Data update

Task/Matrix-chain-multiplication/Ada/matrix-chain-multiplication-1.adb

@@ -0,0 +1,4 @@
+package mat_chain is
+   type Vector is array (Natural range <>) of Integer;
+   procedure Chain_Multiplication (Dims : Vector);
+end mat_chain;

Task/Matrix-chain-multiplication/Ada/matrix-chain-multiplication-2.adb

@@ -0,0 +1,91 @@
+with Ada.Text_IO;           use Ada.Text_IO;
+with Ada.Strings.Unbounded; use Ada.Strings.Unbounded;
+
+package body mat_chain is
+   type Result_Matrix is
+     array (Positive range <>, Positive range <>) of Integer;
+
+   --------------------------
+   -- Chain_Multiplication --
+   --------------------------
+
+   procedure Chain_Multiplication (Dims : Vector) is
+      n : Natural := Dims'Length - 1;
+      S : Result_Matrix (1 .. n, 1 .. n);
+      m : Result_Matrix (1 .. n, 1 .. n);
+      procedure Print (Item : Vector) is
+      begin
+         Put ("Array Dimension  = (");
+         for I in Item'Range loop
+            Put (Item (I)'Image);
+            if I < Item'Last then
+               Put (",");
+            else
+               Put (")");
+            end if;
+         end loop;
+         New_Line;
+      end Print;
+
+      procedure Chain_Order (Item : Vector) is
+         J    : Natural;
+         Cost : Natural;
+         Temp : Natural;
+
+      begin
+         for idx in 1 .. n loop
+            m (idx, idx) := 0;
+         end loop;
+
+         for Len in 2 .. n loop
+            for I in 1 .. n - Len + 1 loop
+               J        := I + Len - 1;
+               m (I, J) := Integer'Last;
+               for K in I .. J - 1 loop
+                  Temp := Item (I - 1) * Item (K) * Item (J);
+                  Cost := m (I, K) + m (K + 1, J) + Temp;
+                  if Cost < m (I, J) then
+                     m (I, J) := Cost;
+                     S (I, J) := K;
+                  end if;
+               end loop;
+            end loop;
+         end loop;
+      end Chain_Order;
+
+      function Optimal_Parens return String is
+         function Construct
+           (S : Result_Matrix; I : Natural; J : Natural)
+            return Unbounded_String
+         is
+            Us         : Unbounded_String := Null_Unbounded_String;
+            Char_Order : Character;
+         begin
+            if I = J then
+               Char_Order := Character'Val (I + 64);
+               Append (Source => Us, New_Item => Char_Order);
+               return Us;
+            else
+               Append (Source => Us, New_Item => '(');
+               Append (Source => Us, New_Item => Construct (S, I, S (I, J)));
+               Append (Source => Us, New_Item => '*');
+               Append
+                 (Source => Us, New_Item => Construct (S, S (I, J) + 1, J));
+               Append (Source => Us, New_Item => ')');
+               return Us;
+            end if;
+         end Construct;
+
+      begin
+         return To_String (Construct (S, 1, n));
+
+      end Optimal_Parens;
+
+   begin
+      Chain_Order (Dims);
+      Print (Dims);
+      Put_Line ("Cost             = " & Integer'Image (m (1, n)));
+      Put_Line ("Optimal Multiply = " & Optimal_Parens);
+   end Chain_Multiplication;
+
+end mat_chain;

Task/Matrix-chain-multiplication/Ada/matrix-chain-multiplication-3.adb

@@ -0,0 +1,14 @@
+with Mat_Chain; use Mat_Chain;
+with Ada.Text_IO; use Ada.Text_IO;
+
+procedure chain_main is
+   V1 : Vector := (5, 6, 3, 1);
+   V2 : Vector := (1, 5, 25, 30, 100, 70, 2, 1, 100, 250, 1, 1000, 2);
+   V3 : Vector := (1000, 1, 500, 12, 1, 700, 2500, 3, 2, 5, 14, 10);
+begin
+   Chain_Multiplication(V1);
+   New_Line;
+   Chain_Multiplication(V2);
+   New_Line;
+   Chain_Multiplication(V3);
+end chain_main;

Task/Matrix-chain-multiplication/Julia/matrix-chain-multiplication-1.jl

@@ -4,8 +4,8 @@ using OffsetArrays
 
 function optim(a)
     n = length(a) - 1
-    u = fill!(OffsetArray{Int}(0:n, 0:n), 0)
-    v = fill!(OffsetArray{Int}(0:n, 0:n), typemax(Int))
+    u = fill!(OffsetArray{Int}(undef, 0:n, 0:n), 0)
+    v = fill!(OffsetArray{Int}(undef, 0:n, 0:n), typemax(Int))
     u[:, 1] .= -1
     v[:, 1] .= 0
     for j in 2:n, i in 1:n-j+1, k in 1:j-1

Task/Matrix-chain-multiplication/V-(Vlang)/matrix-chain-multiplication.v

@@ -0,0 +1,58 @@
+const int_max = max_int // builtin const
+
+struct MatrixChain {
+	mut:
+	may [][]int
+	say [][]int
+	dim []int
+	nir int
+}
+
+fn (mut mc MatrixChain) mat_chain_order() {
+	mc.may = [][]int{len: mc.nir, init: []int{len: mc.nir, init: 0}}
+	mc.say = [][]int{len: mc.nir, init: []int{len: mc.nir, init: 0}}
+	for ial in 0 .. mc.nir {
+		mc.may[ial][ial] = 0
+	}
+	for length in 2 .. mc.nir + 1 {
+		for ial in 0 .. mc.nir - length + 1 {
+			jir := ial + length - 1
+			mc.may[ial][jir] = int_max
+			for kal in ial .. jir {
+				cost := mc.may[ial][kal] + mc.may[kal + 1][jir]
+				+ mc.dim[ial] * mc.dim[kal + 1] * mc.dim[jir + 1]
+				if cost < mc.may[ial][jir] {
+					mc.may[ial][jir] = cost
+					mc.say[ial][jir] = kal
+				}
+			}
+		}
+	}
+}
+
+fn (mut mc MatrixChain) path(air int, bir int) string {
+	if air == bir { return (rune(65 + air)).str() }
+	return "(" + mc.path(air, mc.say[air][bir]) + mc.path(mc.say[air][bir] + 1, bir) + ")"
+}
+
+fn (mut mc MatrixChain) pr_chain_order() {
+	println("Order : " + mc.path(0, mc.nir - 1))
+}
+
+fn main() {
+	dims_2d := [
+		[5, 6, 3, 1],
+		[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],
+	]
+	mut mc := &MatrixChain{}
+	for dims in dims_2d {
+		mc.dim = dims
+		mc.nir = dims.len - 1
+		println("Dims  : $dims")
+		mc.mat_chain_order()
+		mc.pr_chain_order()
+		println("Cost  : ${mc.may[0][mc.nir - 1]}")
+		println("")
+	}
+}