Initial data commit

Task/Matrix-chain-multiplication/Go/matrix-chain-multiplication.go

@@ -0,0 +1,76 @@
+package main
+
+import "fmt"
+
+// PrintMatrixChainOrder prints the optimal order for chain
+// multiplying matrices.
+// Matrix A[i] has dimensions dims[i-1]×dims[i].
+func PrintMatrixChainOrder(dims []int) {
+	n := len(dims) - 1
+	m, s := newSquareMatrices(n)
+
+	// m[i,j] will be minimum number of scalar multiplactions
+	// needed to compute the matrix A[i]A[i+1]…A[j] = A[i…j].
+	// Note, m[i,i] = zero (no cost).
+	// s[i,j] will be the index of the subsequence split that
+	// achieved minimal cost.
+	for lenMinusOne := 1; lenMinusOne < n; lenMinusOne++ {
+		for i := 0; i < n-lenMinusOne; i++ {
+			j := i + lenMinusOne
+			m[i][j] = -1
+			for k := i; k < j; k++ {
+				cost := m[i][k] + m[k+1][j] + dims[i]*dims[k+1]*dims[j+1]
+				if m[i][j] < 0 || cost < m[i][j] {
+					m[i][j] = cost
+					s[i][j] = k
+				}
+			}
+		}
+	}
+
+	// Format and print result.
+	const MatrixNames = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
+	var subprint func(int, int)
+	subprint = func(i, j int) {
+		if i == j {
+			return
+		}
+		k := s[i][j]
+		subprint(i, k)
+		subprint(k+1, j)
+		fmt.Printf("%*s -> %s × %s%*scost=%d\n",
+			n, MatrixNames[i:j+1],
+			MatrixNames[i:k+1],
+			MatrixNames[k+1:j+1],
+			n+i-j, "", m[i][j],
+		)
+	}
+	subprint(0, n-1)
+}
+
+func newSquareMatrices(n int) (m, s [][]int) {
+	// Allocates two n×n matrices as slices of slices but
+	// using only one [2n][]int and one [2n²]int backing array.
+	m = make([][]int, 2*n)
+	m, s = m[:n:n], m[n:]
+	tmp := make([]int, 2*n*n)
+	for i := range m {
+		m[i], tmp = tmp[:n:n], tmp[n:]
+	}
+	for i := range s {
+		s[i], tmp = tmp[:n:n], tmp[n:]
+	}
+	return m, s
+}
+
+func main() {
+	cases := [...][]int{
+		{1, 5, 25, 30, 100, 70, 2, 1, 100, 250, 1, 1000, 2},
+		{1000, 1, 500, 12, 1, 700, 2500, 3, 2, 5, 14, 10},
+	}
+	for _, tc := range cases {
+		fmt.Println("Dimensions:", tc)
+		PrintMatrixChainOrder(tc)
+		fmt.Println()
+	}
+}