Printing brackets in matrix chain multiplication
Here given code implementation process.
// Java Program
// Printing brackets in matrix chain multiplication
public class Multiplication
{
public char name;
public int count;
public Multiplication()
{
this.name = 'A';
this.count = 0;
}
public void showBrackets(int i, int j, int[][] brackets)
{
if (i == j)
{
if (count != 0)
{
System.out.print(name + count);
}
else
{
System.out.print(name);
}
if (name == 'Z')
{
// Useful when dimension size is exceed A..Z
name = 'A';
count++;
}
else
{
// Change name
name++;
}
}
else
{
System.out.print("(");
showBrackets(i, brackets[i][j], brackets);
showBrackets(brackets[i][j] + 1, j, brackets);
System.out.print(")");
}
}
public void matrixChainMultiplication(int[] dims, int size)
{
int n = size - 1;
int[][] result = new int[n][n];
int[][] brackets = new int[n][n];
int cost = 0;
int j = 0;
for (int len = 1; len < n; len++)
{
for (int i = 0; i < n - len; i++)
{
j = i + len;
result[i][j] = Integer.MAX_VALUE;
for (int k = i; k < j; k++)
{
cost = result[i][k] + result[k + 1][j] +
dims[i] * dims[k + 1] * dims[j + 1];
if (cost < result[i][j])
{
result[i][j] = cost;
brackets[i][j] = k;
}
}
}
}
this.name = 'A';
this.count = 0;
// Show Brackets
showBrackets(0, n - 1, brackets);
System.out.print("\n");
}
public static void main(String args[])
{
Multiplication task = new Multiplication();
int[] dims1 = {
10 , 16 , 12 , 6 , 14
};
int[] dims2 = {
8 , 20 , 16 , 10 , 6
};
/*
dims = [10 , 16 , 12 , 6 , 14]
matri× A = 10 × 16
matri× B = 16 × 12
matri× C = 12 × 6
matri× D = 6 × 14
--------------------
(A(BC))D
(16×12×6) + (10×16×6) + (10×6×14)
= 2952
*/
int n = dims1.length;
task.matrixChainMultiplication(dims1, n);
n = dims2.length;
/*
dims = [8 , 20 , 16 , 10 , 6]
matri× A = 8 × 20
matri× B = 20 × 16
matri× C = 16 × 10
matri× D = 10 × 6
A(B(CD)) = 3840
(16×10×6) + (20×16×6 ) + (8×20×6 ) = 3840
*/
task.matrixChainMultiplication(dims2, n);
}
}Output
((A(BC))D)
(A(B(CD)))// Include header file
#include <iostream>
#include <vector>
#include <limits.h>
using namespace std;
// C++ Program
// Printing brackets in matrix chain multiplication
class Multiplication
{
public: char name;
int count;
Multiplication()
{
this->name = 'A';
this->count = 0;
}
void showBrackets(int i, int j, vector<vector<int>> brackets)
{
if (i == j)
{
if (this->count != 0)
{
cout << this->name + this->count;
}
else
{
cout << this->name;
}
if (this->name == 'Z')
{
// Useful when dimension size is exceed A..Z
this->name = 'A';
this->count++;
}
else
{
// Change name
this->name++;
}
}
else
{
cout << "(";
this->showBrackets(i, brackets[i][j], brackets);
this->showBrackets(brackets[i][j] + 1, j, brackets);
cout << ")";
}
}
void matrixChainMultiplication(int dims[], int size)
{
int n = size - 1;
vector<vector<int>> result (n,vector<int>(n,0));
vector<vector<int>> brackets (n,vector<int>(n,0));
int cost = 0;
int j = 0;
for (int len = 1; len < n; len++)
