add heap sort

Author: AaronLinRC

src/main/kotlin/sort/HeapSort.kt

@@ -0,0 +1,56 @@
+package sort
+
+import util.swap
+
+/**
+ * 完全二叉树
+ * i 下标的左孩子 2i + 1
+ *        右孩子 2i + 2
+ *        父节点 (i-1)/2
+ */
+object HeapSort {
+    fun sort(array: IntArray) {
+        array.forEachIndexed { index, i ->
+            heapInsert(index, array)
+        }
+        var heapSize = array.size
+        while (heapSize > 0) {
+            array.swap(0, --heapSize)
+            heapify(heapSize, 0, array)
+        }
+    }
+
+    fun heapify(heapSize: Int, index: Int, array: IntArray) {
+        var leftChildIndex = 2 * index + 1
+        var tempIndex = index
+        while (leftChildIndex < heapSize) {
+            val maxChildIndex = if (leftChildIndex + 1 < heapSize) {
+                if (array[leftChildIndex] >= array[leftChildIndex + 1]) leftChildIndex else leftChildIndex + 1
+            } else {
+                leftChildIndex
+            }
+            if (array[tempIndex] > array[maxChildIndex]) {
+                return
+            } else {
+                array.swap(tempIndex, maxChildIndex)
+                tempIndex = maxChildIndex
+                leftChildIndex = 2 * tempIndex + 1
+            }
+        }
+    }
+
+    private fun heapInsert(index: Int, array: IntArray) {
+        var parentIndex = findParent(index)
+        var insertIndex = index
+
+        while (array[parentIndex] < array[insertIndex]) {
+            array.swap(parentIndex, insertIndex)
+            insertIndex = parentIndex
+            parentIndex = findParent(insertIndex)
+        }
+    }
+
+    private fun findParent(index: Int): Int {
+        return (index - 1) / 2
+    }
+}

src/main/kotlin/sort/QuickSort.kt

@@ -5,6 +5,7 @@ import util.swap
 
 // 随机数下，数学期望 NLogN
 // 无随机数情况，最差情况，单调序列 O(n*n) -> 由于划分值打得很偏
+// 空间复杂度 O(N) -> O(logN)
 object QuickSort {
     fun sort(array: IntArray) {
         rec(0, array.lastIndex, array)

src/main/kotlin/sort/TestSort.kt

@@ -59,4 +59,15 @@ class TestSort {
             Assert.assertTrue(array2.sameAs(array1))
         }
     }
+
+    @Test
+    fun testHeap() {
+        repeat(5) {
+            val array1 = Logarithm.generateRandomArray(50, 50)
+            val array2 = array1.clone()
+            array2.sort()
+            HeapSort.sort(array1)
+            Assert.assertTrue(array2.sameAs(array1))
+        }
+    }
 }