#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?=?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?degree）?{
????????firstNode?=?p1;
????????p?=?firstNode;
????????p1?=?p1->sibling;
????}?else?{
????????firstNode?=?p2;
????????p?=?firstNode;
????????p2?=?p2->sibling;
????}

????while?（p1?!=?NULL?&&?p2?!=?NULL）?{
????????if?（p1->degree?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）?{
????????

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????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
?????目錄???????????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
?????目錄???????????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
?????目錄???????????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
?????目錄???????????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
............此處省略23個文件信息