皮克定理：皮克定理是指一个计算点阵中顶点在格点上的多边形面积公式，该公式可以表示为S=a+b÷2－1，其中a表示多边形内部的点数，b表示多边形落在格点边界上的点数，S表示多边形的面积。

/*Author : lifehappy
*/
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <vector>
#include <iostream>using namespace std;typedef long long ll;int ax[] = {0, -1, -1, -1, 0, 0, 0, 1, 1, 1};
int ay[] = {0, -1, 0, 1, -1, 0, 1, -1, 0, 1};ll Cross(ll x1, ll y1, ll x2, ll y2) {return x1 * y2 - x2 * y1;
}int main() {// freopen("in.txt", "r", stdin);// freopen("out.txt", "w", stdout);// ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);int T;scanf("%d", &T);while(T--) {getchar();char c;ll last_x = 0, last_y = 0;ll ans = 0;while(scanf("%c", &c) && c != '5') {ll now_x = last_x + ax[c - '0'], now_y = last_y + ay[c - '0'];ans += Cross(last_x, last_y, now_x, now_y);last_x = now_x, last_y = now_y;}if(ans < 0) ans = -ans;if(ans & 1) {printf("%lld.5\n", ans >> 1);}else {printf("%lld\n", ans >> 1);}}return 0;
}

/*Author : lifehappy
*/#include<stdio.h>
#include<math.h>typedef int ll;ll Cross(ll x1, ll y1, ll x2, ll y2) {return x1 * y2 - x2 * y1;
}ll gcd(ll a, ll b) {return b ? gcd(b, a % b) : a;
}int main() {// freopen("in.txt", "r", stdin);// freopen("out.txt", "w", stdout);// ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);int T;scanf("%d", &T);for(int cas = 1; cas <= T; cas++) {int n;scanf("%d", &n);ll s = 0, a = 0, b = 0, last_x = 0, last_y = 0;for(int i = 1; i <= n; i++) {ll now_x, now_y;scanf("%d %d", &now_x, &now_y);b += abs(gcd(now_x, now_y));now_x += last_x, now_y += last_y;s += Cross(last_x, last_y, now_x, now_y);last_x = now_x, last_y = now_y;}if(s < 0) s = -s;a = s / 2 + 1 - b / 2;printf("Scenario #%d:\n%d %d %.1f\n\n", cas, a, b, (double)s / 2);}return 0;
}

同上

/*Author : lifehappy
*/
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <vector>
#include <iostream>using namespace std;typedef long long ll;int ax[] = {0, -1, -1, -1, 0, 0, 0, 1, 1, 1};
int ay[] = {0, -1, 0, 1, -1, 0, 1, -1, 0, 1};ll Cross(ll x1, ll y1, ll x2, ll y2) {return x1 * y2 - x2 * y1;
}ll gcd(ll a, ll b) {return b ? gcd(b, a % b) : a;
}int main() {// freopen("in.txt", "r", stdin);// freopen("out.txt", "w", stdout);// ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);ll x1, y1, x2, y2, x3, y3;while(scanf("%lld %lld %lld %lld %lld %lld", &x1, &y1, &x2, &y2, &x3, &y3) && (x1 || y1 || x2 || y2 || x3 || y3)) {ll ans = Cross(x1, y1, x2, y2) + Cross(x2, y2, x3, y3) + Cross(x3, y3, x1, y1);if(ans < 0) ans = -ans;ans >>= 1;ll all = llabs(gcd(x2 - x1, y2 - y1)) + llabs(gcd(x3 - x2, y3 - y2)) + llabs(gcd(x1 - x3, y1 - y3));printf("%lld\n", ans + 1 - (all >> 1));}return 0;
}