POJ2398计算几何叉积判断点在线段左/右侧

Posted 2021-10-21 hesorchen

题目

Toy Storage

二维平面中有一个矩形，放入n块隔板，将矩形分成n+1个区域，隔板保证不相交且两端点在矩形的两条横向线段中。形如下图：

给出m个点，求包含t个点的区域数量。

求解思路

可以用叉积判断一个点在线段的左侧还是右侧。

$\overrightarrow{OA}\times \overrightarrow{OB}=|OA|\times |OB|\times \sin \theta$

叉积为负，说明$\theta 大于\pi$

如果$\overrightarrow{OA}\times \overrightarrow{OB}>0$ 并且 $\overrightarrow{OC}\times \overrightarrow{OD}<0$，说明点O在区域ABCD内。

代码

#include <iostream>
#include <map>
#include <algorithm>
#include <cstring>
using namespace std;

const int N = 1e4 + 5;

struct node
{
    int u, d;
    bool operator<(const node temp) const
    {
        return u < temp.u;
    }
} s[N];
int tong[N];
int ans[N];
int n, m, sx, sy, ex, ey;

typedef struct Point
{
    double x, y;
} Vector;

bool check(Vector A, Vector B)
{
    if (A.x * B.y - A.y * B.x <= 0)
        return 0;
    return 1;
}

void solve()
{
    memset(tong, 0, sizeof tong);
    memset(ans, 0, sizeof ans);
    scanf("%d %d %d %d %d", &m, &sx, &sy, &ex, &ey);
    for (int i = 1; i <= n; i++)
        scanf("%d %d", &s[i].u, &s[i].d);
    sort(s + 1, s + 1 + n);
    s[n + 1].u = s[n + 1].d = ex;

    for (int i = 1; i <= m; i++)
    {
        int x, y;
        scanf("%d %d", &x, &y);
        for (int j = 1; j <= n + 1; j++)
        {
            Vector A, B, C, D;
            A.x = s[j - 1].u - x;
            A.y = sy - y;
            B.x = s[j - 1].d - x;
            B.y = ey - y;

            C.x = s[j].u - x;
            C.y = sy - y;
            D.x = s[j].d - x;
            D.y = ey - y;

            if (check(A, B) && !check(C, D))
            {
                tong[j]++;
                break;
            }
        }
    }
    for (int i = 1; i <= n + 1; i++)
    {
        if (tong[i])
            ans[tong[i]]++;
    }
    printf("Box\\n");

    for (int i = 1; i <= n + 1; i++)
        if (ans[i])
            printf("%d: %d\\n", i, ans[i]);
}

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