堆排序

 

template<typename Item>
class MaxHeap{

private:
    Item *data;
    int count;
    int capacity;

    void shiftUp(int k){
        while( k > 1 && data[k/2] < data[k] ){
            swap( data[k/2], data[k] );
            k /= 2;
        }
    }

public:

    MaxHeap(int capacity){
        data = new Item[capacity+1];
        count = 0;
        this->capacity = capacity;
    }

    ~MaxHeap(){
        delete[] data;
    }

    int size(){
        return count;
    }

    bool isEmpty(){
        return count == 0;
    }

　　//添加新元素
    void insert(Item item){
        assert( count + 1 <= capacity );
        data[count+1] = item;
        count ++;
        shiftUp(count);
    }


public:
    void testPrint(){

        if( size() >= 100 ){
            cout<<"Fancy print can only work for less than 100 int";
            return;
        }

        if( typeid(Item) != typeid(int) ){
            cout <<"Fancy print can only work for int item";
            return;
        }

        cout<<"The Heap size is: "<<size()<<endl;
        cout<<"data in heap: ";
        for( int i = 1 ; i <= size() ; i ++ )
            cout<<data[i]<<" ";
        cout<<endl;
        cout<<endl;

        int n = size();
        int max_level = 0;
        int number_per_level = 1;
        while( n > 0 ) {
            max_level += 1;
            n -= number_per_level;
            number_per_level *= 2;
        }

        int max_level_number = int(pow(2, max_level-1));
        int cur_tree_max_level_number = max_level_number;
        int index = 1;
        for( int level = 0 ; level < max_level ; level ++ ){
            string line1 = string(max_level_number*3-1, ' ');

            int cur_level_number = min(count-int(pow(2,level))+1,int(pow(2,level)));
            bool isLeft = true;
            for( int index_cur_level = 0 ; index_cur_level < cur_level_number ; index ++ , index_cur_level ++ ){
                putNumberInLine( data[index] , line1 , index_cur_level , cur_tree_max_level_number*3-1 , isLeft );
                isLeft = !isLeft;
            }
            cout<<line1<<endl;

            if( level == max_level - 1 )
                break;

            string line2 = string(max_level_number*3-1, ' ');
            for( int index_cur_level = 0 ; index_cur_level < cur_level_number ; index_cur_level ++ )
                putBranchInLine( line2 , index_cur_level , cur_tree_max_level_number*3-1 );
            cout<<line2<<endl;

            cur_tree_max_level_number /= 2;
        }
    }

private:
    void putNumberInLine( int num, string &line, int index_cur_level, int cur_tree_width, bool isLeft){

        int sub_tree_width = (cur_tree_width - 1) / 2;
        int offset = index_cur_level * (cur_tree_width+1) + sub_tree_width;
        assert(offset + 1 < line.size());
        if( num >= 10 ) {
            line[offset + 0] = '0' + num / 10;
            line[offset + 1] = '0' + num % 10;
        }
        else{
            if( isLeft)
                line[offset + 0] = '0' + num;
            else
                line[offset + 1] = '0' + num;
        }
    }

    void putBranchInLine( string &line, int index_cur_level, int cur_tree_width){

        int sub_tree_width = (cur_tree_width - 1) / 2;
        int sub_sub_tree_width = (sub_tree_width - 1) / 2;
        int offset_left = index_cur_level * (cur_tree_width+1) + sub_sub_tree_width;
        assert( offset_left + 1 < line.size() );
        int offset_right = index_cur_level * (cur_tree_width+1) + sub_tree_width + 1 + sub_sub_tree_width;
        assert( offset_right < line.size() );

        line[offset_left + 1] = '/';
        line[offset_right + 0] = '\';
    }
};

 

   
public:
//获取优先级最高的节点
    Item extractMax(){
        assert( count > 0 );
        Item ret = data[1];

        swap( data[1] , data[count] );
        count --;
        shiftDown(1);

        return ret;
    }

    Item getMax(){
        assert( count > 0 );
        return data[1];
    }

private
    void shiftDown(int k){
        while( 2*k <= count ){
            int j = 2*k; // 在此轮循环中,data[k]和data[j]交换位置
            if( j+1 <= count && data[j+1] > data[j] )
                j ++;
            // data[j] 是 data[2*k]和data[2*k+1]中的最大值

            if( data[k] >= data[j] ) break;
            swap( data[k] , data[j] );
            k = j;
        }
    }