{
for (int i = 0; i < n - len; i++)
{
j = i + len;
result[i][j] = INT_MAX;
for (int k = i; k < j; k++)
{
cost = result[i][k] + result[k + 1][j] +
dims[i] *dims[k + 1] *dims[j + 1];
if (cost < result[i][j])
{
result[i][j] = cost;
brackets[i][j] = k;
}
}
}
}
this->name = 'A';
this->count = 0;
// Show Brackets
this->showBrackets(0, n - 1, brackets);
cout << "\n";
}
};
int main()
{
Multiplication *task = new Multiplication();
int dims1[] = {
10 , 16 , 12 , 6 , 14
};
int dims2[] = {
8 , 20 , 16 , 10 , 6
};
/*
dims = [10 , 16 , 12 , 6 , 14]
matri× A = 10 × 16
matri× B = 16 × 12
matri× C = 12 × 6
matri× D = 6 × 14
--------------------
(A(BC))D
(16×12×6) + (10×16×6) + (10×6×14)
= 2952
*/
int n = sizeof(dims1) / sizeof(dims1[0]);
task->matrixChainMultiplication(dims1, n);
n = sizeof(dims2) / sizeof(dims2[0]);
/*
dims = [8 , 20 , 16 , 10 , 6]
matri× A = 8 × 20
matri× B = 20 × 16
matri× C = 16 × 10
matri× D = 10 × 6
A(B(CD)) = 3840
(16×10×6) + (20×16×6 ) + (8×20×6 ) = 3840
*/
task->matrixChainMultiplication(dims2, n);
return 0;
}Output
((A(BC))D)
(A(B(CD)))// Include namespace system
using System;
// Csharp Program
// Printing brackets in matrix chain multiplication
public class Multiplication
{
public char name;
public int count;
public Multiplication()
{
this.name = 'A';
this.count = 0;
}
public void showBrackets(int i, int j, int[,] brackets)
{
if (i == j)
{
if (this.count != 0)
{
Console.Write(this.name + this.count);
}
else
{
Console.Write(this.name);
}
if (this.name == 'Z')
{
// Useful when dimension size is exceed A..Z
this.name = 'A';
this.count++;
}
else
{
// Change name
this.name++;
}
}
else
{
Console.Write("(");
this.showBrackets(i, brackets[i,j], brackets);
this.showBrackets(brackets[i,j] + 1, j, brackets);
Console.Write(")");
}
}
public void matrixChainMultiplication(int[] dims, int size)
{
int n = size - 1;
int[,] result = new int[n,n];
int[,] brackets = new int[n,n];
int cost = 0;
int j = 0;
for (int len = 1; len < n; len++)
{
for (int i = 0; i < n - len; i++)
{
j = i + len;
result[i,j] = int.MaxValue;
for (int k = i; k < j; k++)
{
cost = result[i,k] + result[k + 1,j] + dims[i] *
dims[k + 1] * dims[j + 1];
if (cost < result[i,j])
{
result[i,j] = cost;
brackets[i,j] = k;
}
}
}
}
this.name = 'A';
this.count = 0;
// Show Brackets
this.showBrackets(0, n - 1, brackets);
Console.Write("\n");
}
public static void Main(String[] args)
{
Multiplication task = new Multiplication();
int[] dims1 = {
10 , 16 , 12 , 6 , 14
};
int[] dims2 = {
8 , 20 , 16 , 10 , 6
};
/*
dims = [10 , 16 , 12 , 6 , 14]
matri× A = 10 × 16
matri× B = 16 × 12
matri× C = 12 × 6
matri× D = 6 × 14
--------------------
(A(BC))D
(16×12×6) + (10×16×6) + (10×6×14)
= 2952
*/
int n = dims1.Length;
task.matrixChainMultiplication(dims1, n);
n = dims2.Length;
/*
dims = [8 , 20 , 16 , 10 , 6]
matri× A = 8 × 20
matri× B = 20 × 16
matri× C = 16 × 10
matri× D = 10 × 6
A(B(CD)) = 3840
