SGU 106 The equation 扩展欧几里得好题

扩展欧几里得的应用……见算法竞赛入门经典p.179

注意两点：1.解不等式的时候除负数变号

2.各种特殊情况的判断( a=0 && b=0 && c=0 ) ( a=0 && b=0 && c!=0 ) ( a=0 && b!=0 )( a!=0 && b=0 )

能加深对扩展欧几里得的理解，不错的一题

 #include <cstdio>
 #include <cstring>
 #include <cstdlib>
 #include <cmath>
 #include <algorithm>

 #define LL long long int

 using namespace std;

 void ExGcd( LL a, LL b, LL &d, LL &x, LL &y )
 {
     if ( !b )
         d = a, x = , y = ;
     else
     {
         ExGcd( b, a % b, d, y, x );
         y -= x * ( a / b );
     }
     return;
 }

 int main()
 {
     LL a, b, c, x1, x2, y1, y2;
     while ( scanf( "%I64d%I64d%I64d%I64d%I64d%I64d%I64d", &a, &b, &c, &x1, &x2, &y1, &y2 ) ==  )
     {
         if ( a ==  && b ==  )
         {
             if ( c ==  )
                 printf( "%I64d\n", (x2 - x1 + )*(y2 - y1 + ) );
             else puts("");
             continue;
         }
         if ( a ==  )
         {
             if ( (-c) % b ==  )
             {
                 LL y = (-c) / b;
                 if ( y >= y1 && y <= y2 ) puts("");
                 else puts("");
             }
             else puts("");

             continue;
         }
         if ( b ==  )
         {
             if ( (-c) % a ==  )
             {
                 LL x = (-c) / a;
                 if ( x >= x1 && x <= x2 ) puts("");
                 else puts("");
             }
             else puts("");
             continue;
         }
         LL g, x0, y0;
         ExGcd( a, b, g, x0, y0 );
         if ( (-c) % g ==  ) //如果有解
         {
             x0 = x0 * (-c) / g;
             y0 = y0 * (-c) / g;

             LL aa = a / g;
             LL bb = b / g;
             LL low, high;
             if ( aa >  && bb >  )
             {
                 low  = max( (x0 - x1) / bb, (y0 - y2) / aa );
                 high = min( (x2 - x0) / bb, (y0 - y1) / aa );
                 printf("%I64d\n", high - low +  );
             }
             else if ( aa >  && bb <  )
             {
                 low  = max( (x2 - x0) / bb, (y0 - y2) / aa );
                 high = min( (x0 - x1) / bb, (y0 - y1) / aa );
                 printf("%I64d\n", high - low +  );
             }
             else if ( aa <  && bb >  )
             {
                 low  = max( (x0 - x1) / bb, (y0 - y1) / aa );
                 high = min( (x2 - x0) / bb, (y0 - y2) / aa );
                 printf("%I64d\n", high - low +  );
             }
             else if ( aa <  && bb <  )
             {
                 low  = max( (x2 - x0) / bb, (y0 - y1) / aa );
                 high = min( (x0 - x1) / bb, (y0 - y2) / aa );
                 printf("%I64d\n", high - low +  );
             }
         }
         else puts("");
     }
     return ;
 }