranteed.");
return false;
}
}
return true;
}
/**
* This sets up the scheduling test case and calls the scheduling method.
* @param numStudents the number of students
* @param numSteps the number of steps
* @param signUps which steps each student can do, in order of students and steps
*/
public void makeExperimentAndSchedule(int experimentNum, int numStudents, int numSteps, int[][] signUps) {
System.out.println("----Experiment " + experimentNum + "----");
if (!inputsValid(numStudents, numSteps, signUps)) {
System.out.println("Experiment signup info is invalid");
return;
}
int[][] signUpsLookup = makeSignUpLookup(numSteps, signUps);
int[][] schedule = scheduleExperiments(numStudents, numSteps, signUpsLookup);
printResults(schedule);
System.out.println("");
}
/**
* You can make additional test cases using the same format. In fact the helper functions
* I've provided will even check your test case is set up correctly. Do not touch any of
* of the existing lines. Just make sure to comment out or delete any of your own test cases
* when you submit. The three experiment test cases existing in this main method should be
* the only output when running this file.
*/
public static void main(String args[]){
Main pe = new Main();
// Experiment 1: Example 1 from README, 3 students, 6 steps:
int[][] signUpsExperiment1 = {{1, 2, 3, 5}, {2, 3, 4}, {1, 4, 5, 6}};
pe.makeExperimentAndSchedule(1, 3, 6, signUpsExperiment1);
// Experiment 2: Example 2 from README, 4 students, 8 steps
int[][] signUpsExperiment2 = {{5, 7, 8}, {2, 3, 4, 5, 6}, {1, 5, 7, 8}, {1, 3, 4, 8}};
pe.makeExperimentAndSchedule(2, 4, 8, signUpsExperiment2);
// Experiment 3: Another test case, 5 students, 11 steps
int[][] signUpsExperiment3 = {{7, 10, 11}, {8, 9, 10}, {2, 3, 4, 5, 7}, {1, 5, 6, 7, 8}, {1, 3, 4, 8}};
pe.makeExperimentAndSchedule(3, 5, 11, signUpsExperiment3);
}
}
You are running a physics experiment with n complicated steps that you must do in order,...
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