计算几何公式（随着后续学习持续更新）

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:\n", ncase++);
    printf("%d %d %.1f\n\n", (sum - num + 2) >> 1, num, sum * 0.5);
  }
  return 0;
}