57 lines
1.7 KiB
Java
57 lines
1.7 KiB
Java
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package DynamicProgramming;
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// Matrix-chain Multiplication
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// Problem Statement
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// we have given a chain A1,A2,...,Ani of n matrices, where for i = 1,2,...,n,
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// matrix Ai has dimension pi−1 ×pi
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// , fully parenthesize the product A1A2 ···An in a way that
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// minimizes the number of scalar multiplications.
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public class MatrixChainRecursiveTopDownMemoisation
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{
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static int Memoized_Matrix_Chain(int p[]) {
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int n = p.length ;
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int m[][] = new int[n][n];
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < n; j++) {
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m[i][j] = Integer.MAX_VALUE;
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}
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}
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return Lookup_Chain(m, p, 1, n-1);
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}
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static int Lookup_Chain(int m[][],int p[],int i, int j)
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{
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if ( i == j )
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{
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m[i][j] = 0;
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return m[i][j];
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}
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if ( m[i][j] < Integer.MAX_VALUE )
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{
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return m[i][j];
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}
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else
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{
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for ( int k = i ; k<j ;k++)
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{
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int q = Lookup_Chain(m, p,i , k ) + Lookup_Chain(m, p, k+1 , j) + (p[i-1] * p[k] * p[j]);
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if ( q < m[i][j] )
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{
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m[i][j] = q;
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}
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}
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}
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return m[i][j];
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}
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// in this code we are taking the example of 4 matrixes whose orders are 1x2,2x3,3x4,4x5 respectively
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// output should be Minimum number of multiplications is 38
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public static void main (String[] args)
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{
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int arr[] = { 1, 2, 3, 4 ,5};
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System.out.println("Minimum number of multiplications is " + Memoized_Matrix_Chain(arr));
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}
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}
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