Matrix Chain Multiplication Trick

12 Jul, 2021

For university examination If you want to learn Strassens Matrix Multiplication Formulas then this video is very helpful. That is determine how to parenthisize.

Matrix Chain Multiplication Dynamic Programming Youtube

Then ABC 10305 10560 1500 3000 4500 operations A BC 30560 103060 9000 18000 27000 operations.

Matrix chain multiplication trick. N length p-1 Where n is the total number of elements And length p 5 n 5 - 1 4 n 4 Now we construct two tables m and s. 30000 There are 4 matrices of. For all values of ij set 0.

Cost m i k m k1 j dims i-1dims kdims j. Two matrices can only be multiplied if the number of columns of the first matrix is equal to the number of rows of the second one. In the Chain Matrix Multiplication Problem the fundamental choice is which smaller parts of the chain to calculate first before combining them together.

Clearly the first parenthesization requires less number of operations. S i j k. P 10 20 30 40 30 Output.

Matrix-chainij IF i j THEN return 0 m 1 FOR k i TO j 1 DO q Matrix-chainik Matrix-chaink 1j p i 1 p k p j IF q m THEN m q OD Return m END Matrix-chain Return Matrix-chain1n Running time. 116 116 27 259. .

Please like and subscribe. It is a Method under Dynamic Programming in which previous output is taken as input for next. M 12 303515 15750 M 23 35155 2625 M 34 15510 750 M 45 51020 1000 M 56.

ABCDEFGH is a 3 x 8 matrix computed in 140 steps using ABCDEFGH IJKLMN is a 8 x 9 matrix. The Chain Matrix Multiplication Problem Given dimensions corresponding to matr 5 5 5 ix sequence 5 5 5 where has dimension determinethe multiplicationsequencethat minimizes the number of scalar multiplications in computing. Here Chain means one matrixs column is equal to the second matrixs row always.

Index of the subsequence split that achieved minimal cost. For example say there are five matrices. M 13 MIN M 11 M 23 P0P1P3 M 12 M 33 P0P2P3.

M i j cost. Lets breakdown the problem. Tn nX 1 k1 Tk Tn k O1 2 nX 1 k1 Tk On 2 Tn 1 2 2 Tn 2 2 2 2.

2n Exponential is. Cost Mem-Matrix-Chainp i k Mem-Matrix-Chainp k 1 j pi 1 pk pj. If A a ij is a p x q matrix B b ij is a q x r matrix C c ij is a p x r matrix.

Given an array p which represents the chain of matrices such that the ith matrix Ai is of dimension p i-1 x p i. In Matrix Chain Multiplication Problem we are given some matrices and are asked to multiply them in such a way that the total number of multiplication is minimum. Matrix Chain Multiplication using Dynamic Programming Step-1.

If cost m i j. If cost m i j then update if better m i j cost. ABCDEFG is a 3 x 1 matrix computed in 116 steps using ABCDEFG HIJKLMN is a 1 x 9 matrix computed in 116 steps using HIJKLMN total cost.

Let the input 4 matrices be A B C and D. Length of array P number of elements in P length p 5 From step 3 Follow the steps in Algorithm in Sequence According to Step 1 of Algorithm Matrix-Chain-Order. The minimum number of multiplications are obtained by putting parenthesis in following way A BCD -- 203010 402010 401030 Input.

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