【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。

#include<cstdio>
#include<cstring>
#include<algorithm>
#define MAXN 330
using namespace std;
int n, m;
int g[MAXN][MAXN], x[MAXN];
int Day(char str[]) {
    if (strcmp(str, "MON") == 0)
        return 1;
    if (strcmp(str, "TUE") == 0)
        return 2;
    if (strcmp(str, "WED") == 0)
        return 3;
    if (strcmp(str, "THU") == 0)
        return 4;
    if (strcmp(str, "FRI") == 0)
        return 5;
    if (strcmp(str, "SAT") == 0)
        return 6;
    return 7;
}
int Gauss() {
    int r, c, i, j, k, tmp;
    for (c = k = 0; c < n; c++) {
        for (r = k; r < m; r++) {
            if (g[r][c])
                break;
        }
        if (r < m) {
            if (r != k) {
                for (i = c; i <= n; i++)
                    swap(g[r][i], g[k][i]);
            }
            for (i = k + 1; i < m; i++) {
                if (g[i][c]) {
                    tmp = g[i][c];
                    for (j = c; j <= n; j++) {
                        g[i][j] = g[i][j] * g[k][c] - g[k][j] * tmp;
                        g[i][j] = (g[i][j] % 7 + 7) % 7;
                    }
                }
            }
            k++;
        }
    }
    for (i = tmp = 0; i < m; i++) {
        for (j = 0; j < n; j++) {
            if (g[i][j])
                break;
        }
        if (j == n) {
            if (g[i][n])
                return 1;
            else if (i < n)
                tmp = 1;
        }
    }
    if (tmp || m < n)
        return 0;
    for (i = n - 1; i >= 0; i--) {
        tmp = 0;
        for (j = i + 1; j < n; j++) {
            tmp += x[j] * g[i][j];
            tmp %= 7;
        }
        for (j = 3; j <= 9; j++) {
            if ((tmp + j * g[i][i]) % 7 == g[i][n]) {
                x[i] = j;
                break;
            }
            if (j > 9)
                return 1;
        }
    }
    return 2;
}
int main() {
    int i, j, k, tmp;
    char st[MAXN], nd[MAXN];
    while (scanf("%d%d", &n, &m), n) {
        memset(g, 0, sizeof(g));
        for (i = 0; i < m; i++) {
            scanf("%d %s %s", &k, st, nd);
            while (k--) {
                scanf("%d", &tmp);
                g[i][tmp - 1]++;
            }
            g[i][n] = Day(nd) - Day(st) + 1;
        }
        for (i = 0; i < m; i++) {
            for (j = 0; j <= n; j++)
                g[i][j] = (g[i][j] % 7 + 7) % 7;
        }
        tmp = Gauss();
        if (tmp == 0)
            puts("Multiple solutions.");
        else if (tmp == 1)
            puts("Inconsistent data.");
        else {
            printf("%d", x[0]);
            for (i = 1; i < n; i++)
                printf(" %d", x[i]);
            putchar('\n');
        }
    }
    return 0;
}