UVA 11346 - Probability 数学积分

Consider rectangular coordinate system and point L(X, Y ) which is randomly chosen among all points
in the area A which is deﬁned in the following manner: A = {(x, y)|x ∈ [−a; a];y ∈ [−b; b]}. What is
the probability P that the area of a rectangle that is deﬁned by points (0,0) and (X, Y ) will be greater
than S?
Input
The number of tests N ≤ 200 is given on the ﬁrst line of input. Then N lines with one test case on
each line follow. The test consists of 3 real numbers a > 0, b > 0 ir S ≥ 0.
Output
For each test case you should output one number P and percentage ‘%’ symbol following that number
on a single line. P must be rounded to 6 digits after decimal point.
Sample Input
3
10 5 20
1 1 1
2 2 0
Sample Output
23.348371%
0.000000%
100.000000%

题解：给你x，y，s，问说在x,y与x,y轴形成的矩形内选取一点，和x，y轴形成图形的面积大于s的概率。

题解：

　　　　　　画个图是求个积分

　　　　　　S = s* (ln(x1)- ln(x));

#include <iostream>

#include <cstdio>

#include <cmath>

#include <cstring>

#include <algorithm>

#include <vector>

#include <bitset>

using namespace std ;

typedef long long ll;

const int N =  + ;

int main () {

    int T;

    scanf("%d",&T);

    while(T--) {

            double x,y,s;

        scanf("%lf%lf%lf",&x,&y,&s);

        double x1 = min(x,s / y);

        double S = ;

        if(s > 1e-) S = x1 * y + s * (log(x) - log(x1));

        //cout<<S<<endl;

        double p = 1.0 - S / (x * y);

        p *= ;

        printf("%.6f%%\n", p);

    }

    return ;

}

daima

巴特西

UVA 11346 - Probability 数学积分

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