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最新推荐文章于 2025-05-29 23:36:29 发布

Magic_insky

最新推荐文章于 2025-05-29 23:36:29 发布

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分类专栏： usaco解题报告文章标签： integer input output file c++ each

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Electric Fence
Don Piele

In this problem, `lattice points' in the plane are points with integer coordinates.

In order to contain his cows, Farmer John constructs a triangular electric fence by stringing a "hot" wire from the origin (0,0) to a lattice point [n,m] (0<=;n<32000, 0<m<32000), then to a lattice point on the positive x axis [p,0] (p>0), and then back to the origin (0,0).

A cow can be placed at each lattice point within the fence without touching the fence (very thin cows). Cows can not be placed on lattice points that the fence touches. How many cows can a given fence hold?

PROGRAM NAME: fence9

INPUT FORMAT

The single input line contains three space-separated integers that denote n, m, and p.

SAMPLE INPUT (file fence9.in)

7 5 10

OUTPUT FORMAT

A single line with a single integer that represents the number of cows the specified fence can hold.

SAMPLE OUTPUT (file fence9.out)

皮克定理的简单应用。S=a+1/2*b-1，方格纸中每个小正方形的边长为1，其中a表示多边形内部的格点数，b表示多边形边界上的格点数，S表示多边形的面积。

/*
ID: fwj_ona1
LANG: C++
TASK: fence9
*/

#include <stdio.h>
#include <iostream>
#include <math.h>
using namespace std;

int gcd(int m,int n);
int main ()
{
	freopen ("fence9.in","r",stdin);
    freopen ("fence9.out","w",stdout);
	int n,m,p;
	double s,b;
	scanf("%d%d%d",&n,&m,&p);
	s=p*m*0.5;
	b=p+gcd(m,n)+gcd(abs(n-p),m);
	printf("%d\n",(int)(s+1-b/2));
	return 0;
}

int gcd(int m,int n)
{
	if(n==0)
		return m;
	while(1)
	{
		m = m%n;
		if(m==0)
			return n;
		n = n%m;
		if(n==0)
			return m;
	}
}