78 lines
1.6 KiB
C++
78 lines
1.6 KiB
C++
#include<stdio.h>
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#include<math.h>
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#include<algorithm>
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#define eps 1e-8
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#define PI 3.14159265358979323846
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using namespace std;
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struct pt
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{
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double x, y;
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double ang;
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double p;
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};
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int n;
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int idx[1010];
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pt p[1010];
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inline double toAng(double a, double b)
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{
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double ret = b - a;
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if (ret > 2*PI - eps)
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ret -= 2*PI;
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return ret < -eps ? (ret + 2*PI) : ret;
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}
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bool cmp(int a, int b)
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{
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return p[a].ang < p[b].ang;
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}
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double calc(int a)
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{
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if (p[a].p < eps)
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return 0.0;
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double tp = 0.0;
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int m = n - 1;
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for (int i = 0; i < n; i++)
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{
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if (i != a)tp += log(1.0 - p[i].p);
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p[i].ang = (i == a) ? 10.0 : atan2(p[i].y - p[a].y, p[i].x - p[a].x);
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}
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sort(idx, idx + n, cmp);
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double noP = 0.0, ret = 0.0;
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int r = 0;
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for (int i = 0; i < n - 1; i++)
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{
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while (r - i < m && toAng(p[idx[i]].ang, p[idx[r%m]].ang) < PI)
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{
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noP += log(1.0 - p[idx[r%m]].p);
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r++;
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}
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noP -= log(1.0 - p[idx[i]].p);
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ret += p[idx[i]].p * exp(noP);
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}
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return p[a].p * (ret + exp(tp));
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}
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double solve()
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{
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if (n == 1)
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return p[0].p;
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double ans = 0.0;
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for (int i = 0; i < n; i++)
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{
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ans += calc(i);
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}
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return ans;
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}
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int main()
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{
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while (~scanf("%d", &n))
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{
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for (int i = 0; i < n; i++)
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{
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scanf("%lf %lf %lf", &p[i].x, &p[i].y, &p[i].p);
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p[i].p /= 100.0;
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idx[i] = i;
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}
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printf("%.2lf\n", solve());
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}
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return 0;
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}
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