学步园

大意略。

思路：通过叉积可以算出多边形的有向面积（就算是凹变形也没关系），这样，我们根据移动方向把所有的点存起来，然后算通过多边形面积公式算出结果即可。

#include <iostream>
#include <cstdlib>
#include <cstdio>
#include <string>
#include <cstring>
#include <cmath>
#include <vector>
#include <queue>
#include <stack>
#include <algorithm>
using namespace std;

typedef __int64 LL;

struct Point
{
	int x, y;
	Point(int x = 0, int y = 0) : x(x), y(y) { }
	bool operator < (const Point& a) const
	{
		if(a.x != x) return x < a.x;
		return y < a.y;
	}
};

typedef Point Vector;

Vector operator + (Vector A, Vector B) { return Vector(A.x+B.x, A.y+B.y); }

Vector operator - (Point A, Point B) { return Vector(A.x-B.x, A.y-B.y); }

int Cross(Vector A, Vector B) { return A.x*B.y - A.y*B.x; }

LL PolygonArea2(Point *p, int n)
{
	LL area = 0;
	for(int i = 1; i < n-1; i++)
		area += (LL)Cross(p[i]-p[0], p[i+1]-p[0]);
	return area > 0? area : -area; 
}

Point read_point()
{
	Point A;
	scanf("%d%d", &A.x, &A.y);
	return A;
}

const int maxn = 1000010;

const int dx[] = {0, 1, 1, 1, 0, 0, 0, -1, -1, -1};
const int dy[] = {0, -1, 0, 1, -1, 0, 1, -1, 0, 1};

int n, len;

Point P[maxn];
char dir[maxn];

int pc;

void init()
{
	pc = 1;
}

int idx(char c) { return c - '0'; }

void read_case()
{
	init();
	P[0] = Point(0, 0);
	scanf("%s", dir+1);
	len = strlen(dir+1);
	for(int i = 1; i <= len; i++)
	{
		P[pc++] = Point(P[i-1].x+dx[idx(dir[i])], P[i-1].y+dy[idx(dir[i])]);
	}
}

void solve()
{
	read_case();
	LL ans = PolygonArea2(P, pc);
	if(pc & 1) printf("%I64d.5\n", ans/2);
	else printf("%I64d\n", ans/2);
}

int main()
{
	int T;
	scanf("%d", &T);
	while(T--)
	{
		solve();
	}
	return 0;
}