数据结构 --线性表
一直觉得数据结构是很好的东西，早就说要看，直到现在才静下心来。
下面就从简单的线性表开始，慢慢学习吧。
线性表综合运用：
约瑟夫循环：设有n个人围坐在一个圆桌周围，现在从第s个人开始报数，数到第m的人出列，然后从出列的人下一个人重新开始报数，数到第m的人出列......如此反复直到所有的人全部出列为止。约瑟夫循环问题是：对于任意给定的n,s和m,求出按出列次序得到的n个人员的序列。
1.顺表表实现（数组）
1 // Josephus-seqList.cpp : 定义控制台应用程序的入口点。
2 //
3
4 #include "stdafx.h"
5 #include <stdlib.h>
6 #include <malloc.h>
7 #define MAXNUM 100
8 #define FALSE 0
9 #define TRUE 1
10 #define SPECIAL 2147483647
11 typedef int DataType;
12
13 struct SeqList
14 {
15 DataType element[MAXNUM];
16 int n;
17 };
18
19 typedef struct SeqList* PSeqList;
20
21 PSeqList createNullList_seq(void)
22 {
23 PSeqList palist;
24 palist = (PSeqList)malloc(sizeof(struct SeqList));
25 if(palist != NULL)
26 {
27 palist->n = 0;
28 }
29 else
30 {
31 printf("Out of space!!\n");
32 }
33 return(palist);
34 }
35
36 int insert_seq(PSeqList palist, int p, DataType x)
37 {
38 int q;
39 if(palist->n == MAXNUM)
40 {
41 printf("Overflow!\n");
42 return(FALSE);
43 }
44 if(p < 0 || p > palist->n)
45 {
46 printf("Not exist!\n");
47 return(FALSE);
48 }
49 for(q = palist->n - 1; q >= p; q--)
50 {
51 palist->element[q + 1] = palist->element[q];
52 }
53 palist->element[p] = x;
54 palist->n += 1;
55 return(TRUE);
56 }
57
58 int delete_seq(PSeqList palist, int p)
59 {
60 int q;
61 if(p < 0 || p > palist->n - 1)
62 {
63 printf("Not exist!\n");
64 return(FALSE);
65 }
66 for(q = p; q < palist->n - 1; q++)
67 {
68 palist->element[q] = palist->element[q + 1];
69 }
70 palist->n = palist->n - 1;
71 return(TRUE);
72 }
73
74 int locate_seq(PSeqList palist, DataType x)
75 {
76 int q;
77 for(q = 0; q < palist->n; q++)
78 {
79 if(palist->element[q] == x)
80 return(q);
81 }
82 return (-1);
83 }
84
85 DataType retrieve_seq(PSeqList palist, int p)
86 {
87 if(p >= 0 && p < palist->n)
88 {
89 return(palist->element[p]);
90 }
91 printf("Not exist.\n");
92 return(SPECIAL);
93 }
94
95 int isNullList_seq(PSeqList palist)
96 {
97 return(palist->n == 0);
98 }
99
100 void josephus_seq(PSeqList palist, int s, int m)
101 {
102 int s1,i,w;
103 s1 = s - 1;
104 for(i = palist->n; i > 0; i--)
105 {
106 s1 = (s1 + m - 1) % i;
107 w = retrieve_seq(palist,s1);
108 printf("Out element %d\n", w);
109 delete_seq(palist,s1);
110 }
111 }
112 int _tmain(int argc, _TCHAR* argv[])
113 {
114 PSeqList jos_alist;
115 int i, k;
116 int n,s,m;
117 printf("\nplease input the values(<100) of n = ");
118 scanf_s("%d", &n);
119 printf("please input the value of s = ");
120 scanf_s("%d", &s);
121 printf("please input the value of m = ");
122 scanf_s("%d", &m);
123 jos_alist = createNullList_seq();
124 for(i = 0; i < n; i++)
125 {
126 k = insert_seq(jos_alist, i, i + 1);
127 if(k == FALSE)
128 exit(1);
129 }
130 josephus_seq(jos_alist,s,m);
131 free(jos_alist);
132 return 0;
133 }
134
2 //
3
4 #include "stdafx.h"
5 #include <stdlib.h>
6 #include <malloc.h>
7 #define MAXNUM 100
8 #define FALSE 0
9 #define TRUE 1
10 #define SPECIAL 2147483647
11 typedef int DataType;
12
13 struct SeqList
14 {
15 DataType element[MAXNUM];
16 int n;
17 };
18
19 typedef struct SeqList* PSeqList;
20
21 PSeqList createNullList_seq(void)
22 {
23 PSeqList palist;
24 palist = (PSeqList)malloc(sizeof(struct SeqList));
