feat: add PatienceSort (#5288)

* feat: PatienceSort

* refactor: fix readability issues,a and redundant check

---------

Co-authored-by: alxklm <alx@alx.com>

DIRECTORY.md

@@ -511,6 +511,7 @@
             * [MergeSortRecursive](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/MergeSortRecursive.java)
             * [OddEvenSort](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/OddEvenSort.java)
             * [PancakeSort](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/PancakeSort.java)
+            * [PatienceSort](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/PatienceSort.java)
             * [PigeonholeSort](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/PigeonholeSort.java)
             * [QuickSort](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/QuickSort.java)
             * [RadixSort](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/sorts/RadixSort.java)
@@ -881,6 +882,7 @@
             * [MergeSortTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/sorts/MergeSortTest.java)
             * [OddEvenSortTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/sorts/OddEvenSortTest.java)
             * [PancakeSortTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/sorts/PancakeSortTest.java)
+            * [PatienceSortTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/sorts/PatienceSortTest.java)
             * [QuickSortTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/sorts/QuickSortTest.java)
             * [RadixSortTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/sorts/RadixSortTest.java)
             * [SelectionSortRecursiveTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/sorts/SelectionSortRecursiveTest.java)

src/main/java/com/thealgorithms/sorts/PatienceSort.java

@@ -0,0 +1,112 @@
+package com.thealgorithms.sorts;
+
+import java.util.ArrayList;
+import java.util.Collections;
+import java.util.List;
+import java.util.PriorityQueue;
+
+/**
+ * This class implements the Patience Sort algorithm. Patience Sort is a sorting algorithm that
+ * is particularly good for sorting sequences that are already partially sorted.
+ */
+public class PatienceSort implements SortAlgorithm {
+
+    /**
+     * Sorts an array of comparable elements using the Patience Sort algorithm.
+     *
+     * @param array the array to be sorted
+     * @param <T> the type of elements in the array, must be comparable
+     * @return the sorted array
+     */
+    @Override
+    public <T extends Comparable<T>> T[] sort(T[] array) {
+        if (array.length == 0) {
+            return array;
+        }
+
+        final List<List<T>> piles = formPiles(array);
+        final PriorityQueue<PileNode<T>> pq = mergePiles(piles);
+        extractPiles(array, pq);
+
+        return array;
+    }
+
+    /**
+     * Forms piles from the given array. Each pile is a list of elements where
+     * each element is smaller than the one before it. Binary search is used
+     * to find the appropriate pile for each element.
+     *
+     * @param array the array of elements to be organized into piles
+     * @param <T> the type of elements in the array, must be comparable
+     * @return a list of piles
+     */
+    private static <T extends Comparable<T>> List<List<T>> formPiles(final T[] array) {
+        final List<List<T>> piles = new ArrayList<>();
+        final List<T> lastElements = new ArrayList<>();
+
+        for (T x : array) {
+            int pos = Collections.binarySearch(lastElements, x);
+            if (pos < 0) {
+                pos = -pos - 1;
+            }
+
+            if (pos < piles.size()) {
+                piles.get(pos).add(x);
+                lastElements.set(pos, x);
+            } else {
+                List<T> newPile = new ArrayList<>();
+                newPile.add(x);
+                piles.add(newPile);
+                lastElements.add(x);
+            }
+        }
+
+        return piles;
+    }
+
+    /**
+     * Merges the piles into a priority queue where the smallest elements are
+     * prioritized.
+     *
+     * @param piles the list of piles to be merged
+     * @param <T> the type of elements in the piles, must be comparable
+     * @return a priority queue containing the top element of each pile
+     */
+    private static <T extends Comparable<T>> PriorityQueue<PileNode<T>> mergePiles(final List<List<T>> piles) {
+        PriorityQueue<PileNode<T>> pq = new PriorityQueue<>();
+        for (List<T> pile : piles) {
+            pq.add(new PileNode<>(pile.removeLast(), pile));
+        }
+        return pq;
+    }
+
+    /**
+     * Extracts elements from the priority queue to form the sorted array.
+     *
+     * @param array the array to be filled with sorted elements
+     * @param pq the priority queue containing the elements to be extracted
+     * @param <T> the type of elements in the array, must be comparable
+     */
+    private static <T extends Comparable<T>> void extractPiles(final T[] array, final PriorityQueue<PileNode<T>> pq) {
+        int index = 0;
+        while (!pq.isEmpty()) {
+            PileNode<T> node = pq.poll();
+            array[index++] = node.value;
+            if (!node.pile.isEmpty()) {
+                pq.add(new PileNode<>(node.pile.removeLast(), node.pile));
+            }
+        }
+    }
+
+    /**
+     * A helper record representing a node in the priority queue.
+     *
+     * @param <T> the type of elements in the node, must be comparable
+     */
+    private record PileNode<T extends Comparable<T>>(T value, List<T> pile) implements Comparable<PileNode<T>> {
+        @Override
+        public int compareTo(PileNode<T> other) {
+            return this.value.compareTo(other.value);
+        }
+    }
+}

src/test/java/com/thealgorithms/sorts/PatienceSortTest.java

@@ -0,0 +1,8 @@
+package com.thealgorithms.sorts;
+
+public class PatienceSortTest extends SortingAlgorithmTest {
+    @Override
+    SortAlgorithm getSortAlgorithm() {
+        return new PatienceSort();
+    }
+}