# 3.3.3 - Heap Sort

### 1. 演算法

將{5, 3, 2, 1, 7, 8, 9, 10}

1. 將資料以Bottom-Up方式建立Max-Heap
2. 執行Delete-Max
   1. SWAP(Root, the last node)
   2. 刪除最大值
   3. 將剩下的Heap調整為Max-Heap

![](/files/-LIU-TYCJUzIhttvPr60)

output=10

![](/files/-LIU-dpxD-HW-3ddO8HI)

output=9

![](/files/-LIU-iHkhA6_NeoIsmAf)

```
void HeapSort(char *heap){
    int n = strlen(heap);
    //build heap
    for (int i = n/2-1; i>=0; i--)  //i從最後一個父點開始
        AdjustBottomUp(heap, i, n-1);
    //delete max
    for (int i = n-1;i>0;i--){
        Swap(&heap[0], &heap[i]); //將max移到最後
        for (int j = i/2-1; j>=0; j--)
            AdjustBottomUp(heap, j, i-1);
    }
}
```

### 2. 性質

* Time Complexity: $$O(nlogn)$$ 
  1. 以Bottom-Up建立Heap共花$$O(n)$$ 
  2. 執行Delete-Max，每一回合共花 $$O(logn)$$，共有n回合
* Space Complexity: $$O(1)$$ 

Heap sorting is a **unstable** sorting method.


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