Pick定理
[{LARGE A = i + frac{b}{2} -1}
]
(Code)
#include <cmath>
#include <cstdio>
#include <iostream>
using namespace std;
const int MAXN = 110;
struct node {
int x, y;
} p[MAXN];
inline int gcd(int x, int y) { return y == 0 ? x : gcd(y, x % y); }
inline int area(int a, int b) { return p[a].x * p[b].y - p[a].y * p[b].x; }
int main() {
int t, ncase = 1;
scanf("%d", &t);
while (t--) {
int n, dx, dy, x, y, num = 0, sum = 0;
scanf("%d", &n);
p[0].x = 0, p[0].y = 0;
for (int i = 1; i <= n; i++) {
scanf("%d%d", &x, &y);
p[i].x = x + p[i - 1].x, p[i].y = y + p[i - 1].y;
dx = x, dy = y;
if (x < 0) dx = -x;
if (y < 0) dy = -y;
num += gcd(dx, dy);
sum += area(i - 1, i);
}
if (sum < 0) sum = -sum;
printf("Scenario #%d:
", ncase++);
printf("%d %d %.1f
", (sum - num + 2) >> 1, num, sum * 0.5);
}
return 0;
}