双广，16MS，相当快。
1 # include <stdio.h> 2 # include <string.h> 3 4 # define MAXN (362880 + 5) 5 6 typedef struct 7 { 8 char a[9]; 9 }state; 10 11 typedef struct 12 { 13 int k; 14 char d; 15 }path; 16 17 path p[MAXN]; 18 const char md[4] = {'u','l','r','d'}; 19 const int dir[4][2] = {{-1,0}, {0,-1}, {0,1}, {1,0}}; 20 int fact[9]; 21 22 int front, rear; 23 state cur, nst; /* new state */ 24 char vis[MAXN]; 25 char dist[MAXN]; /* 求的是最短距离( < 100)，可以用 char 类型 */ 26 state Q[MAXN/2]; 27 28 void print_path(int x, char f); 29 char equal(state x, state y); 30 void read(state *s); 31 int inversions(state s); 32 int cantor(state s); 33 void init_fact(void); 34 int bfs_d(state start, state goal); 35 36 int main() 37 { 38 int i; 39 state start, goal; 40 41 init_fact(); 42 43 read(&start); 44 goal.a[8] = 0; 45 for (i = 0; i < 8; ++i) 46 goal.a[i] = i + 1; 47 48 if (inversions(start)%2 == inversions(goal)%2) 49 { 50 if (equal(start, goal)) putchar('\n'); 51 else bfs_d(start, goal); 52 } 53 else puts("unsolvable"); 54 55 return 0; 56 } 57 58 int bfs_d(state start, state goal) 59 { 60 int i, x, y, nx, ny, ct, nt; 61 62 memset(vis, 0, sizeof(vis)); 63 memset(dist, 0, sizeof(dist)); 64 65 front = 1; 66 Q[front] = start; 67 rear = 2; 68 Q[rear++] = goal; 69 vis[cantor(start)] = 1; /* 1 表示从起始节点扩展得到 */ 70 vis[cantor(goal)] = 2; /* 2 表示从目标节点扩展得到 */ 71 72 while (front < rear) 73 { 74 cur = Q[front++]; 75 ct = cantor(cur); 76 for (i = 0; cur.a[i] && i < 9; ++i) ; 77 x = i / 3; 78 y = i % 3; 79 for (i = 0; i < 4; ++i) 80 { 81 nx = x + dir[i][0]; 82 ny = y + dir[i][1]; 83 if (nx>=0 && nx<3 && ny>=0 && ny<3) 84 { 85 nst = cur; 86 nst.a[x*3+y] = cur.a[nx*3+ny]; 87 nst.a[nx*3+ny] = 0; 88 if (!vis[nt = cantor(nst)]) 89 { 90 Q[rear++] = nst; 91 p[nt].k = ct; 92 p[nt].d = i; 93 dist[nt] = dist[ct] + 1; 94 vis[nt] = vis[ct]; 95 } 96 else if (vis[ct] != vis[nt]) 97 { 98 if (vis[ct] == 1) 99 { 100 print_path(ct, 0); 101 putchar(md[i]); 102 print_path(nt, 1); 103 } 104 else 105 { 106 print_path(nt, 0); 107 putchar(md[3-i]); 108 print_path(ct, 1); 109 } 110 return 1 + dist[nt] + dist[ct]; 111 } 112 } 113 } 114 } 115 116 return -1; 117 } 118 119 void read(state *s) 120 { 121 int i; 122 char c[5]; 123 124 for (i = 0; i < 9; ++i) 125 { 126 scanf("%s", c); 127 if (c[0] == 'x') (*s).a[i] = 0; 128 else (*s).a[i] = c[0] - '0'; 129 } 130 } 131 132 int inversions(state s) 133 { 134 char ch; 135 int i, j, ret; 136 137 ret = 0; 138 for (i = 0; i < 9; ++i) 139 { 140 if (s.a[i] == 0) continue; 141 ch = s.a[i]; 142 for (j = i+1; j < 9; ++j) 143 { 144 if (s.a[j] < ch && s.a[j] != 0) 145 ++ret; 146 } 147 } 148 149 return ret; 150 } 151 152 int cantor(state s) 153 { 154 char ch; 155 int i, j, ret, cnt; 156 157 ret = 0; 158 for (i = 0; i < 9; ++i) 159 { 160 cnt = 0; 161 ch = s.a[i]; 162 for (j = i+1; j < 9; ++j) 163 { 164 if (s.a[j] < ch) 165 ++cnt; 166 } 167 ret += cnt*fact[8-i]; 168 } 169 170 return ret; 171 } 172 173 void init_fact(void) 174 { 175 int i; 176 