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

 1 #include <cstdio>

 2 #include <cstring>

 3 #include <cstdlib>

 4 #include <cmath>

 5 #include <algorithm>

 6 

 7 #define LL long long int

 8 

 9 using namespace std;

10 

11 void ExGcd( LL a, LL b, LL &d, LL &x, LL &y )

12 {

13     if ( !b )

14         d = a, x = 1, y = 0;

15     else

16     {

17         ExGcd( b, a % b, d, y, x );

18         y -= x * ( a / b );

19     }

20     return;

21 }

22 

23 int main()

24 {

25     LL a, b, c, x1, x2, y1, y2;

26     while ( scanf( "%I64d%I64d%I64d%I64d%I64d%I64d%I64d", &a, &b, &c, &x1, &x2, &y1, &y2 ) == 7 )

27     {

28         if ( a == 0 && b == 0 )

29         {

30             if ( c == 0 )

31                 printf( "%I64d\n", (x2 - x1 + 1)*(y2 - y1 + 1) );

32             else puts("0");

33             continue;

34         }

35         if ( a == 0 )

36         {

37             if ( (-c) % b == 0 )

38             {

39                 LL y = (-c) / b;

40                 if ( y >= y1 && y <= y2 ) puts("1");

41                 else puts("0");

42             }

43             else puts("0");

44 

45             continue;

46         }

47         if ( b == 0 )

48         {

49             if ( (-c) % a == 0 )

50             {

51                 LL x = (-c) / a;

52                 if ( x >= x1 && x <= x2 ) puts("1");

53                 else puts("0");

54             }

55             else puts("0");

56             continue;

57         }

58         LL g, x0, y0;

59         ExGcd( a, b, g, x0, y0 );

60         if ( (-c) % g == 0 ) //如果有解

61         {

62             x0 = x0 * (-c) / g;

63             y0 = y0 * (-c) / g;

64 

65             LL aa = a / g;

66             LL bb = b / g;

67             LL low, high;

68             if ( aa > 0 && bb > 0 )

69             {

70                 low  = max( (x0 - x1) / bb, (y0 - y2) / aa );

71                 high = min( (x2 - x0) / bb, (y0 - y1) / aa );

72                 printf("%I64d\n", high - low + 1 );

73             }

74             else if ( aa > 0 && bb < 0 )

75             {

76                 low  = max( (x2 - x0) / bb, (y0 - y2) / aa );

77                 high = min( (x0 - x1) / bb, (y0 - y1) / aa );

78                 printf("%I64d\n", high - low + 1 );

79             }

80             else if ( aa < 0 && bb > 0 )

81             {

82                 low  = max( (x0 - x1) / bb, (y0 - y1) / aa );

83                 high = min( (x2 - x0) / bb, (y0 - y2) / aa );

84                 printf("%I64d\n", high - low + 1 );

85             }

86             else if ( aa < 0 && bb < 0 )

87             {

88                 low  = max( (x2 - x0) / bb, (y0 - y1) / aa );

89                 high = min( (x0 - x1) / bb, (y0 - y2) / aa );

90                 printf("%I64d\n", high - low + 1 );

91             }

92         }

93         else puts("0");

94     }

95     return 0;

96 }