- ="alt">="keyword">voidPr
- {="comment">//输出所有点集
_vec_vec
="alt">="keyword">for(="datatypes"> - { ="alt">="keyword">for(="datatypes">
- { ="alt">cout<<
- } ="alt">cout<<endl;
- } ="alt">}
- ="keyword">voidKruskal(K_Chart*K,P_Chart&E) ="alt">{="comment">/*构造最小生成树
- ="comment">输入:加权连通图K ="alt">="comment">输出:E
- ="keyword">for(="datatypes">i=0;i<E.pos;i
)
="alt">{
- E.flag[i]=="keyword">false; ="alt">="keyword">for(="datatypes">
- { ="alt">E.A[j][i]=E.A[i][j]=INT_MAX;
- } ="alt">}
- MSort(K,K,0,K_i-1); ="alt">="datatypes">
- ="datatypes">P1;
="alt">="datatypes">
- ="keyword">do ="alt">{
- P1=K[k].po.P1;
="alt">P2=K[k].po
- ="alt">="keyword">
- { ="alt">E.flag[P1]=="keyword">true;
- E.flag[P2]=="keyword">true; ="alt">
- _vec.push_back(P1);
="alt">
- _vec_vec.push_back(_vec);
="alt">
- counter;
="alt">distance_K
- } ="alt">="keyword">
- { ="alt">="keyword">
- { ="alt">="datatypes">
- ="alt">="keyword">
- { ="alt">E.flag[P1]=="keyword">true;
- ="comment">// ="alt">i=Find_i(P2);
- _vec_vec[i].push_back(P1);
="alt">}
- ="keyword">
="comment">//
(E.flag[P2]
false)
="alt">{
- E.flag[P2]=
="keyword">true;
="alt">="comment">//
- i=Find_i(P1); ="alt">
- } ="alt">distance_K
- counter;
="alt">}
- ="keyword">="comment">//(E.flag[P1]true&&E.flag[P2]true)
="alt">{
- ="datatypes">P1_i=Find_i(P1);
="alt">="datatypes">
- ="keyword">(P1_i!=P2_i)
="alt">{
- ="keyword">(_vec_vec[P1_i].size
>_vec_vec[P2_i].size)
="alt">{
- ="keyword">for(="datatypes">i=0;i<_vec_vec[P2_i].size;i)
="alt">{
- _vec_vec[P1_i].push_back(_vec_vec[P2_i][i]);
="alt">}
- _vec_vec.erase(_vec_vec.begin+P2_i);="comment">//删除点集
="alt">}
- ="keyword">
="alt">{
- ="keyword">for(="datatypes">i=0;i<_vec_vec[P1_i].size;i)
="alt">{
- _vec_vec[P2_i].push_back(_vec_vec[P1_i][i]);
="alt">}
- _vec_vec.erase(_vec_vec.begin+P1_i);="comment">//删除点集
="alt">}
- distance_K
E.A[P1][P2]=E.A[P2][P1]=K[k].value;
="alt">counter - } ="alt">}
- } ="alt">k
- }="keyword">while(counter<E.pos-1);
="alt">="keyword">
- } ="alt">="comment">//为G
- ="keyword">voidInit_P_Chart(="datatypes">pos)
="alt">{
- ="comment">//为G
EK申请空间
="alt">G.A=="keyword"> - E.A=="keyword">
="datatypes">*[pos];
="alt">G.flag=="keyword"> - E.flag=="keyword">="datatypes">bool[pos];
="alt">K=="keyword">
- ="alt">E.po
- ="alt">="keyword">for
- { ="alt">G.A[i]=="keyword">
- E.A[i]=="keyword">="datatypes">[pos];
="alt">G.flag[i]=E.flag[i]=="keyword">false;
- } ="alt">="comment">////为G,E,K
- K_i=0; ="alt">
- ="keyword">for(i=0;i<pos;i)
="alt">="keyword">for(="datatypes">
- { ="alt">E.A[j][i]=E.A[i][j]=INT_MAX;
- ="keyword">(ij)
="alt">{
- G.A[j][i]=G.A[i][j]=0; ="alt">="comment">//continue;
- }="comment">/**/ ="alt">="keyword">
- { ="alt">K[K_i].value=G.A[j][i]=G.A[i][j]=rand
- K[K_i].po.P1=i;
="alt">K[K_i
- } ="alt">
- } ="alt">
- } ="alt">="comment">//释放图
- ="keyword">voidDelete_Chart(="datatypes">pos)
="alt">{
- ="keyword">for(="datatypes">i=0;i<pos;i)
="alt">{
- ="keyword">delete
G.A[i];
="alt">="keyword">delete - } ="alt">="keyword">delete
- ="keyword">deleteG.A;
="alt">="keyword">delete
- ="alt">}
- ="comment">//输出图P,图K ="alt">="keyword">voidPr
- { ="alt">cout<<="
- ="keyword">for(="datatypes">i=0;i<G.pos;i)
="alt">{
- cout<<="
">"";
="alt">="keyword">for(="datatypes"> - { ="alt">="keyword">
- cout<<="">"∞"<<="">"";
="alt">="keyword">
- cout<<G.A[i][j]<<="">"";