25 if(palist != NULL)
26 {
27 palist->n = 0;
28 }
29 else
30 {
31 printf("Out of space!!\n");
32 }
33 return(palist);
34 }
35
36 int insert_seq(PSeqList palist, int p, DataType x)
37 {
38 int q;
39 if(palist->n == MAXNUM)
40 {
41 printf("Overflow!\n");
42 return(FALSE);
43 }
44 if(p < 0 || p > palist->n)
45 {
46 printf("Not exist!\n");
47 return(FALSE);
48 }
49 for(q = palist->n - 1; q >= p; q--)
50 {
51 palist->element[q + 1] = palist->element[q];
52 }
53 palist->element[p] = x;
54 palist->n += 1;
55 return(TRUE);
56 }
57
58 int delete_seq(PSeqList palist, int p)
59 {
60 int q;
61 if(p < 0 || p > palist->n - 1)
62 {
63 printf("Not exist!\n");
64 return(FALSE);
65 }
66 for(q = p; q < palist->n - 1; q++)
67 {
68 palist->element[q] = palist->element[q + 1];
69 }
70 palist->n = palist->n - 1;
71 return(TRUE);
72 }
73
74 int locate_seq(PSeqList palist, DataType x)
75 {
76 int q;
77 for(q = 0; q < palist->n; q++)
78 {
79 if(palist->element[q] == x)
80 return(q);
81 }
82 return (-1);
83 }
84
85 DataType retrieve_seq(PSeqList palist, int p)
86 {
87 if(p >= 0 && p < palist->n)
88 {
89 return(palist->element[p]);
90 }
91 printf("Not exist.\n");
92 return(SPECIAL);
93 }
94
95 int isNullList_seq(PSeqList palist)
96 {
97 return(palist->n == 0);
98 }
99
100 void josephus_seq(PSeqList palist, int s, int m)
101 {
102 int s1,i,w;
103 s1 = s - 1;
104 for(i = palist->n; i > 0; i--)
105 {
106 s1 = (s1 + m - 1) % i;
107 w = retrieve_seq(palist,s1);
108 printf("Out element %d\n", w);
109 delete_seq(palist,s1);
110 }
111 }
112 int _tmain(int argc, _TCHAR* argv[])
113 {
114 PSeqList jos_alist;
115 int i, k;
116 int n,s,m;
117 printf("\nplease input the values(<100) of n = ");
118 scanf_s("%d", &n);
119 printf("please input the value of s = ");
120 scanf_s("%d", &s);
121 printf("please input the value of m = ");
122 scanf_s("%d", &m);
123 jos_alist = createNullList_seq();
124 for(i = 0; i < n; i++)
125 {
126 k = insert_seq(jos_alist, i, i + 1);
127 if(k == FALSE)
128 exit(1);
129 }
130 josephus_seq(jos_alist,s,m);
131 free(jos_alist);
132 return 0;
133 }
134
135
2.链表实现
1 // Josephus_link.cpp : 定义控制台应用程序的入口点。
2 //
3
4 #include "stdafx.h"
5 #include <stdlib.h>
6 #include <malloc.h>
7 #define FALSE 0
8 #define TRUE 1
9 struct Node;
10 typedef struct Node * PNode;
11 typedef int DataType;
12 struct Node
13 {
14 DataType info;
15 PNode link;
16 };
17
18 typedef struct Node * LinkList;
19 typedef LinkList * PLinkList;
20
21 LinkList createNullList_link(void)
22 {
23 LinkList llist;
24 llist = (LinkList)malloc(sizeof(struct Node));
25 if(llist != NULL)
26 llist->link = NULL;
27 return(llist);
28 }
29
30 int insert_link(LinkList llist, int i, DataType x)
31 {
32 PNode p,q;
33 int j = 0;
34 p = llist;
35 while(p != NULL && j < i)
36 {
37 p = p->link;
38 j++;
39 }
40 if(j != i)
41 {
42 printf("The value of i = %d is not reasonable.\n", i);
43 return(0);
44 }
45 q = (PNode)malloc(sizeof(struct Node));
46 if(q == NULL)
47 {
48 printf("Out of space!!!\n");
49 return(0);
50 }
51 else
52 {
53 q->info = x;
54 q->link = p->link;
55 p->link = q;
56 return(1);
57 }
58 }
59
60 int delete_link(LinkList llist, DataType x)
