//HDOJ 4069 Squiggly Sudoku 精确覆盖+搜索/*题意：数独变形 9块弯弯曲曲的区域 每块有9个小格 往这81个格子里面填写1-9的数字，使得每行，每列，每个区域都含有1、2、3...9思路：先搜索标记出每一块 再精确覆盖*/#include<iostream>#include<stdio.h>#include<string.h>#include<queue>using namespace std;#define INF 0x7FFFFFFF#define N 750#define M 350#define V N*Mint n, m, size, row, cnt;int L[V], R[V], U[V], D[V], C[V] , X[V];int S[M], Q[N] , H[N];int s[10][10];bool map[100][100],vis[N];int dir[][2] = {0,-1,1,0,0,1,-1,0};int bx[] = {128,64,32,16};int color[10][10],ans[N];struct node{ int x,y;};void init(){ int i; for (i = 0; i <= m; i++){ S[i] = 0; L[i + 1] = i; R[i] = i + 1; U[i] = D[i] = i; } R[m] = 0; size = m + 1;}void remove(int c){ int i, j; R[L[c]] = R[c]; L[R[c]] = L[c]; for (i = D[c]; i != c; i = D[i]){ for (j = R[i]; j != i; j = R[j]){ D[U[j]] = D[j]; U[D[j]] = U[j]; S[C[j]]--; } }}void resume(int c){ int i, j; R[L[c]] = c; L[R[c]] = c; for (i = D[c]; i != c; i = D[i]){ for (j = R[i]; j != i; j = R[j]){ U[D[j]] = j; D[U[j]] = j; S[C[j]]++; } }}void Link(int r, int c){ D[size] = D[c]; U[size] = c; U[D[c]] = size; D[c] = size; if (H[r] < 0) H[r] = L[size] = R[size] = size; else{ L[size] = H[r]; R[size] = R[H[r]]; L[R[H[r]]] = size; R[H[r]] = size; } S[c]++; C[size] = c; X[size++] = r;}bool Dance(){ int i, j, c, temp; if (R[0] == 0){ ++cnt; if(cnt == 1){ for(i = j = 1; i <= row; ++i) if(vis[i]) ans[j++] = Q[i]; } return cnt > 1; } for (temp = INF, i = R[0]; i; i = R[i]){ if (S[i] < temp){ c = i; temp = S[i]; } } remove(c); for (i = D[c]; i != c; i = D[i]){ vis[X[i]] = true; for (j = R[i]; j != i; j = R[j]) remove(C[j]); if (Dance()) return true; for (j = L[i]; j != i; j = L[j]) resume(C[j]); vis[X[i]] = false; } resume(c); return false;}bool check(int x,int y){ if(x>=1 && x<=9 && y>=1 && y<=9) return true; return false;}void Init(){ int i,j,k,x,y; memset(map,false,sizeof(map)); for(i = 1; i <= 9; ++i){ for(j = 1; j <= 9; ++j){ scanf("%d",&s[i][j]); for(k = 0; k < 4; ++k){ if(s[i][j] >= bx[k]) s[i][j] -= bx[k]; else{ x = i + dir[k][0]; y = j + dir[k][1]; if(check(x,y)) map[(i-1)*9+j][(x-1)*9+y] = true; } } } }}void bfs(int x,int y,int c){ int k; queue<node>Q; node p,q; p.x = x; p.y = y; Q.push(p); while(!Q.empty()){ q = Q.front(); Q.pop(); for(k = 0; k < 4; ++k){ p.x = q.x + dir[k][0]; p.y = q.y + dir[k][1]; if(check(p.x,p.y) && map[(q.x-1)*9+q.y][(p.x-1)*9+p.y] && color[p.x][p.y]==-1){ color[p.x][p.y] = c; Q.push(p); } } }}void Color(){ int i,j,num = 0; memset(color,-1,sizeof(color)); for(i = 1; i <= 9; ++i) for(j = 1; j <= 9; ++j){ if(color[i][j] == -1){ color[i][j] = num; bfs(i,j,num); num++; } }}void Build(){ init(); int i,j,k; row = 0; for(i = 1; i <= 9; ++i){ for(j = 1; j <= 9; ++j){ if(s[i][j] == 0){ for(k = 1; k <= 9; ++k){ H[++row] = -1; Q[row] = k; Link(row,(i-1)*9+k); Link(row,81+(j-1)*9+k); Link(row,162+color[i][j]*9+k); Link(row,243+(i-1)*9+j); } } else{ H[++row] = -1; k = s[i][j]; Q[row] = k; Link(row,(i-1)*9+k); Link(row,81+(j-1)*9+k); Link(row,162+color[i][j]*9+k); Link(row,243+(i-1)*9+j); } } }}int main(){ int T,i,j,num,ca = 1; int x,y; m = 324; scanf("%d",&T); while(T--){ Init(); Color(); Build(); memset(vis,false,sizeof(vis)); cnt = 0; Dance(); printf("Case %d:\n",ca++); if(cnt == 0) puts("No solution"); else if(cnt > 1) puts("Multiple Solutions"); else{ num = 1; for(i = 1; i <= 9; ++i){ for(j = 1; j <= 9; ++j){ printf("%d",ans[num]); if(num%9 == 0) puts(""); num++; } } } } return 0;}
