Hu .26 Shing .281981.29 Matrix chain multiplication

for example below, there 4 sides: a, b, c , final result abc. 10×30 matrix, b 30×5 matrix, c 5×60 matrix, , final result 10×60 matrix. regular polygon example 4-gon, i.e. square:

the matrix product ab 10x5 matrix , bc 30x60 matrix. 2 possible triangulations in example are:

the cost of single triangle in terms of number of multiplications needed product of vertices. total cost of particular triangulation of polygon sum of costs of triangles:

(ab)c: (10×30×5) + (10×5×60) = 1500 + 3000 = 4500 multiplications
a(bc): (30×5×60) + (10×30×60) = 9000 + 18000 = 27000 multiplications

hu & shing developed algorithm finds optimum solution minimum cost partition problem in o(n log n) time.