poj 1265 Area Pick定理

Posted 2020-06-20 yohaha

题目链接

pick定理： 一个计算点阵中顶点在格点上的多边形面积公式：S=a+b÷2-1，其中a表示多边形内部的点数，b表示多边形边界上的点数，s表示多边形的面积

 

知道这个这题就没有难度了。

#include <iostream>
#include <vector>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <map>
#include <set>
#include <string>
#include <queue>
#include <stack>
#include <bitset>
using namespace std;
#define pb(x) push_back(x)
#define ll long long
#define mk(x, y) make_pair(x, y)
#define lson l, m, rt<<1
#define mem(a) memset(a, 0, sizeof(a))
#define rson m+1, r, rt<<1|1
#define mem1(a) memset(a, -1, sizeof(a))
#define mem2(a) memset(a, 0x3f, sizeof(a))
#define rep(i, n, a) for(int i = a; i<n; i++)
#define fi first
#define se second
typedef pair<int, int> pll;
const double PI = acos(-1.0);
const double eps = 1e-8;
const int mod = 1e9+7;
const int inf = 1061109567;
const int dir[][2] = { {-1, 0}, {1, 0}, {0, -1}, {0, 1} };
struct point
{
    int x, y;
}a[105];
int gcd(int x, int y) {
    return y?gcd(y, x%y):x;
}
int main()
{
    int t, n;
    cin>>t;
    for(int casee = 1; casee<=t; casee++) {
        printf("Scenario #%d:\n", casee);
        cin>>n;
        int ans1 = 0, ans3 = 0;
        double ans2 = 0;
        a[0].x = 0, a[0].y = 0;
        for(int i = 1; i<=n; i++) {
            scanf("%d%d", &a[i].x, &a[i].y);
            ans1 += gcd(abs(a[i].x), abs(a[i].y));
            a[i].x+=a[i-1].x, a[i].y+=a[i-1].y;
            ans2 += a[i-1].x*a[i].y-a[i-1].y*a[i].x;
        }
        ans2 = fabs(ans2/2);
        ans3 = ans2+1-ans1/2;
        printf("%d %d %.1f\n\n", ans3, ans1, ans2);
    }
    return 0;
}