(16×10×6) + (20×16×6 ) + (8×20×6 ) = 3840
*/
task.matrixChainMultiplication(dims2, n);
}
}Output
((A(BC))D)
(A(B(CD)))package main
import "math"
import "fmt"
// Go Program
// Printing brackets in matrix chain multiplication
type Multiplication struct {
name byte
count int
}
func getMultiplication() * Multiplication {
var me *Multiplication = &Multiplication {}
me.name = 'A'
me.count = 0
return me
}
func(this *Multiplication) showBrackets(i int,
j int, brackets[][] int) {
if i == j {
if this.count != 0 {
fmt.Print(string(this.name), this.count)
} else {
fmt.Print(string(this.name))
}
if this.name == 'Z' {
// Useful when dimension size is exceed A..Z
this.name = 'A'
this.count++
} else {
// Change name
this.name = this.name + 1
}
} else {
fmt.Print("(")
this.showBrackets(i, brackets[i][j], brackets)
this.showBrackets(brackets[i][j] + 1, j, brackets)
fmt.Print(")")
}
}
func(this *Multiplication) matrixChainMultiplication(dims[] int, size int) {
var n int = size - 1
var result = make([][] int, n)
for i := 0; i < n; i++ {
result[i] = make([]int,n)
}
var brackets = make([][] int, n)
for i := 0; i < n; i++ {
brackets[i] = make([]int,n)
}
var cost int = 0
var j int = 0
for len := 1 ; len < n ; len++ {
for i := 0 ; i < n - len ; i++ {
j = i + len
result[i][j] = math.MaxInt64
for k := i ; k < j ; k++ {
cost = result[i][k] + result[k + 1][j] + dims[i] *
dims[k + 1] * dims[j + 1]
if cost < result[i][j] {
result[i][j] = cost
brackets[i][j] = k
}
}
}
}
this.name = 'A'
this.count = 0
// Show Brackets
this.showBrackets(0, n - 1, brackets)
fmt.Print("\n")
}
func main() {
var task * Multiplication = getMultiplication()
var dims1 = [] int {
10,
16,
12,
6,
14,
}
var dims2 = [] int {
8,
20,
16,
10,
6,
}
/*
dims = [10 , 16 , 12 , 6 , 14]
matri× A = 10 × 16
matri× B = 16 × 12
matri× C = 12 × 6
matri× D = 6 × 14
--------------------
(A(BC))D
(16×12×6) + (10×16×6) + (10×6×14)
= 2952
*/
var n int = len(dims1)
task.matrixChainMultiplication(dims1, n)
n = len(dims2)
/*
dims = [8 , 20 , 16 , 10 , 6]
matri× A = 8 × 20
matri× B = 20 × 16
matri× C = 16 × 10
matri× D = 10 × 6
A(B(CD)) = 3840
(16×10×6) + (20×16×6 ) + (8×20×6 ) = 3840
*/
task.matrixChainMultiplication(dims2, n)
}Output
((A(AB))D)
(A(A(BD)))<?php
// Php Program
// Printing brackets in matrix chain multiplication
class Multiplication
{
public $name;
public $count;
public function __construct()
{
$this->name = 'A';
$this->count = 0;
}
public function showBrackets($i, $j, $brackets)
{
if ($i == $j)
{
if ($this->count != 0)
{
echo(ord($this->name) + $this->count);
}
else
{
echo($this->name);
}
if ($this->name == 'Z')
{
// Useful when dimension size is exceed A..Z
$this->name = 'A';
$this->count++;
}
else
{
// Change name
$this->name++;
}
}
else
{
echo("(");
$this->showBrackets($i, $brackets[$i][$j], $brackets);
$this->showBrackets($brackets[$i][$j] + 1, $j, $brackets);
echo(")");
}
}
public function matrixChainMultiplication($dims, $size)
{
