約瑟夫斯問題（有時(shí)也稱為約瑟夫斯置換），是一個(gè)出現(xiàn)在計(jì)算機(jī)科學(xué)和數(shù)學(xué)中的問題。在計(jì)算機(jī)編程的算法中，類似問題又稱為“約瑟夫環(huán)”，也有的地方叫做“丟手絹”。

問題是這樣的：
有編號從1到n的n個(gè)人圍坐成一圈。從編號為1的人開始報(bào)數(shù)，報(bào)到m的人出局，下一位再從 1 開始報(bào)數(shù)，報(bào)到 m 的人出局，……如此持續(xù)，直到剩下一人為止，假設(shè)此人的原始編號是x。給定 n和 m，求出x。

關(guān)于這個(gè)問題，我已經(jīng)寫了一篇博客。
http://blog.csdn.net/longintchar/article/details/75150621

因?yàn)樽罱诳磧?nèi)核鏈表，想把內(nèi)核鏈表用起來，我又想到了約瑟夫環(huán)。
假設(shè)n=8, m=3，那么淘汰順序應(yīng)該是3 、6、 1、 5 、2 、8 、4，最后剩下7號。

代碼如下。

#include <stdio.h> #include "list.h"#define N 8 //N為總?cè)藬?shù) #define M 3 //從1開始報(bào)數(shù)，報(bào)M的人出局struct person_info {int data; //記錄編號struct list_head list; //內(nèi)核鏈表 };struct person_info person[N] = {0}; //N個(gè)人int main(void) {LIST_HEAD(head); //定義并且初始化頭結(jié)點(diǎn)int i; //雙向循環(huán)鏈表的尾插for (i = 0; i < N; ++i) {person[i].data = i+1; //編號從1開始，所以+1list_add_tail(&person[i].list, &head);} struct person_info *p_person = NULL;struct list_head *cur = NULL;struct list_head *tmp = NULL;int count = 0; //用來計(jì)數(shù)//安全遍歷節(jié)點(diǎn)，報(bào)數(shù)到M時(shí)刪除結(jié)點(diǎn)，直到只剩一個(gè)結(jié)點(diǎn)//循環(huán)停止條件是剩下一個(gè)人while( (&head)->next->next != (&head) ){list_for_each_safe(cur, tmp, &head){ ++count;//模擬計(jì)數(shù)if (M == count) { //小指針轉(zhuǎn)大指針p_person = container_of(cur, struct person_info, list);printf("del:%d\n", p_person->data);list_del(cur); //刪除結(jié)點(diǎn)count = 0; //重新計(jì)數(shù)}} }//打印最后一個(gè)人的編號p_person = container_of((&head)->next, struct person_info, list);printf("winner:%d\n", p_person->data);return 0; }

程序運(yùn)行結(jié)果是：

del:3
del:6
del:1
del:5
del:2
del:8
del:4
winner:7

需要說明的是，以上代碼包含的頭文件"list.h"去哪里找呢？當(dāng)然是內(nèi)核源碼了。

方便起見，我把相關(guān)代碼扒拉出來，略微修改，組成了一個(gè)小而美的"list.h"。有了這個(gè)頭文件，即使到了單片機(jī)上，內(nèi)核鏈表也是可以用的。

