C — 用单向循环链表完成“类约瑟夫环”问题

问题概述

有 n 个人围坐成一圈，其编号为从 1 到 n 的递增数列，每个人有一个正整数密码。先选定一个任意正整数 m，并从 1 号开始报 1，2号报 2，以此类推，报到 m 时停止，该人出局，并把他的密码作为新的 m 值。重复该过程，直到所有人出局，求出局人编号顺序。

修改前代码

#include <stdio.h>
#include <stdlib.h>

typedef struct node {
    int number;
    int password;
    struct node *next;
} node;

node *createCircularLinkedList(int n) {
    node *temp = NULL;
    node *head = (node *) malloc(sizeof(node));
    head->next = head;  // Necessary when n == 1;
    temp = head;
    for (int i = 0; i < n - 1; ++i) {
        temp->next = (node *) malloc(sizeof(node));
        temp = temp->next;
        temp->next = NULL;
    }
    temp->next = head;
    return head;
}

int inputCircularLinkedList(node *head) {
    if (NULL == head)   // If a blank linked list.
        return 0;
    node *temp = head;
    int count = 0;
    int password;
    count = 1;
    do {
        scanf("%d", &password);
        temp->password = password;
        temp->number = count++;
        temp = temp->next;
    } while (temp != head);
    return 1;
}

int printCircularLinkedList(node *head) {   // Just for test.
    if (NULL == head)   // If a blank linked list.
        return 0;
    node *temp = head;
    do {
        printf("%d-%d\n", temp->number, temp->password);
        temp = temp->next;
    } while (temp != head);
    return 1;
}

node *rearOfCircularLinkedList(node *head) {
    node *p = NULL;
    if (NULL == head)   // If a blank linked list.
        return 0;
    p = head;
    while (p->next != head)
        p = p->next;
    return p;
}

node *deleteNodeOfCircularLinkedList(node *head, node *del) {
    if (NULL == head)   // If a blank linked list.
        return 0;
    node *pre = head;
    while (pre->next != del)
        pre = pre->next;
    if (pre->next == head) {
        head = head->next;
    }
    pre->next = del->next;
    free(del);
    return head;
}

int main() {
    int n = 0, m = 0, password = 0;
    node *head = NULL;  // Create a blank linked list.
    printf("Please input m:\n");
    scanf("%d", &m);
    printf("Please input n:\n");
    scanf("%d", &n);
    head = createCircularLinkedList(n);
    printf("Please input password:\n");
    inputCircularLinkedList(head);
    printf("Data received:\n");
    printCircularLinkedList(head);
    printf("Answer:\n");

    node *p = head;
    node *pCopy = NULL;
    int count = 0;

    while (n > 0) {
        for (int i = 0; i < m-1; ++i) {
            p = p->next;
        }   // P should out.
        printf("%d out\n", p->number);
        pCopy = p;
        m=p->password;
        p = p->next;
        head = deleteNodeOfCircularLinkedList(head, pCopy);
        n--;
    }

    return 0;
}

代码问题

1. 循环链表只需要有指针指向其即可，不需要固定头指针或尾指针。

2. 删除函数又重复遍历了一遍链表，效率低下。

3. 当密码为很大的数字时，可以用取余来提高效率。

修改后代码

#include <stdio.h>
#include <stdlib.h>

typedef struct node {
    int number;
    int password;
    struct node *next;
} node;

node *nodePioneerOfCll(int m, node *p) {
    for (int i = 0; i < m - 1; ++i) {
        p = p->next;
    }   // (p+1) - out.
    printf("%d - out\n", p->next->number);
    return p;
}

node *rearOfCll(node *p) {
    while (p->next->number != 1) {
        p = p->next;
    }
    return p;
}

node *createCll(int n) {
    node *temp = NULL;
    node *head = (node *) malloc(sizeof(node));
    head->next = head;  // n == 1
    temp = head;
    for (int i = 0; i < n - 1; ++i) {
        temp->next = (node *) malloc(sizeof(node));
        temp = temp->next;
        temp->next = NULL;
    }
    temp->next = head;  // 尾元素指向头指针
    return head;
}

int inputCll(node *p) {
    if (NULL == p)
        return 0;
    node *temp = p;
    int count = 1;
    do {
        scanf("%d", &temp->password);
        temp->number = count++;
        temp = temp->next;
    } while (temp != p);
    return 1;
}

int printCll(node *p) {
    if (NULL == p)
        return 0;
    node *temp = p;
    do {
        printf("%d-%d\n", temp->number, temp->password);
        temp = temp->next;
    } while (temp != p);
    return 1;
}

int deleteNextNodeOfCll(node *p) {
    if (NULL == p)
        return 0;
    node *del = p->next;
    p->next = p->next->next;
    int m = del->password;
    free(del);
    return m;
}

int main() {
    int n = 0, m = 0, password = 0;
    printf("Please input m:\n");
    scanf("%d", &m);                            // 输入m值
    printf("Please input n:\n");
    scanf("%d", &n);                            // 输入n值
    node *p = createCll(n);                     // 创建有n元循环链表
    printf("Please input password:\n");
    inputCll(p);                                // 输入密码
    printf("Data received:\n");
    printCll(p);                                // 反显密码
    printf("Answer:\n");
    p = rearOfCll(p);                           // p移到尾
    for (; n > 0; n--) {
        p = nodePioneerOfCll(m % n ? m % n : n, p);             // 移到待删节点前驱
        m = deleteNextNodeOfCll(p);             // 删除p后继
    }
    return 0;
}