61 {
62 PNode p, q;
63 p = llist;
64 while(p->link != NULL && p->link->info != x)
65 p = p->link;
66 if(p->link == NULL)
67 {
68 printf("Not exist!\n");
69 return(0);
70 }
71 else
72 {
73 q = p->link;
74 p->link = p->link->link;
75 free(q);
76 return(1);
77 }
78 }
79
80 PNode locate_link(LinkList llist, DataType x)
81 {
82 PNode p;
83 if(llist == NULL)
84 return(NULL);
85 p =llist->link;
86 while(p != NULL && p->info != x)
87 p = p->link;
88 return(p);
89 }
90
91 PNode find_link(LinkList llist, int i)
92 {
93 PNode p;
94 int j;
95 if(i < 0)
96 {
97 printf("The value of i = %d is not reasonable.\n",i);
98 return(NULL);
99 }
100 p = llist;
101 for(j = 0; j <= i; j++)
102 {
103 p = p->link;
104 if(p == NULL)
105 return(NULL);
106 }
107 return(p);
108 }
109
110 int isNullList_link(LinkList llist)
111 {
112 if(llist == NULL)
113 return(1);
114 else
115 return(llist->link == NULL);
116 }
117
118 int init_clink(PLinkList pclist, int n)
119 {
120 PNode p, q;
121 int i;
122 q =(PNode)malloc(sizeof(struct Node));
123 if(q == NULL)
124 return(FALSE);
125 *pclist = q;
126 q->info = 1;
127 q->link = q;
128 if(n == 1)
129 return(TRUE);
130 for(i = 2; i < n + 1; i++)
131 {
132 p = (PNode)malloc(sizeof(struct Node));
133 if(p == NULL)
134 return(FALSE);
135 p->info = i;
136 p->link = q->link;
137 q->link = p;
138 q = p;
139 }
140 return(TRUE);
141 }
142
143 void josephus_clink(PLinkList pclist, int s, int m)
144 {
145 PNode p, pre;
146 int i;
147 p = *pclist;
148 //如果s是第一个节点，特殊处理，通过循环将pre指向最后一个节点
149 if(s==1)
150 {
151 pre = p;
152 p = p->link;
153 while(p != *pclist)
154 {
155 pre = p;
156 p = p->link;
157 }
158 }
159 else
160 {
161 for(i = 1; i < s; i++)
162 {
163 pre = p;
164 p = p->link;
165 }
166 }
167 while(p != p->link)
168 {
169 for(i = 1; i < m; i++)
170 {
171 pre = p;
172 p = p->link;
173 }
174 printf("Out element: %d \n", p->info);
175 //删除第一个节点时特殊处理一下
176 if(*pclist == p)
177 *pclist = p->link;
178 pre->link = p->link;
179 free(p);
180 p = pre->link;
181 }
182 printf("Out element: %d \n", p->info);
183 *pclist = NULL;
184 free(p);
185
186
187 }
188 int _tmain(int argc, _TCHAR* argv[])
189 {
190 LinkList jos_clist;
191 int n,s,m;
192 printf("\nplease input the value of n = ");
193 scanf_s("%d", &n);
194 printf("please input the value of s = ");
195 scanf_s("%d",&s);
196 printf("please input the value of m = ");
197 scanf_s("%d",&m);
198 if(init_clink(&jos_clist,n))
199 josephus_clink(&jos_clist, s,m);
200 else
201 printf("Out of space!\n");
202
203 return 0;
204 }
205
2 //
3
4 #include "stdafx.h"
5 #include <stdlib.h>
6 #include <malloc.h>
7 #define FALSE 0
8 #define TRUE 1
9 struct Node;
10 typedef struct Node * PNode;
11 typedef int DataType;
12 struct Node
13 {
14 DataType info;
15 PNode link;
16 };
17
18 typedef struct Node * LinkList;
19 typedef LinkList * PLinkList;
20
21 LinkList createNullList_link(void)
22 {
23 LinkList llist;
24 llist = (LinkList)malloc(sizeof(struct Node));
25 if(llist != NULL)
26 llist->link = NULL;
27 return(llist);
28 }
29
30 int insert_link(LinkList llist, int i, DataType x)
31 {
32 PNode p,q;
33 int j = 0;
34 p = llist;