#ifndef _LIST_H #define _LIST_H /*/usr/src/linux-headers-4.8.0-36-generic/include/linux/stddef.h *///求偏移量 #define offsetof(TYPE, MEMBER) ((size_t)&((TYPE *)0)->MEMBER)/*/usr/src/linux-headers-4.8.0-36-generic/include/linux/kernel.h *//*** container_of - cast a member of a structure out to the containing structure* @ptr: the pointer to the member.* @type: the type of the container struct this is embedded in.* @member: the name of the member within the struct.**///小指針轉(zhuǎn)大指針 #define container_of(ptr, type, member) ({ \const typeof( ((type *)0)->member ) *__mptr = (ptr); \(type *)( (char *)__mptr - offsetof(type,member) );})/*/usr/src/linux-headers-4.8.0-36-generic/include/linux/types.h */ struct list_head {struct list_head *next, *prev; };/*/usr/src/linux-headers-4.8.0-36-generic/include/linux/list.h */#define LIST_HEAD_INIT(name) { &(name), &(name) }//以下這個(gè)宏用來定義并且初始化頭結(jié)點(diǎn) #define LIST_HEAD(name) \struct list_head name = LIST_HEAD_INIT(name)/* kernel 3.14 */ static inline void __list_add(struct list_head *new,struct list_head *prev,struct list_head *next) {next->prev = new;new->next = next;new->prev = prev;prev->next = new; //kernel 4.8中 這句話是 WRITE_ONCE(prev->next, new); } /*** list_add - add a new entry* @new: new entry to be added* @head: list head to add it after** Insert a new entry after the specified head.* This is good for implementing stacks.*/ static inline void list_add(struct list_head *new, struct list_head *head) {__list_add(new, head, head->next); //頭插 }/*** list_add_tail - add a new entry* @new: new entry to be added* @head: list head to add it before** Insert a new entry before the specified head.* This is useful for implementing queues.*/ static inline void list_add_tail(struct list_head *new, struct list_head *head) {__list_add(new, head->prev, head); //尾插 }/** Delete a list entry by making the prev/next entries* point to each other.** This is only for internal list manipulation where we know* the prev/next entries already!*/ static inline void __list_del(struct list_head * prev, struct list_head * next) {next->prev = prev;prev->next = next; //WRITE_ONCE(prev->next, next); }static inline void list_del(struct list_head *entry) {__list_del(entry->prev, entry->next);//entry->next = LIST_POISON1;//entry->prev = LIST_POISON2; }/*** list_empty - tests whether a list is empty* @head: the list to test.*/ static inline int list_empty(const struct list_head *head) {return head->next == head;//return READ_ONCE(head->next) == head; } /*** list_for_each - iterate over a list* @pos: the &struct list_head to use as a loop cursor.* @head: the head for your list.*/ #define list_for_each(pos, head) \for (pos = (head)->next; pos != (head); pos = pos->next)/*** list_for_each_safe - iterate over a list safe against removal of list entry* @pos: the &struct list_head to use as a loop cursor.* @n: another &struct list_head to use as temporary storage* @head: the head for your list.*/ #define list_for_each_safe(pos, n, head) \for (pos = (head)->next, n = pos->next; pos != (head); \pos = n, n = pos->next)/*** list_entry - get the struct for this entry* @ptr: the &struct list_head pointer.* @type: the type of the struct this is embedded in.* @member: the name of the list_head within the struct.*/ #define list_entry(ptr, type, member) \container_of(ptr, type, member)/*** list_first_entry - get the first element from a list* @ptr: the list head to take the element from.* @type: the type of the struct this is embedded in.* @member: the name of the list_head within the struct.** Note, that list is expected to be not empty.*/ #define list_first_entry(ptr, type, member) \list_entry((ptr)->next, type, member)/*** list_next_entry - get the next element in list* @pos: the type * to cursor* @member: the name of the list_head within the struct.*/ #define list_next_entry(pos, member) \list_entry((pos)->member.next, typeof(*(pos)), member)/*** list_for_each_entry - iterate over list of given type* @pos: the type * to use as a loop cursor.* @head: the head for your list.* @member: the name of the list_head within the struct.*/ #define list_for_each_entry(pos, head, member) \for (pos = list_first_entry(head, typeof(*pos), member); \&pos->member != (head); \pos = list_next_entry(pos, member)) /*** list_for_each_entry_safe - iterate over list of given type safe against removal of list entry* @pos: the type * to use as a loop cursor.* @n: another type * to use as temporary storage* @head: the head for your list.* @member: the name of the list_head within the struct.*/ #define list_for_each_entry_safe(pos, n, head, member) \for (pos = list_first_entry(head, typeof(*pos), member), \n = list_next_entry(pos, member); \&pos->member != (head); \pos = n, n = list_next_entry(n, member))/*** list_for_each_entry_from - iterate over list of given type from the current point* @pos: the type * to use as a loop cursor.* @head: the head for your list.* @member: the name of the list_head within the struct.** Iterate over list of given type, continuing from current position.*///從pos指向的結(jié)構(gòu)體開始遍歷 #define list_for_each_entry_from(pos, head, member) \for (; &pos->member != (head); \pos = list_next_entry(pos, member)) /*** list_for_each_entry_safe_from - iterate over list from current point safe against removal* @pos: the type * to use as a loop cursor.* @n: another type * to use as temporary storage* @head: the head for your list.* @member: the name of the list_head within the struct.** Iterate over list of given type from current point, safe against* removal of list entry.*/ #define list_for_each_entry_safe_from(pos, n, head, member) \for (n = list_next_entry(pos, member); \&pos->member != (head); \pos = n, n = list_next_entry(n, member)) /*** list_for_each_entry_continue - continue iteration over list of given type* @pos: the type * to use as a loop cursor.* @head: the head for your list.* @member: the name of the list_head within the struct.** Continue to iterate over list of given type, continuing after* the current position.*///從pos的下一個(gè)開始遍歷 #define list_for_each_entry_continue(pos, head, member) \for (pos = list_next_entry(pos, member); \&pos->member != (head); \pos = list_next_entry(pos, member))/*** list_for_each_entry_safe_continue - continue list iteration safe against removal* @pos: the type * to use as a loop cursor.* @n: another type * to use as temporary storage* @head: the head for your list.* @member: the name of the list_head within the struct.** Iterate over list of given type, continuing after current point,* safe against removal of list entry.*/ #define list_for_each_entry_safe_continue(pos, n, head, member) \for (pos = list_next_entry(pos, member), \n = list_next_entry(pos, member); \&pos->member != (head); \pos = n, n = list_next_entry(n, member))#endif

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