PS:
你以为的中等题,结果官方解答用了A*
算法。没有现成的数据结构,用C语言实现,不亚于难题,哈哈怪不得连官方答案A*
算法实现里都懒得写C版本了。。。
所以,我就不搞那么复杂啦,就用BFS一步步深入,并把分析的思路记录与此吧。
独立实现一个遍历功能,思路是按一个位转动不同次数,然后第二个位转不同次数,往深处递归的,本质是DFS遍历,代码如下:
char AddOne(char ch) { char ans; if (ch == '9') { return '0'; } ans = ch + 1; return ans; } char MinusOne(char ch) { char ans; if (ch == '0') { return '9'; } ans = ch - 1; return ans; } int g_times; void BfsFindMinTimes(char *cur, char *target, int depth) { // 终止条件 if (depth == 4) { return; } // 迭代搜索 char ch1 = *cur; char ch2 = *target; while (ch1 != ch2) { int tmp = ch1 - ch2; tmp = abs(tmp); if (tmp > 5) { g_times += 10 - tmp; // need to rever dir tmp = 10 - tmp; while (tmp--) { ch1 = MinusOne(ch1); } } else { g_times += tmp; while (tmp--) { ch1 = AddOne(ch1); } } } *cur = *target; BfsFindMinTimes(cur + 1, target + 1, depth + 1); return; } // BFS int openLock(char ** deadends, int deadendsSize, char * target) { g_times = 0; char cur[5] = "0000"; // 初始值 // special case if (strcmp(cur, target) == 0) { return 0; } int i; for (i = 0; i < deadendsSize; i++) { if (strcmp(cur, deadends[i]) == 0) { return -1; } } BfsFindMinTimes(cur, target, 0); return g_times; }
由于原始版本思路泛化能力较弱,参考labuladong的思路,真正的从BFS入手,穷举所有可能。代码如下:
char* AddOne(char *in, int j) { char *res = (char *)malloc(sizeof(char) * 5); if (res == NULL) { return NULL; } memcpy(res, in, 5); char ch = res[j]; if (ch == '9') { res[j] = '0'; return res; } res[j] = ch + 1; return res; } char* MinusOne(char *in, int j) { char *s = (char *)malloc(sizeof(char) * 5); if (s == NULL) { return NULL; } memcpy(s, in, 5); char ch = s[j]; if (ch == '0') { s[j] = '9'; return s; } s[j] = ch - 1; return s; } typedef struct QueList { int cnt; // 转动次数 char *s; // 当前密码 struct QueList *next; // 下个可能密码 } StruQueList, *PtrStruQueList; void Init(StruQueList **pQue, char *s, int cnt) { (*pQue) = (PtrStruQueList)malloc(sizeof(StruQueList)); (*pQue)->cnt = cnt; char *str = (char *)malloc(sizeof(char) * (strlen(s) + 1)); if (str == NULL) { return; } memcpy(str, s, strlen(s) + 1); (*pQue)->s = str; (*pQue)->next = NULL; } PtrStruQueList NodeExpand(StruQueList **queList, PtrStruQueList queListLastNode) { int i; char *s; // 临时转动1次, 当前节点演变出8种可能 char *cur = (*queList)->s; int cnt = (*queList)->cnt; for (i = 0; i < 4; i++) { s = AddOne(cur, i); printf("%s\n", s); Init(&queListLastNode->next, s, cnt + 1); queListLastNode = queListLastNode->next; s = MinusOne(cur, i); printf("%s\n", s); Init(&queListLastNode->next, s, cnt + 1); queListLastNode = queListLastNode->next; } printf("\n"); return queListLastNode; } // 按队列和BFS的方法来表达每次只转一次,对应的所有可能 void BfsFindMinTimes(char *cur, char *target) { // 初始化队列 0000 PtrStruQueList queList, queListCurLevelLast, queListLastNode; queList = (PtrStruQueList)malloc(sizeof(StruQueList)); if (queList == NULL) { return; // if malloc is failed } Init(&queList, cur, 0); queListCurLevelLast = queList; queListLastNode = NodeExpand(&queList, queListCurLevelLast); queListCurLevelLast = queListLastNode; queList = queList->next; // 得到两个队列的指针,一个是当前指向,一个是层级对应的新开头 // 从所有层每个节点中迭代新的可能 while (queList != NULL) { queListCurLevelLast = queListLastNode; // 遍历当前层所有节点 while (queList != queListCurLevelLast) { queListLastNode = NodeExpand(&queList, queListLastNode); queList = queList->next; } queListLastNode = NodeExpand(&queList, queListLastNode); // 当前层最后一个节点 queList = queList->next; printf("\n\n"); } return; } // BFS int openLock(char ** deadends, int deadendsSize, char * target) { char cur[5] = "0000"; // 初始值 // special case if (strcmp(cur, target) == 0) { return 0; } int i; for (i = 0; i < deadendsSize; i++) { if (strcmp(cur, deadends[i]) == 0) { return -1; } } BfsFindMinTimes(cur, target); return 1; }
接着在此基础上继续改进,加上终止条件,实现找到target就停止遍历。
char* AddOne(char *in, int j) { char *res = (char *)malloc(sizeof(char) * 5); if (res == NULL) { return NULL; } memcpy(res, in, 5); char ch = res[j]; if (ch == '9') { res[j] = '0'; return res; } res[j] = ch + 1; return res; } char* MinusOne(char *in, int j) { char *s = (char *)malloc(sizeof(char) * 5); if (s == NULL) { return NULL; } memcpy(s, in, 5); char ch = s[j]; if (ch == '0') { s[j] = '9'; return s; } s[j] = ch - 1; return s; } typedef struct QueList { int cnt; // 转动次数 char *s; // 当前密码 struct QueList *next; // 下个可能密码 } StruQueList, *PtrStruQueList; void Init(StruQueList **pQue, char *s, int cnt) { (*pQue) = (PtrStruQueList)malloc(sizeof(StruQueList)); (*pQue)->cnt = cnt; char *str = (char *)malloc(sizeof(char) * (strlen(s) + 1)); if (str == NULL) { return; } memcpy(str, s, strlen(s) + 1); (*pQue)->s = str; (*pQue)->next = NULL; } // 大于0,则表示匹配成功,返回转动次数 // 等于0,则表示无异常 // 小于0,则表示出错 int NodeExpand(StruQueList **queList, StruQueList **ptrQueListLastNode, char *target) { int i; char *s; // 转动1次, 当前节点演变出8种可能 char *cur = (*queList)->s; int cnt = (*queList)->cnt; for (i = 0; i < 4; i++) { s = AddOne(cur, i); printf("%s\n", s); Init(&(*ptrQueListLastNode)->next, s, cnt + 1); if (strcmp(s, target) == 0) { // 终止条件 return cnt + 1; } *ptrQueListLastNode = (*ptrQueListLastNode)->next; s = MinusOne(cur, i); printf("%s\n", s); Init(&(*ptrQueListLastNode)->next, s, cnt + 1); if (strcmp(s, target) == 0) { return cnt + 1; } *ptrQueListLastNode = (*ptrQueListLastNode)->next; } printf("\n"); return 0; } // 按队列和BFS的方法来表达每次只转一次,对应的所有可能 int BfsFindMinTimes(char *cur, char *target) { int ret; // 初始化队列 0000 PtrStruQueList queList, queListCurLevelLast, queListLastNode; queList = (PtrStruQueList)malloc(sizeof(StruQueList)); if (queList == NULL) { return; // if malloc is failed } Init(&queList, cur, 0); queListLastNode = queList; ret = NodeExpand(&queList, &queListLastNode, target); if (ret > 0) { // 终止条件 return ret; } queListCurLevelLast = queListLastNode; queList = queList->next; // 得到两个队列的指针,一个是当前指向,一个是层级对应的新开头 // 从所有层每个节点中迭代新的可能 while (queList != NULL) { // 遍历当前层所有节点 while (queList != queListCurLevelLast) { int ret = NodeExpand(&queList, &queListLastNode, target); if (ret > 0) { // 终止条件 return ret; } queList = queList->next; } int ret = NodeExpand(&queList, &queListLastNode, target); // 当前层最后一个节点 if (ret > 0) { // 终止条件 return ret; } queList = queList->next; queListCurLevelLast = queListLastNode; printf("\n\n"); } return -1; // 遍历完所有无匹配 } // BFS int openLock(char ** deadends, int deadendsSize, char * target) { char cur[5] = "0000"; // 初始值 // special case if (strcmp(cur, target) == 0) { return 0; } int i; for (i = 0; i < deadendsSize; i++) { if (strcmp(cur, deadends[i]) == 0) { return -1; } } int ret = BfsFindMinTimes(cur, target); return ret; }
添加HASH数据结构,熟悉uthash,添加约束条件。
主要约束条件:
不走回头路,比如往前转动了一次的结果,不允许再往后转动回去。实现的主要思路是,增加一个visit记录所有已经有的遍历结果,如果出现相同的则跳过并且不记录。主要用uthash哈希表,减少查找时间。
不能越过deadends,也是类似visit的hash表查找思路实现。hash表时间复杂度为O(1),不过是以空间换时间,减少时间同时会增长空间。
终止条件,由于该思路本身就是从转动次数0开始往外扩展的,类似一种贪心算法思想,每步都是最优的了。一旦匹配上目标,当前转动次数就是最小的,所以可以直接返回。
提交通过的hash版本代码如下:
typedef struct HashTable { char str[5]; // key UT_hash_handle hh; // table head } StruHashTable; typedef struct QueList { int cnt; // 转动次数 char *s; // 当前密码 struct QueList *next; // 下个可能密码 } StruQueList, *PtrStruQueList; #define STR_SIZE 5 #define STR_LEN 4 int g_curLevelCnt; char* AddOne(char *in, int j) { char *res = (char *)malloc(sizeof(char) * STR_SIZE); if (res == NULL) { return NULL; } memcpy(res, in, STR_SIZE); char ch = res[j]; if (ch == '9') { res[j] = '0'; return res; } res[j] = ch + 1; return res; } char* MinusOne(char *in, int j) { char *s = (char *)malloc(sizeof(char) * STR_SIZE); if (s == NULL) { return NULL; } memcpy(s, in, STR_SIZE); char ch = s[j]; if (ch == '0') { s[j] = '9'; return s; } s[j] = ch - 1; return s; } void Init(StruQueList **pQue, char *s, int cnt) { (*pQue) = (PtrStruQueList)malloc(sizeof(StruQueList)); (*pQue)->cnt = cnt; char *str = (char *)malloc(sizeof(char) * STR_SIZE); if (str == NULL) { return; } memcpy(str, s, STR_SIZE); (*pQue)->s = str; (*pQue)->next = NULL; g_curLevelCnt++; } // 大于0,则表示匹配成功,返回转动次数 // 等于0,则表示无异常 // 小于0,则表示出错 int NodeExpand(StruQueList **queList, StruQueList **ptrQueListLastNode, char *target, StruHashTable **ptrDead, StruHashTable **ptrVisit) { int i; char *s; StruHashTable *hashTmp1, *hashTmp2; // 转动1次, 当前节点演变出8种可能 char *cur = (*queList)->s; int cnt = (*queList)->cnt; for (i = 0; i < 4; i++) { s = AddOne(cur, i); // 如果与target匹配 if (strcmp(s, target) == 0) { // 终止条件 