usaco-3.4-fence9-passed

这个要知道一个公式；

可以算是一道数学题吧。如果知道皮克定理就行了。皮克定理说明了其面积S和内部格点数目a、边上格点数目b的关系：S = a + b/2 - 1。

根据三角形面积公式求出S。如果知道了b，那么三角形内部格点数目a也就求出来了。

可以证明，一条直线((0,0),(n,m))上的格点数等于n与m的最大公约数+1。

即b=gcd(n,m)+1. gcd(n,m)为n与m的最大公约数。

/*
ID: qq104801
LANG: C++
TASK: fence9
*/

#include <iostream>
#include <fstream>
#include <cstring>
#include <vector>
#include <queue>
#include <stack>
#include <algorithm>
using namespace std;

#define nmax 27

int gcd(int a,int b)
{
    return b==0?a:gcd(b,a%b);
}

void test()
{
    freopen("fence9.in","r",stdin);
    freopen("fence9.out","w",stdout);
    int n,m,p,b=0,s;
    cin>>n>>m>>p;
    s=(m*p)/2;
    b+=gcd(n,m);
    if(n!=p)b+=gcd(abs(n-p),m);
    else b+=m;
    b+=p;
    cout<<s+1-(b/2)<<endl;
}

int main ()
{
    test();
    return 0;
}

test data:

USACO Training
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USER: cn tom [qq104801]
TASK: fence9
LANG: C++

Compiling...
Compile: OK

Executing...
   Test 1: TEST OK [0.003 secs, 3372 KB]
   Test 2: TEST OK [0.005 secs, 3372 KB]
   Test 3: TEST OK [0.005 secs, 3372 KB]
   Test 4: TEST OK [0.008 secs, 3372 KB]
   Test 5: TEST OK [0.008 secs, 3372 KB]
   Test 6: TEST OK [0.008 secs, 3372 KB]
   Test 7: TEST OK [0.008 secs, 3372 KB]
   Test 8: TEST OK [0.008 secs, 3372 KB]
   Test 9: TEST OK [0.005 secs, 3372 KB]
   Test 10: TEST OK [0.008 secs, 3372 KB]
   Test 11: TEST OK [0.005 secs, 3372 KB]
   Test 12: TEST OK [0.005 secs, 3372 KB]

All tests OK.

YOUR PROGRAM (‘fence9‘) WORKED FIRST TIME! That‘s fantastic -- and a rare thing. Please accept these special automated congratulations.

Here are the test data inputs:

------- test 1 ----
1 1 2
------- test 2 ----
2 2 4
------- test 3 ----
10 20 10
------- test 4 ----
0 100 100
------- test 5 ----
0 200 20000
------- test 6 ----
100 200 50
------- test 7 ----
10000 100 10
------- test 8 ----
0 20000 2
------- test 9 ----
200 30000 30000
------- test 10 ----
30000 30000 30001
------- test 11 ----
15000 100 30000
------- test 12 ----
0 31999 31999

Keep up the good work!
Thanks for your submission!