//测试
int main() {

    MaxHeap<int> maxheap = MaxHeap<int>(100);

    srand(time(NULL));
    for( int i = 0 ; i < 63 ; i ++ ){
        maxheap.insert( rand()%100 );
    }

    while( !maxheap.isEmpty() )
        cout<<maxheap.extractMax()<<" ";
    cout<<endl;

    return 0;
}

堆排序：

template<typename T>
void heapSort2(T arr[], int n){

    MaxHeap<T> maxheap = MaxHeap<T>(arr,n);
    for( int i = n-1 ; i >= 0 ; i-- )
        arr[i] = maxheap.extractMax();

}

测试：

int main() {

    int n = 1000000;

    // 测试1 一般性测试
    cout<<"Test for Random Array, size = "<<n<<", random range [0, "<<n<<"]"<<endl;
    int* arr1 = SortTestHelper::generateRandomArray(n,0,n);
    int* arr2 = SortTestHelper::copyIntArray(arr1, n);
    int* arr3 = SortTestHelper::copyIntArray(arr1, n);
    int* arr4 = SortTestHelper::copyIntArray(arr1, n);
    int* arr5 = SortTestHelper::copyIntArray(arr1, n);

    SortTestHelper::testSort("Merge Sort", mergeSort, arr1, n);
    SortTestHelper::testSort("Quick Sort", quickSort, arr2, n);
    SortTestHelper::testSort("Quick Sort 3 Ways", quickSort3Ways, arr3, n);
    SortTestHelper::testSort("Heap Sort 1", heapSort1, arr4, n);
    SortTestHelper::testSort("Heap Sort 2", heapSort2, arr5, n);

    delete[] arr1;
    delete[] arr2;
    delete[] arr3;
    delete[] arr4;
    delete[] arr5;

    cout<<endl;


    // 测试2 测试近乎有序的数组
    int swapTimes = 100;
    cout<<"Test for Random Nearly Ordered Array, size = "<<n<<", swap time = "<<swapTimes<<endl;
    arr1 = SortTestHelper::generateNearlyOrderedArray(n,swapTimes);
    arr2 = SortTestHelper::copyIntArray(arr1, n);
    arr3 = SortTestHelper::copyIntArray(arr1, n);
    arr4 = SortTestHelper::copyIntArray(arr1, n);
    arr5 = SortTestHelper::copyIntArray(arr1, n);

    SortTestHelper::testSort("Merge Sort", mergeSort, arr1, n);
    SortTestHelper::testSort("Quick Sort", quickSort, arr2, n);
    SortTestHelper::testSort("Quick Sort 3 Ways", quickSort3Ways, arr3, n);
    SortTestHelper::testSort("Heap Sort 1", heapSort1, arr4, n);
    SortTestHelper::testSort("Heap Sort 2", heapSort2, arr5, n);

    delete[] arr1;
    delete[] arr2;
    delete[] arr3;
    delete[] arr4;
    delete[] arr5;

    cout<<endl;


    // 测试3 测试存在包含大量相同元素的数组
    cout<<"Test for Random Array, size = "<<n<<", random range [0,10]"<<endl;
    arr1 = SortTestHelper::generateRandomArray(n,0,10);
    arr2 = SortTestHelper::copyIntArray(arr1, n);
    arr3 = SortTestHelper::copyIntArray(arr1, n);
    arr4 = SortTestHelper::copyIntArray(arr1, n);
    arr5 = SortTestHelper::copyIntArray(arr1, n);

    SortTestHelper::testSort("Merge Sort", mergeSort, arr1, n);
    SortTestHelper::testSort("Quick Sort", quickSort, arr2, n);
    SortTestHelper::testSort("Quick Sort 3 Ways", quickSort3Ways, arr3, n);
    SortTestHelper::testSort("Heap Sort 1", heapSort1, arr4, n);
    SortTestHelper::testSort("Heap Sort 2", heapSort2, arr5, n);

    delete[] arr1;
    delete[] arr2;
    delete[] arr3;
    delete[] arr4;
    delete[] arr5;

    return 0;
}

改进：

public:

    MaxHeap(int capacity){
        data = new Item[capacity+1];
        count = 0;
        this->capacity = capacity;
    }

    MaxHeap(Item arr[], int n){
        data = new Item[n+1];
        capacity = n;

        for( int i = 0 ; i < n ; i ++ )
            data[i+1] = arr[i];
        count = n;

        for( int i = count/2 ; i >= 1 ; i -- )
            shiftDown(i);
    }

template<typename T>
void heapSort2(T arr[], int n){

    MaxHeap<T> maxheap = MaxHeap<T>(arr,n);
    for( int i = n-1 ; i >= 0 ; i-- )
        arr[i] = maxheap.extractMax();

}