Poj3440--coin Toss (probability of geometry)

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The main topic: give the N*m a rectangle, each square side length is T, there is a coin, the diameter is C, randomly thrown to the rectangle ( Center in the rectangle ), there may appear in the figure of 5, that is, covering 1, 2, 3, 4 squares, ask coverage 1, 2, 3, What is the probability of 4 squares?

First consider the shape of the rectangle, divided into (1,n), (n,m)

for (1), the probability of A1 is 1, and the other is 0.

for (1,n) may cover 1, 2, respectively, consider each case, to find out the location of the center may exist, calculate the probability

for (n,m) may cover 1, 2, 3, 4, consider each case, and the position of the square (in the corner, on the edge, in the interior), calculate the position of the center may exist, calculate the probability, for 3 of the area is not good. Find the area of 1, 2, 4. Minus 1, they get 3 probability.

#include <cstdio> #include <cstring> #include <cmath> #include <algorithm>using namespace std;  Define PI ACOs ( -1.0) int n, m;d ouble T, C, is;d ouble A1, A2, A3, A4; void Solve () {a1 = (t-c/2.0) * (t-c/2.0) *4.0    + (t-c/2.0) * (t-c) * (n-2+m-2) *2.0 + (t-c) * (t-c) * (n-2) * (m-2);    A1/= is;    A2 = (t-c) * (c/2.0) * ((n-1) *m+ (m-1) *n) *2.0 + (c/2.0) * (c/2.0) * (n-1+m-1) * *;    A2/= is;    a4 = (c/2.0) * (c/2.0) *pi* (n-1) * (m-1);    A4/= is;    A3 = 1.0-a1-a2-a4; return;}    int main () {int s, step = 0;    scanf ("%d", &s);        while (s--) {scanf ("%d%d%lf%lf", &n, &m, &t, &c);        if (n > M) swap (N,M);        is = t*t*n*m;            if (n = = 1 && m = = 1) {a1 = 1.0;        a2 = a3 = a4 = 0.0;            } else if (n = = 1) {a1 = t* (t-c/2.0) *2.0 + t* (t-c) * (m-2);            A1/= is;            A2 = 1.0-A1;        a3 = a4 = 0.0; } else Solve () ;        if (step) printf ("\ n");        printf ("Case%d:\n", ++step);        printf ("Probability of covering 1 tiles =%.4lf%%\n", a1*100);        printf ("Probability of covering 2 tiles =%.4lf%%\n", a2*100);        printf ("Probability of covering 3 tiles =%.4lf%%\n", a3*100);    printf ("Probability of covering 4 tiles =%.4lf%%\n", a4*100); } return 0;}

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Poj3440--coin Toss (probability of geometry)