implement matrix chain multiplication

Author: himanshub16

dynamic-programming/matrix-multiplication.go

@@ -0,0 +1,61 @@
+// matrix chain multiplication problem
+// https://en.wikipedia.org/wiki/Matrix_chain_multiplication
+// www.geeksforgeeks.org/dynamic-programming-set-8-matrix-chain-multiplication/
+
+// package main
+package matrixChainMultiplication
+
+import "fmt"
+
+func min(a, b int) int {
+	if a > b {
+		return b
+	} else {
+		return a
+	}
+}
+
+func matrixChainRec(D []int, i, j int) int {
+	// d[i-1] x d[i] : dimension of matrix i
+	if i == j {
+		return 0
+	}
+	q := 1 << 32
+	for k := i; k < j; k++ {
+		prod := matrixChainRec(D, i, k) + matrixChainRec(D, k+1, j) + D[i-1]*D[k]*D[j]
+		q = min(prod, q)
+	}
+	return q
+}
+
+func matrixChainDp(D []int) int {
+	// d[i-1] x d[i] : dimension of matrix i
+	N := len(D)
+
+	dp := make([][]int, N) // dp[i][j] = matrixChainRec(D, i, j)
+	for i := 0; i < N; i++ {
+		dp[i] = make([]int, N)
+		dp[i][i] = 0
+	}
+
+	for l := 2; l < N; l++ {
+		for i := 1; i < N-l+1; i++ {
+			j := i + l - 1
+			dp[i][j] = 1 << 31
+			for k := i; k < j; k++ {
+				prod := dp[i][k] + dp[k+1][j] + D[i-1]*D[k]*D[j]
+				dp[i][j] = min(prod, dp[i][j])
+			}
+		}
+	}
+
+	return dp[1][N-1]
+}
+
+/*
+func main() {
+	D := []int{2, 2, 2, 2, 2} // 4 matrices
+	fmt.Print(matrixChainRec(D, 1, 4), "\n")
+	fmt.Print(matrixChainDp(D), "\n")
+}
+*/