35 while(p != NULL && j < i)
36 {
37 p = p->link;
38 j++;
39 }
40 if(j != i)
41 {
42 printf("The value of i = %d is not reasonable.\n", i);
43 return(0);
44 }
45 q = (PNode)malloc(sizeof(struct Node));
46 if(q == NULL)
47 {
48 printf("Out of space!!!\n");
49 return(0);
50 }
51 else
52 {
53 q->info = x;
54 q->link = p->link;
55 p->link = q;
56 return(1);
57 }
58 }
59
60 int delete_link(LinkList llist, DataType x)
61 {
62 PNode p, q;
63 p = llist;
64 while(p->link != NULL && p->link->info != x)
65 p = p->link;
66 if(p->link == NULL)
67 {
68 printf("Not exist!\n");
69 return(0);
70 }
71 else
72 {
73 q = p->link;
74 p->link = p->link->link;
75 free(q);
76 return(1);
77 }
78 }
79
80 PNode locate_link(LinkList llist, DataType x)
81 {
82 PNode p;
83 if(llist == NULL)
84 return(NULL);
85 p =llist->link;
86 while(p != NULL && p->info != x)
87 p = p->link;
88 return(p);
89 }
90
91 PNode find_link(LinkList llist, int i)
92 {
93 PNode p;
94 int j;
95 if(i < 0)
96 {
97 printf("The value of i = %d is not reasonable.\n",i);
98 return(NULL);
99 }
100 p = llist;
101 for(j = 0; j <= i; j++)
102 {
103 p = p->link;
104 if(p == NULL)
105 return(NULL);
106 }
107 return(p);
108 }
109
110 int isNullList_link(LinkList llist)
111 {
112 if(llist == NULL)
113 return(1);
114 else
115 return(llist->link == NULL);
116 }
117
118 int init_clink(PLinkList pclist, int n)
119 {
120 PNode p, q;
121 int i;
122 q =(PNode)malloc(sizeof(struct Node));
123 if(q == NULL)
124 return(FALSE);
125 *pclist = q;
126 q->info = 1;
127 q->link = q;
128 if(n == 1)
129 return(TRUE);
130 for(i = 2; i < n + 1; i++)
131 {
132 p = (PNode)malloc(sizeof(struct Node));
133 if(p == NULL)
134 return(FALSE);
135 p->info = i;
136 p->link = q->link;
137 q->link = p;
138 q = p;
139 }
140 return(TRUE);
141 }
142
143 void josephus_clink(PLinkList pclist, int s, int m)
144 {
145 PNode p, pre;
146 int i;
147 p = *pclist;
148 //如果s是第一个节点，特殊处理，通过循环将pre指向最后一个节点
149 if(s==1)
150 {
151 pre = p;
152 p = p->link;
153 while(p != *pclist)
154 {
155 pre = p;
156 p = p->link;
157 }
158 }
159 else
160 {
161 for(i = 1; i < s; i++)
162 {
163 pre = p;
164 p = p->link;
165 }
166 }
167 while(p != p->link)
168 {
169 for(i = 1; i < m; i++)
170 {
171 pre = p;
172 p = p->link;
173 }
174 printf("Out element: %d \n", p->info);
175 //删除第一个节点时特殊处理一下
176 if(*pclist == p)
177 *pclist = p->link;
178 pre->link = p->link;
179 free(p);
180 p = pre->link;
181 }
182 printf("Out element: %d \n", p->info);
183 *pclist = NULL;
184 free(p);
185
186
187 }
188 int _tmain(int argc, _TCHAR* argv[])
189 {
190 LinkList jos_clist;
191 int n,s,m;
192 printf("\nplease input the value of n = ");
193 scanf_s("%d", &n);
194 printf("please input the value of s = ");
195 scanf_s("%d",&s);
196 printf("please input the value of m = ");
197 scanf_s("%d",&m);
198 if(init_clink(&jos_clist,n))
199 josephus_clink(&jos_clist, s,m);
200 else
201 printf("Out of space!\n");
202
203 return 0;
204 }
205
206
运行结果：
please input the value of n =8
please input the value of s =1
please input the value of m =4
Out element: 4
Out element: 8
Out element: 5
Out element: 2
Out element: 1
Out element: 3
Out element: 7
Out element: 6
