Poj--2947（数学，高斯消元，模线性方程）

2014-09-18 22:44:04

思路：比较裸的高斯消元+同余方程。注意几点：（1）对所有输入模7！Gauss过程中也要模7 （2）多解是由自由变元个数决定。

  1 /*************************************************************************
  2     > File Name: 2947.cpp
  3     > Author: Nature
  4     > Mail: 564374850@qq.com
  5     > Created Time: Thu 18 Sep 2014 08:34:31 PM CST
  6 ************************************************************************/
  7 
  8 #include <cstdio>
  9 #include <cstring>
 10 #include <cstdlib>
 11 #include <cmath>
 12 #include <vector>
 13 #include <queue>
 14 #include <map>
 15 #include <iostream>
 16 #include <algorithm>
 17 using namespace std;
 18 typedef long long ll;
 19 const int INF = 1 << 29;
 20 
 21 inline int Gcd(int a,int b){ return b == 0 ? a : Gcd(b,a % b); }
 22 inline int Lcm(int a,int b){ return a / Gcd(a,b) * b; }
 23 
 24 int n,m;
 25 int A[305][305];
 26 
 27 int Check(char *s){
 28     if(strcmp(s,"MON") == 0) return 1;
 29     if(strcmp(s,"TUE") == 0) return 2;
 30     if(strcmp(s,"WED") == 0) return 3;
 31     if(strcmp(s,"THU") == 0) return 4;
 32     if(strcmp(s,"FRI") == 0) return 5;
 33     if(strcmp(s,"SAT") == 0) return 6;
 34     if(strcmp(s,"SUN") == 0) return 7;
 35 }
 36 
 37 int Gauss(){
 38     int equ,var; equ = m; var = n;
 39     int i,j,k,r,col,LCM,ta,tb;
 40     col = 0;
 41     for(i = 0; i < equ && col < var; ++i,++col){
 42         r = i;
 43         for(j = i + 1; j < equ; ++j)
 44             if(abs(A[j][col]) > abs(A[r][col])) r = j;
 45         if(r != i)
 46             for(j = col; j <= var; ++j) swap(A[i][j],A[r][j]);
 47         if(A[i][col] == 0){
 48             --i;
 49             continue;
 50         }
 51         for(k = i + 1; k < equ; ++k) if(A[k][col]){
 52             LCM = Lcm(abs(A[i][col]),abs(A[k][col]));
 53             ta = LCM / abs(A[i][col]);
 54             tb = LCM / abs(A[k][col]);
 55             if(A[i][col] * A[k][col] < 0) ta = -ta;
 56             for(j = col; j <= var; ++j)
 57                 A[k][j] = ((A[k][j] * tb - A[i][j] * ta) % 7+ 7) % 7;
 58         }
 59     }
 60     for(k = i; k < equ; ++k) if(A[k][col] != 0)
 61         return -2;
 62     if(var - i > 0)
 63         return -1;
 64     for(i = var - 1; i >= 0; --i){
 65         for(j = i + 1; j < var; ++j){
 66             A[i][var] = ((A[i][var] - A[i][j] * A[j][var]) % 7 + 7) % 7;
 67         }
 68         while(A[i][var] % A[i][i] != 0) A[i][var] += 7;
 69         A[i][var] /= A[i][i];
 70         while(A[i][var] < 3) A[i][var] += 7;
 71         while(A[i][var] > 9) A[i][var] -=7;
 72     }
 73     return 1;
 74 }
 75 
 76 
 77 
 78 int main(){
 79     int num,a;
 80     char st[10],ed[10];
 81     while(scanf("%d%d",&n,&m) != EOF){
 82         if(n == 0 && m == 0)
 83             break;
 84         memset(A,0,sizeof(A));
 85         for(int i = 0; i < m; ++i){
 86             scanf("%d%s%s",&num,st,ed);
 87             while(num--){
 88                 scanf("%d",&a);
 89                 A[i][a - 1]++;
 90                 A[i][a - 1] %= 7;
 91             }
 92             A[i][n] = (Check(ed) - Check(st) + 1 + 7) % 7;
 93         }
 94         int t = Gauss();
 95         if(t == -2) printf("Inconsistent data.\n");
 96         else if(t == -1) printf("Multiple solutions.\n");
 97         else{
 98             printf("%d",A[0][n]);
 99             for(int i = 1; i < n; ++i) printf(" %d",A[i][n]);
100             puts("");
101         }
102     }
103     return 0;
104 }

 

posted @ 2014-09-18 22:46  Naturain  阅读(175)  评论(0)    收藏  举报