【POJ】2947 Widget Factory

列出同余方程，高斯消元。
无穷解的同时，可能出现无解，所以先判无穷解，再判无解。
最后枚举答案，还可能无解。
  1 #include<cstdio>
  2 #include<cstring>
  3 #include<algorithm>
  4 #define MAXN 330
  5 using namespace std;
  6 int n, m;
  7 int g[MAXN][MAXN], x[MAXN];
  8 int Day(char str[]) {
  9     if (strcmp(str, "MON") == 0)
 10         return 1;
 11     if (strcmp(str, "TUE") == 0)
 12         return 2;
 13     if (strcmp(str, "WED") == 0)
 14         return 3;
 15     if (strcmp(str, "THU") == 0)
 16         return 4;
 17     if (strcmp(str, "FRI") == 0)
 18         return 5;
 19     if (strcmp(str, "SAT") == 0)
 20         return 6;
 21     return 7;
 22 }
 23 int Gauss() {
 24     int r, c, i, j, k, tmp;
 25     for (c = k = 0; c < n; c++) {
 26         for (r = k; r < m; r++) {
 27             if (g[r][c])
 28                 break;
 29         }
 30         if (r < m) {
 31             if (r != k) {
 32                 for (i = c; i <= n; i++)
 33                     swap(g[r][i], g[k][i]);
 34             }
 35             for (i = k + 1; i < m; i++) {
 36                 if (g[i][c]) {
 37                     tmp = g[i][c];
 38                     for (j = c; j <= n; j++) {
 39                         g[i][j] = g[i][j] * g[k][c] - g[k][j] * tmp;
 40                         g[i][j] = (g[i][j] % 7 + 7) % 7;
 41                     }
 42                 }
 43             }
 44             k++;
 45         }
 46     }
 47     for (i = tmp = 0; i < m; i++) {
 48         for (j = 0; j < n; j++) {
 49             if (g[i][j])
 50                 break;
 51         }
 52         if (j == n) {
 53             if (g[i][n])
 54                 return 1;
 55             else if (i < n)
 56                 tmp = 1;
 57         }
 58     }
 59     if (tmp || m < n)
 60         return 0;
 61     for (i = n - 1; i >= 0; i--) {
 62         tmp = 0;
 63         for (j = i + 1; j < n; j++) {
 64             tmp += x[j] * g[i][j];
 65             tmp %= 7;
 66         }
 67         for (j = 3; j <= 9; j++) {
 68             if ((tmp + j * g[i][i]) % 7 == g[i][n]) {
 69                 x[i] = j;
 70                 break;
 71             }
 72             if (j > 9)
 73                 return 1;
 74         }
 75     }
 76     return 2;
 77 }
 78 int main() {
 79     int i, j, k, tmp;
 80     char st[MAXN], nd[MAXN];
 81     while (scanf("%d%d", &n, &m), n) {
 82         memset(g, 0, sizeof(g));
 83         for (i = 0; i < m; i++) {
 84             scanf("%d %s %s", &k, st, nd);
 85             while (k--) {
 86                 scanf("%d", &tmp);
 87                 g[i][tmp - 1]++;
 88             }
 89             g[i][n] = Day(nd) - Day(st) + 1;
 90         }
 91         for (i = 0; i < m; i++) {
 92             for (j = 0; j <= n; j++)
 93                 g[i][j] = (g[i][j] % 7 + 7) % 7;
 94         }
 95         tmp = Gauss();
 96         if (tmp == 0)
 97             puts("Multiple solutions.");
 98         else if (tmp == 1)
 99             puts("Inconsistent data.");
100         else {
101             printf("%d", x[0]);
102             for (i = 1; i < n; i++)
103                 printf(" %d", x[i]);
104             putchar('\n');
105         }
106     }
107     return 0;
108 }
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