加快蛮力，在MATLAB中找到具有特定均值的分布(Speed up brute force for finding distribution with specific mean in MATLAB)

 我有一个关于课程成绩的以下信息， 
 
 
 
 共有21名学生。 
 
 
 3个已知等级是：一个1.3 ，一个1.7和一个1.8 。 
 
 
 我知道有20名学生的成绩在1.6到2.5之间。 
 
 
 一名学生的成绩在1.0到1.5之间 - 这显然是1.3级。 
 
 
 课程平均为1.9 
 
 
 等级给出1位小数，例如2.2或2.3但不是2.25 。 
 
 
 以下代码计算其他18名学生的可能成绩，其中成绩必须在上述约束范围内。 
 
 我正在使用蛮力的方式来做到这一点，比如： 
 
clear all

grades = zeros([1,21])

%certain grades
grades(1) = 1.3;
grades(2) = 1.7;
grades(3) = 1.8;

a = 1.6
b = 2.59
cnt = 0;
while 1
    grades(4:end) = round(((b - a).*rand(21 - 3,1) + a)/0.1)*0.1;
    if mean(grades) == 1.9
       cnt = cnt + 1;
       savedres(cnt,:) = grades; 
    end
end
 
 首先，我想知道如何在没有“暴力攻击”的情况下解决这个问题，其次我想知道上述方法是否正确？ 
 
 最后，有没有办法知道我有多少不同的解决方案（例如我可以预先分配savedres矢量）？ 

I have the following information about grades in a course, 
 
 
 
There is a total of 21 students.
 
 
3 known grades are: one 1.3, one 1.7 and one 1.8. 
 
 
I know that 20 students have a grade in between 1.6 and 2.5. 
 
 
One student has a grade in between 1.0 and 1.5 - which is obviously the grade 1.3. 
 
 
The course average is 1.9 
 
 
Grades are given to 1 decimal place, e.g. 2.2 or 2.3 but never 2.25.
 
 
The following code calculates the possible grades of the other 18 students, where the grades must lay within the above constraints.
 
I am using a brute force way to do this, like:
 
clear all

grades = zeros([1,21])

%certain grades
grades(1) = 1.3;
grades(2) = 1.7;
grades(3) = 1.8;

a = 1.6
b = 2.59
cnt = 0;
while 1
    grades(4:end) = round(((b - a).*rand(21 - 3,1) + a)/0.1)*0.1;
    if mean(grades) == 1.9
       cnt = cnt + 1;
       savedres(cnt,:) = grades; 
    end
end
 
Firstly, I want to know how to solve this without a "brute force attack", secondly I wonder if the above method is correct?
 
Lastly, is there a way of knowing how many different solutions I have to expect (so I could preallocate the savedres vector for example)?

原文：https://stackoverflow.com/questions/45707993