return cnt + 1; } // 如果在deadends HASH_FIND(hh, *ptrDead, s, sizeof(char) * STR_SIZE, hashTmp1); // 如果已遍历 HASH_FIND(hh, *ptrVisit, s, sizeof(char) * STR_SIZE, hashTmp2); if (hashTmp1 == NULL && hashTmp2 == NULL) { // 不在dead里也没在visit里 Init(&(*ptrQueListLastNode)->next, s, cnt + 1); *ptrQueListLastNode = (*ptrQueListLastNode)->next; hashTmp1 = (StruHashTable *)malloc(sizeof(StruHashTable)); // 增加一个hash节点 if (hashTmp1 == NULL) { return -1; } memcpy(hashTmp1->str, s, STR_SIZE); HASH_ADD(hh, *ptrVisit, str, sizeof(char) * STR_SIZE, hashTmp1); // printf("%s\n", s); } else { free(s); } s = MinusOne(cur, i); // 如果与target匹配 if (strcmp(s, target) == 0) { // 终止条件 return cnt + 1; } // 如果在deadends HASH_FIND(hh, *ptrDead, s, sizeof(char) * STR_SIZE, hashTmp1); // 如果已遍历 HASH_FIND(hh, *ptrVisit, s, sizeof(char) * STR_SIZE, hashTmp2); if (hashTmp1 == NULL && hashTmp2 == NULL) { // 不在dead里也没在visit里 Init(&(*ptrQueListLastNode)->next, s, cnt + 1); *ptrQueListLastNode = (*ptrQueListLastNode)->next; hashTmp1 = (StruHashTable *)malloc(sizeof(StruHashTable)); // 增加一个hash节点 if (hashTmp1 == NULL) { return -1; } memcpy(hashTmp1->str, s, STR_SIZE); HASH_ADD(hh, *ptrVisit, str, sizeof(char) * STR_SIZE, hashTmp1); // printf("%s\n", s); } else { free(s); } } // printf("\n"); return 0; } // 按队列和BFS的方法来表达每次只转一次,对应的所有可能 int openLock(char ** deadends, int deadendsSize, char * target) { char cur[STR_SIZE] = "0000"; // 初始值 int i, ret; // special case if (strcmp(cur, target) == 0) { return 0; } // 初始化hash StruHashTable *dead = NULL; // 表头最开始都为空 StruHashTable *hashTmp; for (i = 0; i < deadendsSize; i++) { HASH_FIND(hh, dead, deadends[i], sizeof(char) * STR_SIZE, hashTmp); // 键值所占空间sizeof(char) * 5 if (hashTmp == NULL) { // 之前未出现 hashTmp = (StruHashTable *)malloc(sizeof(StruHashTable)); // 增加一个hash节点 if (hashTmp == NULL) { return -1; } memcpy(hashTmp->str, deadends[i], STR_SIZE); HASH_ADD(hh, dead, str, sizeof(char) * STR_SIZE, hashTmp); // str表示操作结构体中的键值,追加到hashtable中 } } // special case HASH_FIND(hh, dead, target, sizeof(char) * STR_SIZE, hashTmp); if (hashTmp != NULL) { return -1; // deanends contain target } HASH_FIND(hh, dead, cur, sizeof(char) * STR_SIZE, hashTmp); if (hashTmp != NULL) { return -1; // deanends contain target } // 初始化队列 0000 StruHashTable *visit = NULL; // 表头最开始都为空 PtrStruQueList queList, queListCurLevelLast, queListLastNode; queList = (PtrStruQueList)malloc(sizeof(StruQueList)); if (queList == NULL) { return -1; // if malloc is failed } g_curLevelCnt = 0; Init(&queList, cur, 0); hashTmp = (StruHashTable *)malloc(sizeof(StruHashTable)); // 增加一个hash节点 if (hashTmp == NULL) { return -1; } memcpy(hashTmp->str, queList->s, STR_SIZE); // printf("%p\n", visit); HASH_ADD(hh, visit, str, sizeof(char) * STR_SIZE, hashTmp); // 