Ruby实现的矩阵连乘算法

动态规划解决矩阵连乘问题，随机产生矩阵序列，输出形如((a1(a2a3))(a4a5))的结果。

代码：

#encoding: utf-8
=begin
author: xu jin, 4100213
date: oct 28, 2012
matrixchain
to find an optimum order by using matrixchain algorithm
example output:
the given array is:[30, 35, 15, 5, 10, 20, 25]
the optimum order is:((a1(a2a3))((a4a5)a6))
the total number of multiplications is: 15125

the random array is：[5, 8, 8, 2, 5, 9]
the optimum order is:((a1(a2a3))(a4a5))
the total number of multiplications is: 388 
=end

infintiy = 1 / 0.0
p = [30, 35, 15, 5, 10, 20, 25]
m, s = array.new(p.size){array.new(p.size)}, array.new(p.size){array.new(p.size)}

def matrix_chain_order(p, m, s)
   n = p.size - 1
   (1..n).each{|i| m[i][i] = 0} 
   for r in (2..n) do
     for i in (1..n - r + 1) do
       j = r + i - 1
       m[i][j] = infintiy
       for k in (i...j) do
         q = m[i][k] + m[k + 1][j] + p[i - 1] * p[k] * p[j]                  
         m[i][j], s[i][j] = q, k if(q < m[i][j]) 
       end
     end
   end
end 

def print_optimal_parens(s, i, j)
   if(i == j) then
    print "a" + i.to_s
   else 
    print "("
    print_optimal_parens(s, i, s[i][j])
    print_optimal_parens(s, s[i][j] + 1, j)
    print ")"
   end
end

def process(p, m, s)
   matrix_chain_order(p, m, s)
   print "the optimum order is:"
   print_optimal_parens(s, 1, p.size - 1)
   printf("\nthe total number of multiplications is: %d\n\n", m[1][p.size - 1])
end

puts "the given array is:" + p.to_s
process(p, m, s)

#produce a random array
p = array.new
x = rand(10)
(0..x).each{|index| p[index] = rand(10) + 1}
puts "the random array is：" + p.to_s
m, s = array.new(p.size){array.new(p.size)}, array.new(p.size){array.new(p.size)}
process(p, m, s)