MatrixChainMultiplication.java

Dynamic program

dynamic-programming/MatrixChainMultiplication.java

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+// Dynamic Programming Python implementation of Matrix
+// Chain Multiplication.
+public class MatrixChainMultiplication {
+// Matrix Ai has dimension p[i-1] x p[i] for i = 1..n
+		static int MatrixChainOrder(int p[], int n) {
+			/* For simplicity of the program, one extra row and one
+			extra column are allocated in m[][].  0th row and 0th
+			column of m[][] are not used */
+			int m[][] = new int[n][n];
+
+			int i, j, k, L, q;
+
+			/* m[i,j] = Minimum number of scalar multiplications needed
+			to compute the matrix A[i]A[i+1]...A[j] = A[i..j] where
+			dimension of A[i] is p[i-1] x p[i] */
+
+			// cost is zero when multiplying one matrix.
+			for (i = 1; i < n; i++)
+				m[i][i] = 0;
+
+			// L is chain length.
+			for (L=2; L<n; L++) {
+				for (i=1; i<n-L+1; i++) {
+					j = i+L-1;
+					if(j == n) continue;
+					m[i][j] = Integer.MAX_VALUE;
+					for (k=i; k<=j-1; k++) {
+					// q = cost/scalar multiplications
+						q = m[i][k] + m[k+1][j] + p[i-1]*p[k]*p[j];
+						if (q < m[i][j])
+							m[i][j] = q;
+					}
+				}
+			}
+		return m[1][n-1];
+		}
+
+		// Driver program to test above function
+		public static void main(String args[]) {
+			int arr[] = new int[] {1, 2, 3, 4};
+			int size = arr.length;
+			System.out.println("Minimum number of multiplications is "+
+			MatrixChainOrder(arr, size));
+		}
+}