="alt">}
- cout<<endl; ="alt">}
- ="comment">/* ="alt">="comment">for(i=0;i<K_i;i
- ="comment">{ ="alt">="comment">cout<<""<<K[i].po
- ="comment">} ="alt">="comment">*/
- } ="alt">
- { ="alt">="datatypes">time_tt;
- srand((unsigned)time(&t)); ="alt">
- ="datatypes">charc; ="alt">="keyword">do
- { ="alt">="comment">//清空
- _vec_vec.clear;
="alt">distance_P=0;
- distance_K=0; ="alt">="datatypes">
- ="keyword">do ="alt">{
- system(="">"cls");
="alt">cout<<="
- cin>>pos;
="alt">}="keyword">while(po
- ="comment">//为GE申请空间且
化、、、
="alt">Init_P_Chart(po - Pr_P_Chart(G,K);
="alt">Prim(G,E);="comment">//
- cout<<="">"\n以上生成树由Prim算法求得最小生成树为(如下):";="comment">//
="alt">Pr
- cout<<="">"以上最小生成树路径长度:"<<distance_P<<endl;="comment">//
="alt">Kruskal(K,E);
- cout<<="">"\n以上生成树由Kruskal算法求得最小生成树为(如下):";="comment">//
="alt">Pr
- cout<<="">"以上最小生成树路径长度:"
<<distance_K<<endl;="comment">//
="alt">Delete_Chart(po - cout<<="">"\n\n!!!按任意键继续Esc退出
!!!"<<endl;
="alt">}="keyword">while((c=getch - ="keyword">
;
="alt">}
_Vec
i=0;i<_vec_vec.size;i)
j=0;j<_vec_vec[i].size;j)
_vec_vec[i][j]<<="">"";
Kruskal算法
组成G最小生成树边集合*/
j=i;j<E.pos;j)
k=0,counter=0;
P2;
.P2;
(E.flag[P1]="keyword">false&&E.flag[P2]
="keyword">false)
_vec.clear;
_vec.push_back(P2);
E.A[P1][P2]=E.A[P2][P1]=K[k].value;
(E.flag[P1]="keyword">false||E.flag[P2]="keyword">false)
i;
(E.flag[P1]="keyword">false)
_vec_vec[i].push_back(P2);
E.A[P1][P2]=E.A[P2][P1]=K[k].value;
P2_i=Find_i(P2);
;
;
;
EK申请空间且化、、、
="datatypes">*[pos];
="datatypes">bool[pos];
K_Chart[pos*(pos-1)/2];
s=G.pos=pos;
(="datatypes">
i=0;i<pos;i)
="datatypes">[pos];
化、、、
j=i;j<pos;j)
%20+1;
].po.P2=j;
空间GEK
E.A[i];
K;
E.A;
_P_Chart(="keyword">constP_Chart&G,="keyword">constK_Chart*K)
">"\n\n";
j=0;j<G.pos;j)
(G.A[i][j]INT_MAX)
)
.P1<<"--"<<K[i].po.P2<<":"<<K[i].value<<endl;
="keyword">void
化
pos;
">"\n\n\n请输入生成树点数(>0):";
s<=0);
s);
_P_Chart(E,K);="comment">//
_P_Chart(E,K);
s);
)!=27);
应用 1．实验题目
用 kruskal 算法和 prim算法构造任意
个无向图最小生成树
2．实验目
1)掌握最小生成树
概念及其基本性质； 2)掌握最优子结构性质
证明思路方法； 3)掌握贪心法
设计思想并能熟练运用 3．实验要求
1)证明最小生成树满足最优子结构性质；
2)实现 kruskal和 prim算法；
3)设计测试数据
对上述两个算法进行效率比较数据结构:
/*定义用于Prim算法求解最小生成树结构体:
flag
标志对应点是否加入最小生成树(点)集合A[i][j]
存放点i到点j权重 po
s记录该最小生成树点数 */typedef struct P_Chart
{
bool *flag ;
**A ; pos ;} P_Chart ;
//存放
条边两个点typedef struct Po
{
P1 ; P2 ;} Po
;/*定义用于Kruskal算法求解最小生成树结构体:
value
记录边权重po
存放该边两个点*/typedef struct K_Chart
{
value ;Po
po ;} K_Chart ;
//存放点
集合--向量typedef vector<
> Int_Vec ;//存放点集
集合--(向量)向量typedef vector<Int_Vec> Int_Vec_Vec ;//
声明://为G
E K申请空间且化、、、void Init_P_Chart(
pos)//释放图
空间G E K void Delete_Chart(
pos)//输出图P ,图K
void Pr
_P_Chart(const P_Chart& G ,const K_Chart *K )/*构造最小生成树
Prim算法输入:加权连通图 G
输出:E
组成 G 最小生成树边集合 *///
化最小生成树顶点集合void Prim( P_Chart& G ,P_Chart& E )
// 将K1[s..t]归并排序为K2[s..t]
void MSort( K_Chart *K1 ,K_Chart *K2 ,
s, t) //查找点po
在哪个点集集合_vec_vec哪个点集//查找成功返回该点集位置
否则返回-1 Find_i( po )void Kruskal( K_Chart *K ,P_Chart& E )
{/*构造最小生成树
Kruskal算法输入:加权连通图 K
输出:E
组成 G 最小生成树边集合 */void Kruskal( K_Chart *K ,P_Chart& E )
{/*构造最小生成树
Kruskal算法输入:加权连通图 K
输出:E
组成 G 最小生成树边集合 */// 将K1[s..t]归并排序为K2[s..t]
void MSort( K_Chart *K1 ,K_Chart *K2 ,
s, t) //查找点po
在哪个点集集合_vec_vec哪个点集//查找成功返回该点集位置
否则返回-1 Find_i( po ) /*构造最小生成树
Kruskal算法输入:加权连通图 K
输出:E
组成 G 最小生成树边集合 */void Kruskal( K_Chart *K ,P_Chart& E )
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