DLX精确覆盖 poj2676 Sudoku

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传送门：点击打开链接

题意：求数独

思路：早就听说了DLX精确覆盖的强大，看了两天终于勉强算是看懂了，关于DLX的详细介绍可以参考下面3位大神总结的

DLX的原理：点击打开链接

DLX用C++的实现代码：点击打开链接

DLX的建图技巧：点击打开链接

要注意的几个地方就是，DLX有两种模式，一种是精确覆盖，一种是重复覆盖。

重复覆盖中包含了一个A*的估计函数，用来剪枝

然后就是把握好建图（感觉这个非常关键）

DLX中包含了许多链表的妙用，比如如何建立循环链表，如何循环除了本身以外的所有其他节点，如何在链表中删除和恢复删除等等，写的非常的飘逸~

#include<map>#include<set>#include<cmath>#include<stack>#include<queue>#include<cstdio>#include<cctype>#include<string>#include<vector>#include<cstring>#include<iostream>#include<algorithm>#include<functional>#define fuck printf("fuck")#define FIN freopen("input.txt","r",stdin)#define FOUT freopen("output.txt","w+",stdout)using namespace std;typedef long long LL;const int MX = 1000 + 5;const int MN = 1000000 + 5;const int INF = 0x3f3f3f3f;int ans[MX][MX];struct DLX {    int m, n;    int H[MX], S[MX];    int Row[MN], Col[MN], rear;    int L[MN], R[MN], U[MN], D[MN];    void Init(int _m, int _n) {        m = _m; n = _n;        rear = n;        for(int i = 0; i <= n; i++) {            S[i] = 0;            L[i] = i - 1;            R[i] = i + 1;            U[i] = D[i] = i;        }        L[0] = n; R[n] = 0;        for(int i = 1; i <= m; i++) {            H[i] = -1;        }    }    void Link(int r, int c) {        int rt = ++rear;        Row[rt] = r; Col[rt] = c; S[c]++;        D[rt] = D[c]; U[D[c]] = rt;        U[rt] = c; D[c] = rt;        if(H[r] == -1) {            H[r] = L[rt] = R[rt] = rt;        } else {            int id = H[r];            R[rt] = R[id]; L[R[id]] = rt;            L[rt] = id; R[id] = rt;        }    }    void Remove(int c) {        R[L[c]] = R[c]; L[R[c]] = L[c];        for(int i = D[c]; i != c; i = D[i]) {            for(int j = R[i]; j != i; j = R[j]) {                D[U[j]] = D[j]; U[D[j]] = U[j];                S[Col[j]]--;            }        }    }    void Resume(int c) {        for(int i = U[c]; i != c; i = U[i]) {            for(int j = L[i]; j != i; j = L[j]) {                D[U[j]] = U[D[j]] = j;                S[Col[j]]++;            }        }        R[L[c]] = L[R[c]] = c;    }    bool Dance(int cnt) {        if(R[0] == 0) return true;        int c = R[0];        for(int i = R[0]; i != 0; i = R[i]) {            if(S[i] < S[c]) c = i;        }        Remove(c);        for(int i = D[c]; i != c; i = D[i]) {            for(int j = R[i]; j != i; j = R[j]) Remove(Col[j]);            int r = Row[i];            ans[(r - 1) / 81 + 1][((r - 1) % 81) / 9 + 1] = ((r - 1) % 81) % 9 + 1;            if(Dance(cnt + 1)) return true;            for(int j = L[i]; j != i; j = L[j]) Resume(Col[j]);        }        Resume(c);        return false;    }} G;int S[MX][MX], vis[10];void check(int x, int y) {    for(int i = 1; i <= 9; i++) vis[i] = 0;    for(int i = 1; i <= 9; i++) {        vis[S[i][y]] = vis[S[x][i]] = 1;    }    int tx = (x - 1) / 3 + 1, ty = (y - 1) / 3 + 1;    for(int i = (tx - 1) * 3 + 1; i <= tx * 3; i++) {        for(int j = (ty - 1) * 3 + 1; j <= ty * 3; j++) {            vis[S[i][j]] = 1;        }    }}int main() {    int T; //FIN;    scanf("%d", &T);    while(T--) {        G.Init(9 * 9 * 9, 4 * 9 * 9);        for(int i = 1; i <= 9; i++) {            for(int j = 1; j <= 9; j++) {                scanf("%1d", &S[i][j]);            }        }        for(int i = 1; i <= 9; i++) {            for(int j = 1; j <= 9; j++) {                int tx = (i - 1) / 3 + 1, ty = (j - 1) / 3 + 1, tp = (tx - 1) * 3 + ty;                if(!S[i][j]) {                    check(i, j);                    for(int k = 1; k <= 9; k++) {                        if(vis[k]) continue;                        int id = ((i - 1) * 9 + j - 1) * 9 + k;                        G.Link(id, (i - 1) * 9 + j);                        G.Link(id, 9 * 9 + (i - 1) * 9 + k);                        G.Link(id, 2 * 9 * 9 + (j - 1) * 9 + k);                        G.Link(id, 3 * 9 * 9 + (tp - 1) * 9 + k);                    }                } else {                    int k = S[i][j];                    int id = ((i - 1) * 9 + j - 1) * 9 + k;                    G.Link(id, (i - 1) * 9 + j);                    G.Link(id, 9 * 9 + (i - 1) * 9 + k);                    G.Link(id, 2 * 9 * 9 + (j - 1) * 9 + k);                    G.Link(id, 3 * 9 * 9 + (tp - 1) * 9 + k);                }            }        }        int ret = G.Dance(0);        for(int i = 1; i <= 9; i++) {            for(int j = 1; j <= 9; j++) {                if(S[i][j]) printf("%d", S[i][j]);                else printf("%d", ans[i][j]);            }            printf("\n");        }    }    return 0;}

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