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AssignmentUsingBitmask
algorithm (TheAlgorithms#5792)
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src/main/java/com/thealgorithms/dynamicprogramming/AssignmentUsingBitmask.java
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package com.thealgorithms.dynamicprogramming; | ||
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import java.util.ArrayList; | ||
import java.util.Arrays; | ||
import java.util.List; | ||
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/** | ||
* The AssignmentUsingBitmask class is used to calculate the total number of ways | ||
* tasks can be distributed among people, given specific constraints on who can perform which tasks. | ||
* The approach uses bitmasking and dynamic programming to efficiently solve the problem. | ||
* | ||
* @author Hardvan | ||
*/ | ||
public final class AssignmentUsingBitmask { | ||
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private final int totalTasks; | ||
private final int[][] dp; | ||
private final List<List<Integer>> task; | ||
private final int finalMask; | ||
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/** | ||
* Constructor for the AssignmentUsingBitmask class. | ||
* | ||
* @param taskPerformed a list of lists, where each inner list contains the tasks that a person can perform. | ||
* @param total the total number of tasks. | ||
*/ | ||
public AssignmentUsingBitmask(List<List<Integer>> taskPerformed, int total) { | ||
this.totalTasks = total; | ||
this.dp = new int[1 << taskPerformed.size()][total + 1]; | ||
for (int[] row : dp) { | ||
Arrays.fill(row, -1); | ||
} | ||
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this.task = new ArrayList<>(totalTasks + 1); | ||
for (int i = 0; i <= totalTasks; i++) { | ||
this.task.add(new ArrayList<>()); | ||
} | ||
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// Final mask to check if all persons are included | ||
this.finalMask = (1 << taskPerformed.size()) - 1; | ||
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// Fill the task list | ||
for (int i = 0; i < taskPerformed.size(); i++) { | ||
for (int j : taskPerformed.get(i)) { | ||
this.task.get(j).add(i); | ||
} | ||
} | ||
} | ||
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/** | ||
* Counts the ways to assign tasks until the given task number with the specified mask. | ||
* | ||
* @param mask the bitmask representing the current state of assignments. | ||
* @param taskNo the current task number being processed. | ||
* @return the number of ways to assign tasks. | ||
*/ | ||
private int countWaysUntil(int mask, int taskNo) { | ||
if (mask == finalMask) { | ||
return 1; | ||
} | ||
if (taskNo > totalTasks) { | ||
return 0; | ||
} | ||
if (dp[mask][taskNo] != -1) { | ||
return dp[mask][taskNo]; | ||
} | ||
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int totalWays = countWaysUntil(mask, taskNo + 1); | ||
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// Assign tasks to all possible persons | ||
for (int p : task.get(taskNo)) { | ||
// If the person is already assigned a task | ||
if ((mask & (1 << p)) != 0) { | ||
continue; | ||
} | ||
totalWays += countWaysUntil(mask | (1 << p), taskNo + 1); | ||
} | ||
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dp[mask][taskNo] = totalWays; | ||
return dp[mask][taskNo]; | ||
} | ||
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/** | ||
* Counts the total number of ways to distribute tasks among persons. | ||
* | ||
* @return the total number of ways to distribute tasks. | ||
*/ | ||
public int countNoOfWays() { | ||
return countWaysUntil(0, 1); | ||
} | ||
} |
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src/test/java/com/thealgorithms/dynamicprogramming/AssignmentUsingBitmaskTest.java
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package com.thealgorithms.dynamicprogramming; | ||
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import static org.junit.jupiter.api.Assertions.assertEquals; | ||
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import java.util.Arrays; | ||
import java.util.List; | ||
import org.junit.jupiter.api.Test; | ||
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public final class AssignmentUsingBitmaskTest { | ||
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@Test | ||
public void testCountNoOfWays() { | ||
int totalTasks = 5; | ||
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List<List<Integer>> taskPerformed = Arrays.asList(Arrays.asList(1, 3, 4), Arrays.asList(1, 2, 5), Arrays.asList(3, 4)); | ||
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AssignmentUsingBitmask assignment = new AssignmentUsingBitmask(taskPerformed, totalTasks); | ||
int ways = assignment.countNoOfWays(); | ||
assertEquals(10, ways); | ||
} | ||
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@Test | ||
public void testNoPossibleAssignments() { | ||
int totalTasks = 3; | ||
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List<List<Integer>> taskPerformed = Arrays.asList(Arrays.asList(2), Arrays.asList(3)); | ||
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AssignmentUsingBitmask assignment = new AssignmentUsingBitmask(taskPerformed, totalTasks); | ||
int ways = assignment.countNoOfWays(); | ||
assertEquals(1, ways); | ||
} | ||
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@Test | ||
public void testSinglePersonMultipleTasks() { | ||
int totalTasks = 3; | ||
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List<List<Integer>> taskPerformed = Arrays.asList(Arrays.asList(1, 2, 3)); | ||
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AssignmentUsingBitmask assignment = new AssignmentUsingBitmask(taskPerformed, totalTasks); | ||
int ways = assignment.countNoOfWays(); | ||
assertEquals(3, ways); | ||
} | ||
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@Test | ||
public void testMultiplePeopleSingleTask() { | ||
int totalTasks = 1; | ||
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List<List<Integer>> taskPerformed = Arrays.asList(Arrays.asList(1), Arrays.asList(1)); | ||
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AssignmentUsingBitmask assignment = new AssignmentUsingBitmask(taskPerformed, totalTasks); | ||
int ways = assignment.countNoOfWays(); | ||
assertEquals(0, ways); | ||
} | ||
} |