Create Matrix_chain_multiplication_alogorithm_problem_DP.java

Matrix_chain_multiplication_alogorithm_problem_DP.java

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+class Main
+{
+    // Function to find the most efficient way to multiply
+    // a given sequence of matrices
+    public static int matrixChainMultiplication(int[] dims, int i, int j)
+    {
+        // base case: one matrix
+        if (j <= i + 1) {
+            return 0;
+        }
+
+        // stores the minimum number of scalar multiplications (i.e., cost)
+        // needed to compute matrix `M[i+1] … M[j] = M[i…j]`
+        int min = Integer.MAX_VALUE;
+
+        // take the minimum over each possible position at which the
+        // sequence of matrices can be split
+
+        /*
+            (M[i+1]) × (M[i+2]………………M[j])
+            (M[i+1]M[i+2]) × (M[i+3…………M[j])
+            …
+            …
+            (M[i+1]M[i+2]…………M[j-1]) × (M[j])
+        */
+
+        for (int k = i + 1; k <= j - 1; k++)
+        {
+            // recur for `M[i+1]…M[k]` to get an `i × k` matrix
+            int cost = matrixChainMultiplication(dims, i, k);
+
+            // recur for `M[k+1]…M[j]` to get an `k × j` matrix
+            cost += matrixChainMultiplication(dims, k, j);
+
+            // cost to multiply two `i × k` and `k × j` matrix
+            cost += dims[i] * dims[k] * dims[j];
+
+            if (cost < min) {
+                min = cost;
+            }
+        }
+
+        // return the minimum cost to multiply `M[j+1]…M[j]`
+        return min;
+    }
+
+    // Matrix Chain Multiplication Problem
+    public static void main(String[] args)
+    {
+        // Matrix `M[i]` has dimension `dims[i-1] × dims[i]` for `i=1…n`
+        // input is 10 × 30 matrix, 30 × 5 matrix, 5 × 60 matrix
+        int[] dims = { 10, 30, 5, 60 };
+
+        System.out.print("The minimum cost is " +
+                matrixChainMultiplication(dims, 0, dims.length - 1));
+    }
+}