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 = 1, y = 0;
    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 ) == 7 )
    {
        if ( a == 0 && b == 0 )
        {
            if ( c == 0 )
                printf( "%I64d
", (x2 - x1 + 1)*(y2 - y1 + 1) );
            else puts("0");
            continue;
        }
        if ( a == 0 )
        {
            if ( (-c) % b == 0 )
            {
                LL y = (-c) / b;
                if ( y >= y1 && y <= y2 ) puts("1");
                else puts("0");
            }
            else puts("0");

            continue;
        }
        if ( b == 0 )
        {
            if ( (-c) % a == 0 )
            {
                LL x = (-c) / a;
                if ( x >= x1 && x <= x2 ) puts("1");
                else puts("0");
            }
            else puts("0");
            continue;
        }
        LL g, x0, y0;
        ExGcd( a, b, g, x0, y0 );
        if ( (-c) % g == 0 ) //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 > 0 && bb > 0 )
            {
                low  = max( (x0 - x1) / bb, (y0 - y2) / aa );
                high = min( (x2 - x0) / bb, (y0 - y1) / aa );
                printf("%I64d
", high - low + 1 );
            }
            else if ( aa > 0 && bb < 0 )
            {
                low  = max( (x2 - x0) / bb, (y0 - y2) / aa );
                high = min( (x0 - x1) / bb, (y0 - y1) / aa );
                printf("%I64d
", high - low + 1 );
            }
            else if ( aa < 0 && bb > 0 )
            {
                low  = max( (x0 - x1) / bb, (y0 - y1) / aa );
                high = min( (x2 - x0) / bb, (y0 - y2) / aa );
                printf("%I64d
", high - low + 1 );
            }
            else if ( aa < 0 && bb < 0 )
            {
                low  = max( (x2 - x0) / bb, (y0 - y1) / aa );
                high = min( (x0 - x1) / bb, (y0 - y2) / aa );
                printf("%I64d
", high - low + 1 );
            }
        }
        else puts("0");
    }
    return 0;
}