POJ2947Widget Factory(高斯消元解同模方程)

  1 #include <map>
  2 #include <set>
  3 #include <stack>
  4 #include <queue>
  5 #include <cmath>
  6 #include <ctime>
  7 #include <vector>
  8 #include <cstdio>
  9 #include <cctype>
 10 #include <cstring>
 11 #include <cstdlib>
 12 #include <iostream>
 13 //#include <algorithm>
 14 using namespace std;
 15 #define INF 0x3f3f3f3f
 16 #define inf ((LL)1<<40)
 17 #define lson k<<1, L, mid
 18 #define rson k<<1|1, mid+1, R
 19 #define mem0(a) memset(a,0,sizeof(a))
 20 #define mem1(a) memset(a,-1,sizeof(a))
 21 #define mem(a, b) memset(a, b, sizeof(a))
 22 #define FOPENIN(IN) freopen(IN, "r", stdin)
 23 #define FOPENOUT(OUT) freopen(OUT, "w", stdout)
 24 template<class T> T ABS ( T a) { return a >= 0 ? a : -a;   }
 25 template<class T> T CMP_MIN ( T a, T b ) { return a < b;   }
 26 template<class T> T CMP_MAX ( T a, T b ) { return a > b;   }
 27 template<class T> T MAX ( T a, T b ) { return a > b ? a : b; }
 28 template<class T> T MIN ( T a, T b ) { return a < b ? a : b; }
 29 template<class T> T GCD ( T a, T b ) { return b ? GCD ( b, a % b ) : a; }
 30 template<class T> T LCM ( T a, T b ) { return a / GCD ( a, b ) * b;     }
 31 template<class T> void SWAP( T& a, T& b ) { T t = a; a = b;  b = t;     }
 32 
 33 typedef __int64 LL;
 34 //typedef long long LL;
 35 const int MAXN = 310;
 36 const int MAXM = 110000;
 37 const double eps = 1e-14;
 38 const double PI = 4.0 * atan(1.0);
 39 
 40 char str[7][10] = {"MON", "TUE", "WED", "THU", "FRI", "SAT", "SUN"};
 41 
 42 int findNum(char *s)
 43 {
 44     for(int i = 0; i < 7; i ++ )
 45     {
 46         if(strcmp(str[i], s) == 0) return i;
 47     }
 48     return 0;
 49 }
 50 int n, m, k, cnt[MAXN];
 51 int var, equ, a[MAXN][MAXN], ans[MAXN];
 52 
 53 void init()
 54 {
 55     int x;
 56     char st[10], ed[10];
 57     mem0(a);
 58     var = n;
 59     equ = m;
 60     for(int i = 0; i < m; i ++ )
 61     {
 62         mem0(cnt);
 63         scanf("%d %s %s", &k, st, ed);
 64         for(int j = 0; j < k; j ++ )
 65         {
 66             scanf("%d", &x);
 67             cnt[x-1] ++;
 68         }
 69         a[i][var] = findNum(ed) - findNum(st) + 1;
 70         for(int j = 0; j < var; j ++ )
 71             a[i][j] = cnt[j] % 7;
 72     }
 73 }
 74 
 75 void exgcd(int a, int b, int& x, int& y)
 76 {
 77     if(!b) { x = 1; y = 0; }
 78     else { exgcd(b, a % b, y, x); y -= x*(a/b); }
 79 }
 80 
 81 int gauss()
 82 {
 83     int x, y;
 84     int k, col = 0;
 85     for(k = 0; k < equ && col < var; k ++, col ++)
 86     {
 87         int Max = 0, row = -1;
 88         for(int r = k ; r < equ; r ++)
 89         {
 90             if( Max < ABS(a[r][col]) )
 91                 Max = ABS( a[r][col] ), row = r;
 92         }
 93         if(row == -1)
 94         {
 95             k--;
 96             continue;
 97         }
 98         for(int c = col; c <= var; c ++)
 99             SWAP(a[k][c], a[row][c]);
100         for(int r = k + 1; r < equ; r ++)
101         {
102             if(a[r][col])
103             {
104                 int lcm = LCM(ABS(a[k][col]), ABS(a[r][col]));
105                 int ta = lcm / a[r][col];
106                 int tb = lcm / a[k][col];
107                 if(a[r][col] * a[k][col] < 0) tb = -tb;
108                 for(int c = col; c <= var; c ++ )
109                 {
110                     a[r][c] = a[r][c] * ta - a[k][c] * tb;
111                     a[r][c] = (a[r][c] % 7 + 7) % 7;
112                 }
113             }
114         }
115     }
116     for(int r = k; r < equ; r ++)
117     {
118         if(a[r][var]) return -1;
119     }
120     if(k < var) return 1;
121     for(int r = var - 1; r >= 0; r --)
122     {
123         int tmp = a[r][var];
124         for(int c = var - 1; c > r; c -- )
125         {
126             tmp -= ans[c] * a[r][c] % 7;
127         }
128         tmp = (tmp % 7 + 7) % 7;
129         exgcd(a[r][r], 7, x, y);
130         ans[r] = (tmp * x % 7 + 7) % 7;
131         if(ans[r] < 3) ans[r] += 7;
132     }
133     return 0;
134 }
135 
136 int main()
137 {
138     //FOPENIN("in.txt");
139     while(~scanf("%d %d", &n, &m) && (n || m))
140     {
141         init();
142         int free_num = gauss();
143         if(free_num == -1)
144         {
145             printf("Inconsistent data.\n");
146         }
147         else if(free_num == 1)
148         {
149             printf("Multiple solutions.\n");
150         }
151         else
152         {
153             for(int i = 0; i < var; i ++ )
154             {
155                 printf("%d%c", ans[i], i == var-1 ? ‘\n‘ : ‘ ‘);
156             }
157         }
158     }
159     return 0;
160 }