feat(sorts): add TournamentSort (winner-tree)

Author: GziXnine

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

@@ -0,0 +1,84 @@
+package com.thealgorithms.sorts;
+
+import java.util.Arrays;
+
+/**
+ * Tournament Sort algorithm implementation.
+ *
+ * Tournament sort builds a winner tree (a complete binary tree storing the index
+ * of the smallest element in each subtree). It then repeatedly extracts the
+ * winner (minimum) and updates the path from the removed leaf to the root.
+ *
+ * Time Complexity:
+ * - Best case: O(n log n)
+ * - Average case: O(n log n)
+ * - Worst case: O(n log n)
+ *
+ * Space Complexity: O(n) – additional winner-tree storage
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Tournament_sort">Tournament Sort Algorithm</a>
+ * @see SortAlgorithm
+ */
+public class TournamentSort implements SortAlgorithm {
+
+    @Override
+    public <T extends Comparable<T>> T[] sort(T[] array) {
+        if (array == null || array.length < 2) {
+            return array;
+        }
+
+        final int n = array.length;
+        final int leafCount = nextPowerOfTwo(n);
+
+        // Winner tree represented as an array:
+        // - Leaves live at [leafCount .. 2*leafCount)
+        // - Internal nodes live at [1 .. leafCount)
+        // Each node stores an index into the original array or -1 for "empty".
+        final int[] tree = new int[2 * leafCount];
+        Arrays.fill(tree, -1);
+
+        for (int i = 0; i < n; i++) {
+            tree[leafCount + i] = i;
+        }
+
+        for (int node = leafCount - 1; node >= 1; node--) {
+            tree[node] = winnerIndex(array, tree[node * 2], tree[node * 2 + 1]);
+        }
+
+        final T[] result = array.clone();
+        for (int out = 0; out < n; out++) {
+            final int winner = tree[1];
+            result[out] = array[winner];
+
+            int node = leafCount + winner;
+            tree[node] = -1;
+
+            for (node /= 2; node >= 1; node /= 2) {
+                tree[node] = winnerIndex(array, tree[node * 2], tree[node * 2 + 1]);
+            }
+        }
+
+        System.arraycopy(result, 0, array, 0, n);
+        return array;
+    }
+
+    private static int nextPowerOfTwo(int n) {
+        int power = 1;
+        while (power < n) {
+            power <<= 1;
+        }
+        return power;
+    }
+
+    private static <T extends Comparable<T>> int winnerIndex(T[] array, int leftIndex, int rightIndex) {
+        if (leftIndex == -1) {
+            return rightIndex;
+        }
+        if (rightIndex == -1) {
+            return leftIndex;
+        }
+
+        // If equal, prefer the left element to keep ordering deterministic.
+        return SortUtils.less(array[rightIndex], array[leftIndex]) ? rightIndex : leftIndex;
+    }
+}

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

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+package com.thealgorithms.sorts;
+
+public class TournamentSortTest extends SortingAlgorithmTest {
+
+    @Override
+    SortAlgorithm getSortAlgorithm() {
+        return new TournamentSort();
+    }
+}