二项堆Binomial Heap

二项堆（Binomial Heap）的c语言完全实现，包括添加，删除，和找到最小值，删除最小值

#include 
#include 
#include “queue.h“
typedef int ElemType;

// basic structure of binomial heap
typedef struct Node {
    ElemType key;
    int degree;
    struct Node *p;
    struct Node *child;
    struct Node *sibling;
}Node;

// the head of binomial heap
typedef struct heap{
    Node * head;
}*BinomialHeap;

// generate a node valuing key
Node * generateNode（ElemType key） {
    Node * x = （Node *） malloc（sizeof（Node））;
    if （x == NULL） {
        printf（“memory allocation of node failed“）;
        exit（-1）;
    }
    x->key = key;
    x->p = NULL;
    x->child = NULL;
    x->sibling = NULL;
    x->degree = 0;
    return x;
}
// generate an empty binomial heap
BinomialHeap makeBinomialHeap（） {
    BinomialHeap h = （BinomialHeap） malloc（sizeof（struct heap））;
    if（!h） {
        printf（“the memory allocation of heap failed!\n“）;
        exit（-1）;
    }
    h->head = NULL;
    return h;
}

// find the minimum key from the binomial heap
// and return thr minimum node‘s pointer
Node * binomialHeapMinimum（BinomialHeap h） {
    Node * y = NULL;
    Node * x = h->head;
    if（x != NULL） {
        int min = x->key;
        y = x;
        x = x->sibling;
        while （x != NULL） {
            if（x->key < min） {
                min = x->key;
                y = x;
            }
            x = x->sibling;
        }
    }
    return y;
}

// links the Bk-1 tree rooted at node y to the Bk-1 tree
// rooted at node z; that is it makes z the parent of y.
// Node z thus becomes the root of a Bk tree
void binomiallink（Node * y Node *z） {
    y->p = z;
    y->sibling = z->child;
    z->child = y;
    z->degree += 1;
}

// merge the root lists of h1 and h2 into a single linked list
// that is sorted into monotonically increasing order.
Node * binomialMerge（BinomialHeap h1 BinomialHeap h2） {
    Node * firstNode = NULL;
    Node * p = NULL;
    Node * p1 = h1->head;
    Node * p2 = h2->head;
    if （p1 == NULL || p2 == NULL） {
        if（p1 == NULL） {
            firstNode = p2;
        } else {
            firstNode = p1;
        }
        return firstNode;
    }

    if （p1->degree < p2->degree） {
        firstNode = p1;
        p = firstNode;
        p1 = p1->sibling;
    } else {
        firstNode = p2;
        p = firstNode;
        p2 = p2->sibling;
    }

    while （p1 != NULL && p2 != NULL） {
        if （p1->degree < p2->degree） {
            p->sibling = p1;
            p = p1;
            p1 = p1->sibling;
        } else {
            p->sibling = p2;
            p = p2;
            p2 = p2->sibling;
        }
    }
    if （p1 != NULL） {
        p->sibling = p1;
    } else {
        p->sibling = p2;
    }
    return firstNode;
}

// unite heaps h1 and h2 returning the resulting heap.
BinomialHeap binomialHeapUnion（BinomialHeap *h1 BinomialHeap *h2） {
    BinomialHeap h = makeBinomialHeap（）;
    h->head = binomialMerge（*h1 *h2）;
    free（*h1）;
    *h1 = NULL;
    free（*h2）;
    *h2 = NULL;

    if （h->head == NULL） {
        

 属性            大小     日期    时间   名称
----------- ---------  ---------- -----  ----
     目录           0  2017-02-18 03:08  BinomialHeap\
     文件        6691  2017-02-18 03:08  BinomialHeap\main.c
     文件         443  2017-02-17 06:28  BinomialHeap\queue.h
     文件         170  2017-02-17 05:48  BinomialHeap\CMakeLists.txt
     文件        1251  2017-02-17 06:36  BinomialHeap\queue.c
     目录           0  2017-02-18 03:08  BinomialHeap\cmake-build-debug\
     文件       17550  2017-02-18 03:08  BinomialHeap\cmake-build-debug\BinomialHeap
     文件        1416  2017-02-17 00:55  BinomialHeap\cmake-build-debug\cmake_install.cmake
     文件        6072  2017-02-17 05:48  BinomialHeap\cmake-build-debug\BinomialHeap.cbp
     文件        5702  2017-02-17 05:48  BinomialHeap\cmake-build-debug\Makefile
     文件       32184  2017-02-17 00:55  BinomialHeap\cmake-build-debug\CMakeCache.txt
     目录           0  2017-02-18 03:09  BinomialHeap\.idea\
     文件       24585  2017-02-18 03:09  BinomialHeap\.idea\workspace.xml
     文件         137  2017-02-17 00:57  BinomialHeap\.idea\misc.xml
     文件          97  2017-02-17 00:57  BinomialHeap\.idea\BinomialHeap.iml
     文件         276  2017-02-17 00:55  BinomialHeap\.idea\modules.xml
     目录           0  2017-02-18 03:08  BinomialHeap\cmake-build-debug\CMakeFiles\
     文件       12612  2017-02-17 00:55  BinomialHeap\cmake-build-debug\CMakeFiles\feature_tests.bin
     文件         282  2017-02-17 05:48  BinomialHeap\cmake-build-debug\CMakeFiles\clion-log.txt
     文件        2449  2017-02-17 05:48  BinomialHeap\cmake-build-debug\CMakeFiles\Makefile.cmake
     文件        3416  2017-02-17 05:48  BinomialHeap\cmake-build-debug\CMakeFiles\Makefile2
     文件           2  2017-02-17 05:48  BinomialHeap\cmake-build-debug\CMakeFiles\progress.marks
     文件         675  2017-02-17 00:55  BinomialHeap\cmake-build-debug\CMakeFiles\CMakeDirectoryInformation.cmake
     文件          85  2017-02-17 05:48  BinomialHeap\cmake-build-debug\CMakeFiles\cmake.check_cache
     文件       10011  2017-02-17 00:55  BinomialHeap\cmake-build-debug\CMakeFiles\feature_tests.cxx
     文件         688  2017-02-17 00:55  BinomialHeap\cmake-build-debug\CMakeFiles\feature_tests.c
     文件       40161  2017-02-17 00:55  BinomialHeap\cmake-build-debug\CMakeFiles\CMakeOutput.log
     文件          59  2017-02-17 05:48  BinomialHeap\cmake-build-debug\CMakeFiles\clion-environment.txt
     文件         263  2017-02-17 05:48  BinomialHeap\cmake-build-debug\CMakeFiles\TargetDirectories.txt
     目录           0  2017-02-18 03:08  BinomialHeap\cmake-build-debug\CMakeFiles\BinomialHeap.dir\
     文件        5744  2017-02-17 06:36  BinomialHeap\cmake-build-debug\CMakeFiles\BinomialHeap.dir\queue.c.o
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