Heapsort algorithm

最新推荐文章于 2022-06-24 22:42:21 发布

citylove

最新推荐文章于 2022-06-24 22:42:21 发布

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分类专栏： my work 文章标签： algorithm subroutine build input numbers structure

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The heap data structure is an array object than can be viewd as a complete binary tree. Heapsort algorithm mainly utilizes the property of the max-heap or min-heap (the program below introduces the max-heap) to sort the array and costs O(nlg n) ,which is asymptotically optimal comparison sort.

Please refer to Introduction to Algorithms to get more details about the heapsort.

/* the purpose of this program is to sort the array by using heap. The subroutine INPUT_ARRAY is to input the numbers of the array. the subroutine MAX_HEAPIFY is to maintain the property of MAX-HEAP by permutating the i node and its children node which ara not consisten with the property of MAX-HEAP. BUILD_MAX-HEAP is used to build a max-heap. Heapsort subroutine converts the heap into the descending sorted array. */ #include<iostream> using namespace std; int *INPUT_ARRAY( int &array_size ) ; void MAX_HEAPIFY( int *A, int i, int heap_size ); void BUILD_MAX_HEAP( int *A , int heap_size ); void HEAPSORT( int *A, int heap_size ); int main() { int heap_size=0, *pArray; pArray = INPUT_ARRAY( heap_size ) ; BUILD_MAX_HEAP( pArray , heap_size ); HEAPSORT( pArray , heap_size ); int i; for( i=0; i < heap_size; i++ ) cout << pArray[i]<<", "; cout << endl; delete [] pArray; return 0; } int *INPUT_ARRAY( int &array_size ) //using array to represent heap { int i; cout << "determine the size of the array :"; cin >> array_size; int *array = new int[array_size]; cout << "input numbers: "; for( i=0; i < array_size; i++ ) cin >> array[i]; cout << endl; return array; } /* warning: the beginning of the array index is 0, not 1 the last index of the array is equal to (heap_size-1), not heap_size */ void MAX_HEAPIFY( int *A, int i, int heap_size ) //maintain the property of max-heap { int l, r, largest; l = 2*i; r = 2*i+1; if( l < heap_size && A[l] > A[i] ) //find the largest number among i node and its children nodes largest = l; else largest = i; if( r < heap_size && A[r] > A[largest] ) largest = r; if( largest != i ) { swap( A[i], A[largest] ); MAX_HEAPIFY( A , largest, heap_size ); } } void BUILD_MAX_HEAP( int *A , int heap_size ) //build max-heap by calling MAX_HEAPIFY function { int i; for( i = (heap_size-1)/2 ; i >= 0; i-- ) MAX_HEAPIFY( A, i, heap_size ); } void HEAPSORT( int *A, int heap_size ) //using heap to sort array { int i; BUILD_MAX_HEAP( A , heap_size ); for( i = heap_size-1; i >=1 ; i-- ) { swap( A[0], A[i] ); heap_size--; MAX_HEAPIFY( A , 0, heap_size ); } }