增加一个已遍历状态 // printf("%p\n", visit); g_curLevelCnt = 0; queListLastNode = queList; ret = NodeExpand(&queList, &queListLastNode, target, &dead, &visit); if (ret > 0) { // 终止条件 return ret; } queListCurLevelLast = queListLastNode; queList = queList->next; // 得到两个队列的指针,一个是当前指向,一个是层级对应的新开头 // 从所有层每个节点中迭代新的可能 while (queList != NULL) { // 遍历当前层所有节点 int len = g_curLevelCnt; g_curLevelCnt = 0; for (i = 0; i < len; i++) { ret = NodeExpand(&queList, &queListLastNode, target, &dead, &visit); if (ret > 0) { // 终止条件 return ret; } queList = queList->next; } // printf("\n\n"); } return -1; // 遍历完所有无匹配 }
代码精简:删除和提炼冗余信息。
typedef struct HashTable { char str[5]; // key UT_hash_handle hh; // table head } StruHashTable; typedef struct QueList { int cnt; // 转动次数 char *s; // 当前密码 struct QueList *next; // 下个可能密码 } StruQueList, *PtrStruQueList; #define STR_SIZE 5 #define STR_LEN 4 int g_curLevelCnt; char* AddOne(char *in, int j) { char *res = (char *)malloc(sizeof(char) * STR_SIZE); if (res == NULL) { return NULL; } memcpy(res, in, STR_SIZE); char ch = res[j]; if (ch == '9') { res[j] = '0'; return res; } res[j] = ch + 1; return res; } char* MinusOne(char *in, int j) { char *s = (char *)malloc(sizeof(char) * STR_SIZE); if (s == NULL) { return NULL; } memcpy(s, in, STR_SIZE); char ch = s[j]; if (ch == '0') { s[j] = '9'; return s; } s[j] = ch - 1; return s; } void Init(StruQueList **pQue, char *s, int cnt) { (*pQue) = (PtrStruQueList)malloc(sizeof(StruQueList)); (*pQue)->cnt = cnt; char *str = (char *)malloc(sizeof(char) * STR_SIZE); if (str == NULL) { return; } memcpy(str, s, STR_SIZE); (*pQue)->s = str; (*pQue)->next = NULL; g_curLevelCnt++; } void InitDeadHash(char **deadends, int deadendsSize, StruHashTable **ptrDead) { int i; StruHashTable *hashTmp; for (i = 0; i < deadendsSize; i++) { HASH_FIND(hh, *ptrDead, deadends[i], sizeof(char) * STR_SIZE, hashTmp); // 键值所占空间sizeof(char) * 5 if (hashTmp == NULL) { // 之前未出现 hashTmp = (StruHashTable *)malloc(sizeof(StruHashTable)); // 增加一个hash节点 if (hashTmp == NULL) { return; } memcpy(hashTmp->str, deadends[i], STR_SIZE); HASH_ADD(hh, *ptrDead, str, sizeof(char) * STR_SIZE, hashTmp); // str表示操作结构体中的键值,追加到hashtable中 } } return; } void InitQueAndVisitHash(char *cur, StruQueList **ptrQueList, StruHashTable **ptrVisit) { StruHashTable *hashTmp; *ptrQueList = (PtrStruQueList)malloc(sizeof(StruQueList)); if (*ptrQueList == NULL) { return; // if malloc is failed } g_curLevelCnt = 0; Init(ptrQueList, cur, 0); hashTmp = (StruHashTable *)malloc(sizeof(StruHashTable)); // 增加一个hash节点 if (hashTmp == NULL) { return; } memcpy(hashTmp->str, (*ptrQueList)->s, STR_SIZE); HASH_ADD(hh, *ptrVisit, str, sizeof(char) * STR_SIZE, hashTmp); // 增加一个已遍历状态 return; } int DealCurStr(char *s, char *target, int cnt, StruQueList **ptrQueListLastNode, StruHashTable **ptrDead, StruHashTable **ptrVisit) { StruHashTable *hashTmp1, *hashTmp2; // 如果与target匹配 if (strcmp(s, target) == 0) { // 终止条件 return cnt + 1; } // 如果在deadends HASH_FIND(hh, *ptrDead, s, sizeof(char) * STR_SIZE, hashTmp1); // 如果已遍历 HASH_FIND(hh, *ptrVisit, s, sizeof(char) * STR_SIZE, hashTmp2); if (hashTmp1 == NULL && hashTmp2 == NULL) { // 不在dead里也没在visit里 Init(&(*ptrQueListLastNode)->next, s, cnt + 1); *ptrQueListLastNode = (*ptrQueListLastNode)->next; hashTmp1 = (StruHashTable *)malloc(sizeof(StruHashTable)); // 增加一个hash节点 if (hashTmp1 == NULL) { return -1; } memcpy(hashTmp1->str, s, STR_SIZE); HASH_ADD(hh, *ptrVisit, str, sizeof(char) * STR_SIZE, hashTmp1); // printf("%s\n", s); } else { free(s); } return 0; } // 大于0,则表示匹配成功,返回转动次数 // 等于0,则表示无异常 // 小于0,则表示出错 int NodeExpand(StruQueList *queList, StruQueList **ptrQueListLastNode, char *target, StruHashTable **ptrDead, StruHashTable **ptrVisit) { int i, ret; char *s; // 转动1次, 当前节点演变出8种可能 char *cur = queList->s; int cnt = queList->cnt; for (i = 0; i < 4; i++) { s = AddOne(cur, i); ret = DealCurStr(s, target, cnt, ptrQueListLastNode, ptrDead, ptrVisit); if (ret > 0) { return ret; } s = MinusOne(cur, i); ret = DealCurStr(s, target, cnt, ptrQueListLastNode, ptrDead, ptrVisit); if (ret > 0) { return ret; } } // printf("\n"); return 0; } int LevelTraverse(StruQueList *queList, StruQueList **ptrQueListLastNode, char *target, StruHashTable **ptrDead, StruHashTable **ptrVisit) { // 得到两个队列的指针,一个是当前指向,一个是层级对应的新开头 // 从所有层每个节点中迭代新的可能 int i, ret; while (queList != NULL) { // 遍历当前层所有节点 int len = g_curLevelCnt; g_curLevelCnt = 0; for (i = 0; i < len; i++) { ret = NodeExpand(queList, ptrQueListLastNode, target, ptrDead, ptrVisit); if (ret > 0) { // 终止条件 return ret; } queList = queList->next; } // printf("\n\n"); } return 0; } // 按队列和BFS的方法来表达每次只转一次,对应的所有可能 int openLock(char ** deadends, int deadendsSize, char * target) { char cur[STR_SIZE] = "0000"; // 初始值 int ret; // special case if (strcmp(cur, target) == 0) { return 0; } // 初始化dead hash StruHashTable *dead = NULL; // 表头最开始都为空 StruHashTable *hashTmp, *hashTmp1, *hashTmp2; InitDeadHash(deadends, deadendsSize, &dead); // special case HASH_FIND(hh, dead, target, sizeof(char) * STR_SIZE, hashTmp1); HASH_FIND(hh, dead, cur, sizeof(char) * STR_SIZE, hashTmp2); if (hashTmp1 != NULL || hashTmp2 != NULL) { return -1; // deanends contain target } // 初始化队列0000和visit hash StruHashTable *visit = NULL; // 表头最开始都为空 PtrStruQueList queList, queListLastNode; InitQueAndVisitHash(cur, &queList, &visit); queListLastNode = queList; ret = LevelTraverse(queList, &queListLastNode, target, &dead, &visit); if (ret > 0) { // 终止条件 return ret; } return -1; // 遍历完所有无匹配 }
A*
算法