Add AssignmentUsingBitmask algorithm (#5792)

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<List<Integer>> 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<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);
+        }
+
+        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);
+    }
+}