hust1017 Dancing Links

发表于 分类于

这题因为建图卡了好久，Dancing Links 的入门题，不想多说什么。想了解的请参看 Knuth 的论文。

这里学会了一个很方便的双向链表插入算法，如果要将 xx 插入到双向链表中，只要先更新 xx 的指针域，然后调用 dlx 的第二步就可以了。

在 init 函数有所实现。

我的代码：

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cstring>

using namespace std;

const int nColumn = 1100;
const int nRow = 1100;
const int nNode = nRow * nColumn;
const int head = 0;
const int oo = 0x3f3f3f3f;

int right[nNode], left[nNode], up[nNode], down[nNode];
int cnt[nColumn];
int result[nNode], nResult;
int row[nRow][nColumn], column[nColumn][nRow];
int cntRow[nRow], cntColumn[nColumn];
int nR, nC;

int getColumn(int id) {
  if (id % nC)
    return id % nC;
  else
    return nC;
}

int getId(int r, int c) { return r * nC + c; }

int getRow(int id) { return (id - 1) / nC; }

void remove(const int& x) {
  left[right[x]] = left[x];
  right[left[x]] = right[x];
  for (int r = down[x]; r != x; r = down[r]) {
    for (int c = right[r]; c != r; c = right[c]) {
      up[down[c]] = up[c];
      down[up[c]] = down[c];
      cnt[getColumn(c)]--;
    }
  }
}

void resume(const int& x) {
  for (int r = up[x]; r != x; r = up[r]) {
    for (int c = left[r]; c != r; c = left[c]) {
      cnt[getColumn(c)]++;
      up[down[c]] = c;
      down[up[c]] = c;
    }
  }
  left[right[x]] = x;
  right[left[x]] = x;
}

bool dfs(const int& k) {
  if (right[head] == head) {
    nResult = k;
    return true;
  }
  int S = oo, x = 0;
  for (int t = right[head]; t != head; t = right[t]) {
    if (cnt[t] < S) {
      S = cnt[t];
      x = t;
    }
  }
  remove(x);
  for (int r = down[x]; r != x; r = down[r]) {
    result[k] = getRow(r);
    for (int c = right[r]; c != r; c = right[c]) {
      remove(getColumn(c));
    }
    if (dfs(k + 1)) return true;
    for (int c = left[r]; c != r; c = left[c]) {
      resume(getColumn(c));
    }
  }
  resume(x);
  return false;
}

bool init(int r, int c) {
  int id, pre;
  // deal with list heads
  left[head] = c;
  right[head] = 1;
  for (int i = 1; i <= c; i++) {
    left[i] = i - 1;
    right[i] = (i + 1) % (c + 1);
    up[i] = down[i] = i;
    cnt[i] = cntColumn[i];
    if (cnt[i] == 0) return false;
  }
  // deal with columns
  for (int i = 1; i <= c; i++) {
    for (int j = 0; j < cnt[i]; j++) {
      id = getId(column[i][j], i);
      up[id] = i;
      down[id] = down[i];
      up[down[id]] = id;
      down[up[id]] = id;
      left[id] = right[id] = id;
    }
  }
  // deal with rows
  for (int i = 1; i <= r; i++) {
    for (int j = 1; j < cntRow[i]; j++) {
      id = getId(i, row[i][j]);
      pre = getId(i, row[i][j - 1]);
      left[id] = pre;
      right[id] = right[pre];
      left[right[id]] = id;
      right[left[id]] = id;
    }
  }
  return true;
}

int main() {
  int x;
  while (~scanf("%d%d", &nR, &nC)) {
    for (int i = 1; i <= nC; i++) {
      cntColumn[i] = 0;
    }
    for (int i = 1; i <= nR; i++) {
      scanf("%d", &cntRow[i]);
      for (int j = 0; j < cntRow[i]; j++) {
        scanf("%d", &x);
        row[i][j] = x;
        column[x][cntColumn[x]++] = i;
      }
    }
    if (!init(nR, nC)) {
      puts("NO");
      continue;
    }
    if (!dfs(0)) {
      puts("NO");
      continue;
    }
    printf("%d", nResult);
    for (int i = 0; i < nResult; i++) {
      printf(" %d", result[i]);
    }
    puts("");
  }
  return 0;
}