177 fact[0] = 1; 178 for (i = 1; i < 9; ++i) 179 { 180 fact[i] = i * fact[i-1]; 181 } 182 } 183 184 void print_path(int x, char f) 185 { 186 if (p[x].k == 0) return; 187 if (!f) 188 { 189 print_path(p[x].k, f); 190 putchar(md[p[x].d]); 191 } 192 else 193 { 194 putchar(md[3-p[x].d]); 195 print_path(p[x].k, f); 196 } 197 } 198 199 char equal(state x, state y) 200 { 201 int i; 202 203 for (i = 0; i < 9; ++i) 204 if (x.a[i] != y.a[i]) return 0; 205 206 return 1; 207 }
有点长。
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优化了一下：16MS（C）
1 # include <stdio.h> 2 # include <string.h> 3 4 # define N 9 5 # define MAXN (362880 + 10) 6 7 typedef struct{ int k; char d; }foot; 8 typedef struct{ char a[N]; }state; 9 10 const char md[4] = {'u', 'l', 'r', 'd'}; 11 const char d[4][2] = {{-1,0}, {0,-1}, {0,1}, {1,0}}; 12 const int fact[9] = {1, 1, 2, 6, 24, 120, 720, 720*7, 720*56}; 13 14 state Q[MAXN/10]; 15 char vis[MAXN]; 16 foot p[MAXN]; 17 18 int cantor(state s) 19 { 20 char ch; 21 int i, j, cnt, ret; 22 23 ret = 0; 24 for (i = 0; i < N-1; ++i) 25 { 26 cnt = 0; 27 ch = s.a[i]; 28 for (j = i+1; j < N; ++j) 29 if (s.a[j] < ch) ++cnt; 30 ret += cnt*fact[8-i]; 31 } 32 33 return ret; 34 } 35 36 char bool_inv(state s) 37 { 38 char ch, ret; 39 int i, j; 40 41 ret = 0; 42 for (i = 0; i < N-1; ++i) 43 { 44 if ((ch = s.a[i]) == 0) continue; 45 for (j = i+1; j < N; ++j) 46 if (s.a[j] && s.a[j] < ch) ret = 1 - ret; 47 } 48 49 return ret; 50 } 51 52 void print_path(int x, char f) 53 { 54 if (p[x].k == 0) return ; 55 if (f) putchar(md[3-p[x].d]); 56 print_path(p[x].k, f); 57 if (!f) putchar(md[p[x].d]); 58 } 59 60 void bfs(state start, state goal) 61 { 62 char t; 63 state cur, nst; 64 int front, rear, i; 65 int x, y, nx, ny, ct, nt; 66 67 Q[front = 1] = start; 68 Q[rear = 2] = goal; 69 vis[cantor(start)] = 1; 70 vis[cantor(goal)] = 2; 71 72 while (front <= rear) 73 { 74 cur = Q[front++]; 75 ct = cantor(cur); 76 for (i = 0; cur.a[i] && i < N; ++i) ; 77 x = i / 3; y = i % 3; 78 for (i = 0; i < 4; ++i) 79 { 80 nx = x + d[i][0]; ny = y + d[i][1]; 81 if (nx>=0 && nx<3 && ny>=0 && ny<3) 82 { 83 nst = cur; 84 nst.a[x*3+y] = cur.a[nx*3+ny]; 85 nst.a[nx*3+ny] = 0; 86 nt = cantor(nst); 87 if (!vis[nt]) 88 { 89 Q[++rear] = nst; 90 p[nt].k = ct; 91 p[nt].d = i; 92 vis[nt] = vis[ct]; 93 } 94 else if (vis[ct] != vis[nt]) 95 { 96 t = (vis[ct]==1 ? 1:0); 97 print_path(t ? ct:nt, 0); 98 putchar(md[t ? i:3-i]); 99 print_path(t ? nt:ct, 1); 100 putchar('\n'); 101 return ; 102 } 103 } 104 } 105 } 106 } 107 108 int main() 109 { 110 char i, c[5]; 111 state start, goal; 112 113 for (i = 0; i < N; ++i) 114 { 115 scanf("%s", c); 116 start.a[i] = (c[0]=='x' ? 0:c[0]-'0'); 117 } 118 goal.a[8] = 0; 119 for (i = 0; i < N-1; ++i) 120 goal.a[i] = i + 1; 121 122 for (i = 0; start.a[i] == goal.a[i] && i < N; ++i) ; 123 if (i == N) puts(""); 124 else if (bool_inv(start) != bool_inv(goal)) puts("unsolvable"); 125 else bfs(start, goal); 126 127 return 0; 128 }