diff --git a/DIRECTORY.md b/DIRECTORY.md index e7a08a12abac..e511ab40b329 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -262,6 +262,7 @@ * [TilingProblem](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/divideandconquer/TilingProblem.java) * dynamicprogramming * [Abbreviation](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/dynamicprogramming/Abbreviation.java) + * [AssignmentUsingBitmask](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/dynamicprogramming/AssignmentUsingBitmask.java) * [BoardPath](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/dynamicprogramming/BoardPath.java) * [BoundaryFill](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/dynamicprogramming/BoundaryFill.java) * [BruteForceKnapsack](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/dynamicprogramming/BruteForceKnapsack.java) @@ -866,6 +867,7 @@ * [TilingProblemTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/divideandconquer/TilingProblemTest.java) * dynamicprogramming * [AbbreviationTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/AbbreviationTest.java) + * [AssignmentUsingBitmaskTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/AssignmentUsingBitmaskTest.java) * [BoardPathTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/BoardPathTest.java) * [BoundaryFillTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/BoundaryFillTest.java) * [BruteForceKnapsackTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/dynamicprogramming/BruteForceKnapsackTest.java) diff --git a/src/main/java/com/thealgorithms/dynamicprogramming/AssignmentUsingBitmask.java b/src/main/java/com/thealgorithms/dynamicprogramming/AssignmentUsingBitmask.java new file mode 100644 index 000000000000..5a894ca004b7 --- /dev/null +++ b/src/main/java/com/thealgorithms/dynamicprogramming/AssignmentUsingBitmask.java @@ -0,0 +1,91 @@ +package com.thealgorithms.dynamicprogramming; + +import java.util.ArrayList; +import java.util.Arrays; +import java.util.List; + +/** + * 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 { + + private final int totalTasks; + private final int[][] dp; + private final List> task; + private final int finalMask; + + /** + * 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> taskPerformed, int total) { + this.totalTasks = total; + this.dp = new int[1 << taskPerformed.size()][total + 1]; + for (int[] row : dp) { + Arrays.fill(row, -1); + } + + this.task = new ArrayList<>(totalTasks + 1); + for (int i = 0; i <= totalTasks; i++) { + this.task.add(new ArrayList<>()); + } + + // Final mask to check if all persons are included + this.finalMask = (1 << taskPerformed.size()) - 1; + + // Fill the task list + for (int i = 0; i < taskPerformed.size(); i++) { + for (int j : taskPerformed.get(i)) { + this.task.get(j).add(i); + } + } + } + + /** + * 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]; + } + + int totalWays = countWaysUntil(mask, taskNo + 1); + + // 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); + } + + dp[mask][taskNo] = totalWays; + return dp[mask][taskNo]; + } + + /** + * 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); + } +} diff --git a/src/test/java/com/thealgorithms/dynamicprogramming/AssignmentUsingBitmaskTest.java b/src/test/java/com/thealgorithms/dynamicprogramming/AssignmentUsingBitmaskTest.java new file mode 100644 index 000000000000..0258f3950510 --- /dev/null +++ b/src/test/java/com/thealgorithms/dynamicprogramming/AssignmentUsingBitmaskTest.java @@ -0,0 +1,54 @@ +package com.thealgorithms.dynamicprogramming; + +import static org.junit.jupiter.api.Assertions.assertEquals; + +import java.util.Arrays; +import java.util.List; +import org.junit.jupiter.api.Test; + +public final class AssignmentUsingBitmaskTest { + + @Test + public void testCountNoOfWays() { + int totalTasks = 5; + + List> taskPerformed = Arrays.asList(Arrays.asList(1, 3, 4), Arrays.asList(1, 2, 5), Arrays.asList(3, 4)); + + AssignmentUsingBitmask assignment = new AssignmentUsingBitmask(taskPerformed, totalTasks); + int ways = assignment.countNoOfWays(); + assertEquals(10, ways); + } + + @Test + public void testNoPossibleAssignments() { + int totalTasks = 3; + + List> taskPerformed = Arrays.asList(Arrays.asList(2), Arrays.asList(3)); + + AssignmentUsingBitmask assignment = new AssignmentUsingBitmask(taskPerformed, totalTasks); + int ways = assignment.countNoOfWays(); + assertEquals(1, ways); + } + + @Test + public void testSinglePersonMultipleTasks() { + int totalTasks = 3; + + List> taskPerformed = Arrays.asList(Arrays.asList(1, 2, 3)); + + AssignmentUsingBitmask assignment = new AssignmentUsingBitmask(taskPerformed, totalTasks); + int ways = assignment.countNoOfWays(); + assertEquals(3, ways); + } + + @Test + public void testMultiplePeopleSingleTask() { + int totalTasks = 1; + + List> taskPerformed = Arrays.asList(Arrays.asList(1), Arrays.asList(1)); + + AssignmentUsingBitmask assignment = new AssignmentUsingBitmask(taskPerformed, totalTasks); + int ways = assignment.countNoOfWays(); + assertEquals(0, ways); + } +}