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. 2021 Feb 26;7:e395. doi: 10.7717/peerj-cs.395

Table 9. Comparison of proposed model with dynamic programing.

No. of matrix Sequence of dimensions Optimal parenthesis DP Multiplications GCO Multiplications Variation
10 5,10,21,78,12,15,20,18,6,22,25 (((((((((M1*M2)*M3)*M4)*M5)*M6)*M7)*M8)*M9)*M10) 22,070 22,070 0%
20 3,15,28,21,19,10,25,16,29,5,28,31,11,14,9,17,4,21,19,3,34 (((((((((((((((((M1*M2)*M3)*M4)*M5)*M6)*M7)*M8)*M9)*M10)*M11)*M12)*M13)*M14)*M15)*M16)*(M17*(M18*M19)))*M20) 15,909 15,909 0%
30 8,31,10,14,11,15,28,12,2,20,25,16,19,9,40,21,8,19,28,34,37,40,28,30,29,45,13,20,33,44,58 ((M1*(M2*(M3*(M4*(M5*(M6*(M7*M8)))))))*(((((((((((((((((((((M9*M10)*M11)*M12)*M13)*M14)*M15)*M16)*M17)*M18)*M19)*M20)*M21)*M22)*M23)*M24)*M25)*M26)*M27)*M28)*M29)*M30)) 37,996 37,996 0%
40 8,31,10,14,11,15,28,12,2,20,25,16,19,9,40,21,8,19,28,34,37,3,15,28,21,19,10,25,16,29,5,28,31,11,14,9,17,42,21,19,53 ((M1*(M2*(M3*(M4*(M5*(M6*(M7*M8)))))))*(((((((((((((((((((((((((((((((M9*M10)*M11)*M12)*M13)*M14)*M15)*M16)*M17)*M18)*M19)*M20)*M21)*M22)*M23)*M24)*M25)*M26)*M27)*M28)*M29)*M30)*M31)*M32)*M33)*M34)*M35)*M36)*M37)*M38)*M39)*M40)) 31,260 31,260 0%
50 5,6,2,13,24,5,16,18,13,4,11,31,15,13,14,10,15,13,18,19,14,15,13,23,44,12,9,26,6,14,32,19,22,32,2,21,11,12,25,19,20,33,22,32,77,21,34,44,26,43,32 (((M1*M2)*(((((((M3*M4)*M5)*M6)*M7)*M8)*M9)*(M10*(M11*(M12*(M13*(M14*(M15*(M16*(M17*(M18*(M19*(M20*(M21*(M22*(M23*(M24*(M25*(M26*(M27*(M28*(M29*(M30*(M31*(M32*(M33*M34))))))))))))))))))))))))))*(((((((((((((((M35*M36)*M37)*M38)*M39)*M40)*M41)*M42)*M43)*M44)*M45)*M46)*M47)*M48)*M49)*M50)) 44,778 44,778 0%
58 6,2,13,24,5,16,18,13,4,11,31,15,13,14,10,15,13,18,19,14,15,13,23,44,12,9,26,6,4,2,22,32,32,2,21,11,12,25,19,20,33,22,32,21,34,44,26,43,32,33,22,32,21,34,44,26,43,32,78 ((M1*((((((((M2*M3)*M4)*M5)*M6)*M7)*M8)*(M9*(M10*(M11*(M12*(M13*(M14*(M15*(M16*(M17*(M18*(M19*(M20*(M21*(M22*(M23*(M24*(M25*(M26*(M27*(M28*M29)))))))))))))))))))))*(M30*(M31*(M32*M33)))))*((((((((((((((((((((((((M34*M35)*M36)*M37)*M38)*M39)*M40)*M41)*M42)*M43)*M44)*M45)*M46)*M47)*M48)*M49)*M50)*M51)*M52)*M53)*M54)*M55)*M56)*M57)*M58)) 60,600 60,600 0%