package DynamicProgramming;

// Matrix-chain Multiplication
// Problem Statement
// we have given a chain A1,A2,...,Ani of n matrices, where for i = 1,2,...,n, 
// matrix Ai has dimension pi−1 ×ばつpi
// , fully parenthesize the product A1A2 ···An in a way that
// minimizes the number of scalar multiplications.

public class MatrixChainRecursiveTopDownMemoisation
{
 static int Memoized_Matrix_Chain(int p[]) {
 int n = p.length ;
 int m[][] = new int[n][n];
 for (int i = 0; i < n; i++) {
 for (int j = 0; j < n; j++) {
 m[i][j] = Integer.MAX_VALUE;
 }
 }
 return Lookup_Chain(m, p, 1, n-1);
 }

 static int Lookup_Chain(int m[][],int p[],int i, int j)
 {
 if ( i == j )
 {
 m[i][j] = 0;
 return m[i][j];
 }
 if ( m[i][j] < Integer.MAX_VALUE )
 {
 return m[i][j];
 }
 
 else 
 {
 for ( int k = i ; k<j ;k++)
 {
 int q = Lookup_Chain(m, p,i , k ) + Lookup_Chain(m, p, k+1 , j) + (p[i-1] * p[k] * p[j]);
 if ( q < m[i][j] )
 {
 m[i][j] = q;
 }
 }
 }
 return m[i][j];
 }
 // in this code we are taking the example of 4 matrixes whose orders are 1x2,2x3,3x4,4x5 respectively
 // output should be Minimum number of multiplications is 38
 public static void main (String[] args)
 {
 
 int arr[] = { 1, 2, 3, 4 ,5};
 System.out.println("Minimum number of multiplications is " + Memoized_Matrix_Chain(arr));
 }
}