Random Point in Triangle

Posted on | In , , ,

题目链接

题意

有一个三角形，在其中任意选一点P，定义其v为P分割出的三个小三角形中面积最大值，问v期望。

思路

学会了个套路，不会算的话就模拟，答案一定是正比于总面积，计算系数就行了。

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#ifndef ONLINE_JUDGE
#define dbg(x...) do{cout << "\033[33;1m" << #x << "->" ; err(x);} while (0)
void err(){cout << "\033[39;0m" << endl;}
template<template<typename...> class T, typename t, typename... A>
void err(T<t> a, A... x){for (auto v: a) cout << v << ' '; err(x...);}
template<typename T, typename... A>
void err(T a, A... x){cout << a << ' '; err(x...);}
#else
#define dbg(...)
#endif
#define inf 1ll << 50
struct node
{
	double x, y;
	node(double x = 0, double y = 0): x(x), y(y) {}
};

double dis(node a, node b)
{
	return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
}

double s(node a, node b, node c)
{
	double ab = dis(a, b);
	double bc = dis(b, c);
	double ac = dis(a, c);
	double p = (ab + bc + ac) / 2;
	return sqrt(p * (p - ab) * (p - bc) * (p - ac));
}

int main()
{
	node p1 = node(0, 0);
	node p2 = node(1, 1);
	node p3 = node(2, 0);
	int t = 10000000;
	double cur = 0, ans = 0.0;
//	printf("%.6f\n", cur);
	srand((unsigned)time(NULL));
	while (t--)
	{
		double x, y;
		double ss;
		while (1)
		{
			x = rand() % 1000000 * 2.0 / 1000000.0;
			y = rand() % 1000000 * 1.0 / 1000000.0;

			node nn = node(x, y);
			ss = max(s(p1, p2, nn), max(s(p1, p3, nn), s(p2, p3, nn)));
			if (isnan(ss))
			continue;
			if (y >= 0 && x + y <= 2 && y - x <= 0)
				break;
		}
		cur += ss;
		if (cur >= 1000000.0)
		{
			ans += cur / 10000000.0;
			cur = 0.0;
		}
	}
	//printf("%.6f %.6f\n", ans, cur);
	ans += (double)cur / 10000000.0;
	printf("%.6f\n", ans * 36.0);
	return 0;
}
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pii;
int main()
{
    ll x1, x2, x3, y1, y2, y3;
    while (scanf("%lld%lld%lld%lld%lld%lld", &x1, &y1, &x2, &y2, &x3, &y3) != EOF)
    {
        double S = 0.0;
        ll ans = 0;
        ans = 11 * ((x1 * y2 + y1 * x3 + x2 * y3) - (x1 * y3 + y2 * x3 + y1 * x2));
        ans = abs(ans);
        printf("%lld\n", ans);
    }
    return 0;
}
0%