Examples Of Matrix Chain Multiplication
A is a 20 40 matrix B is a 40 2 matrix and. 211 -4-2 -16 18 32.
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Tn nX 1 k1 Tk Tn k O1 2 nX 1 k1 Tk On 2 Tn 1 2 2 Tn 2 2 2 2.
Examples of matrix chain multiplication. Recursion tree for Matrix-chain14 22 34 23 44 11 22 14 11 24 12 34 44 33 44 11 12 3323 13. Initialize for k i to j 1 do try all possible splits costRec-Matrix-Chainp i k Rec-Matrix-Chainp k 1 j pi 1pkpj. L 2 to 4 because n 4 for i 1 to n this means.
For example for four matrices A B C and D we would have. Example Problem of Matrix Chain Multiplication Example-1. N 5 arr 40 20 30 10 30 Output.
Example of Matrix Chain Multiplication Example. There are 4 matrices of dimension 40x20 20x30 30x10 10x30. This gives us the answer well need to put in the first row second column of the answer matrix.
ABCD A BCD AB CD A BCD A B CD. The matrices have size 4 x 10 10 x 3 3 x. Step2 for i in range 1 to N-1.
We are given the sequence 4 10 3 12 20 and 7. In other words no matter how the product is parenthesized the result obtained will remain the same. For example suppose.
M 1 3 264. For i 1 to 4 because n 4 for i1 m i i0 m 1 10 Similarly for i 2 3 4 m 2 2 m 33 m 44 0 ie. The number of operations are - 203010 402010 401030 26000.
M 1 x M 2 M 3 M 1 M 2 x M 3 After solving both cases we choose the case in which minimum output is there. Say the matrices are named as A B C D. Following that we multiply the elements along the first row of matrix A with the corresponding elements down the second column of matrix B then add the results.
The matrices have size 4 x 10 10 x 3 3 x 12 12 x 20 20 x 7. Matrix Chain Multiplication Consider the case multiplying these 4 matrices. Let us proceed with working away from the diagonal.
Out of all possible combinations the most efficient way is ABCD. As Comparing both output 264 is minimum in both cases so we insert 264 in table and M 1 x M 2 M 3 this combination is chosen for the output making. Rec-Matrix-Chainarray p int i int j if i j mi i 0.
ABCD - This is a 2x2 multiplied. 43 0 0 3 43 5 3. Recalling Matrix Multiplication The product of a matrix and a matrix is a matrix given by for and.
We need to compute M ij 0 i j 5. AB C D A BC D AB CD A BC D A B CD. In the given input.
We need to compute M ij 0 i j 5. END Matrix-chain Return Matrix-chain1n Running time. Basic case else mi j infinity.
When l - 2. There are many options because matrix multiplication is associative. ABC 40 x 2 x 60 20 x 40 x 60 48 000 operations ABC.
For example for four matrices A B C and D there are five possible options. Step3 for i in range 2 to N-1. We know that the matrix multiplication is associative so four matrices ABCD we can multiply A BCD AB CD ABCD A BCD in these sequences.
We are given the sequence 4 10 3 12 20 and 7. Then ABC 10305 10560 1500 3000 4500 operations ABC 30560 103060 9000 18000 27000 operations. For example suppose A is a 10 30 matrix B is a 30 5 matrix and C is a 5 60 matrix.
1 then. We compute the optimal solution for the product of 2 matrices. Example of Matrix Chain Multiplication.
Algorithm For Matrix Chain Multiplication Step1 Create a dp matrix and set all values with a big valueINFINITY. The matrices have size 4 x 10 10 x 3 3 x 12 12 x 20 20 x 7. 2n Exponential is.
C is a 2 60 matrix then. We are given the sequence 4 10 3 12 20 and 7. Problem is that we compute the same result over and over again.
In other words no matter how the product is parenthesized the result obtained will remain the same. ABCD - This is a 2x4 multiplied by a 4x1 so 2x4x1 8 multiplications plus whatever work it will take to multiply BCD. There are two cases by which we can solve this multiplication.
We are given the sequence 4 10 3 12 20 and 7. Matrix Chain Multiplication Problem Prachi Joshi Example. Like these sequences our task is to find which ordering is efficient to multiply.
We know M i i 0 for all i. Here are many options because matrix multiplication is associative. The matrices have size 4 x 10 10 x 3 3 x 12 12 x 20 20 x 7.
Fill all the diagonal entries 0 in the table m Now l 2 to n l 2 to 4 because n 4 Case 1.
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