$n = $size - 1;
$result = array_fill(0, $n, array_fill(0, $n, 0));
$brackets = array_fill(0, $n, array_fill(0, $n, 0));
$cost = 0;
$j = 0;
for ($len = 1; $len < $n; $len++)
{
for ($i = 0; $i < $n - $len; $i++)
{
$j = $i + $len;
$result[$i][$j] = PHP_INT_MAX;
for ($k = $i; $k < $j; $k++)
{
$cost = $result[$i][$k] + $result[$k + 1][$j] + $dims[$i] *
$dims[$k + 1] * $dims[$j + 1];
if ($cost < $result[$i][$j])
{
$result[$i][$j] = $cost;
$brackets[$i][$j] = $k;
}
}
}
}
$this->name = 'A';
$this->count = 0;
// Show Brackets
$this->showBrackets(0, $n - 1, $brackets);
echo("\n");
}
}
function main()
{
$task = new Multiplication();
$dims1 = array(10, 16, 12, 6, 14);
$dims2 = array(8, 20, 16, 10, 6);
/*
dims = [10 , 16 , 12 , 6 , 14]
matri× A = 10 × 16
matri× B = 16 × 12
matri× C = 12 × 6
matri× D = 6 × 14
--------------------
(A(BC))D
(16×12×6) + (10×16×6) + (10×6×14)
= 2952
*/
$n = count($dims1);
$task->matrixChainMultiplication($dims1, $n);
$n = count($dims2);
/*
dims = [8 , 20 , 16 , 10 , 6]
matri× A = 8 × 20
matri× B = 20 × 16
matri× C = 16 × 10
matri× D = 10 × 6
A(B(CD)) = 3840
(16×10×6) + (20×16×6 ) + (8×20×6 ) = 3840
*/
$task->matrixChainMultiplication($dims2, $n);
}
main();Output
((A(BC))D)
(A(B(CD)))// Node JS Program
// Printing brackets in matrix chain multiplication
class Multiplication
{
constructor()
{
this.name = 'A';
this.count = 0;
}
showBrackets(i, j, brackets)
{
if (i == j)
{
if (this.count != 0)
{
process.stdout.write("" + this.name.charCodeAt(0) + this.count);
}
else
{
process.stdout.write(this.name);
}
if (this.name == 'Z')
{
// Useful when dimension size is exceed A..Z
this.name = 'A';
this.count++;
}
else
{
// Change name
this.name = String. fromCharCode(this.name.charCodeAt(0) +
1);
}
}
else
{
process.stdout.write("(");
this.showBrackets(i, brackets[i][j], brackets);
this.showBrackets(brackets[i][j] + 1, j, brackets);
process.stdout.write(")");
}
}
matrixChainMultiplication(dims, size)
{
var n = size - 1;
var result = Array(n).fill(0).map(() => new Array(n).fill(0));
var brackets = Array(n).fill(0).map(() => new Array(n).fill(0));
var cost = 0;
var j = 0;
for (var len = 1; len < n; len++)
{
for (var i = 0; i < n - len; i++)
{
j = i + len;
result[i][j] = Number.MAX_VALUE;
for (var k = i; k < j; k++)
{
cost = result[i][k] + result[k + 1][j] + dims[i] *
dims[k + 1] * dims[j + 1];
if (cost < result[i][j])
{
result[i][j] = cost;
brackets[i][j] = k;
}
}
}
}
this.name = 'A';
this.count = 0;
// Show Brackets
this.showBrackets(0, n - 1, brackets);
process.stdout.write("\n");
}
}
function main()
{
var task = new Multiplication();
var dims1 = [10, 16, 12, 6, 14];
var dims2 = [8, 20, 16, 10, 6];
/*
dims = [10 , 16 , 12 , 6 , 14]
matri× A = 10 × 16
matri× B = 16 × 12
matri× C = 12 × 6
matri× D = 6 × 14
--------------------
(A(BC))D
(16×12×6) + (10×16×6) + (10×6×14)
= 2952
*/
var n = dims1.length;
task.matrixChainMultiplication(dims1, n);
n = dims2.length;
/*
dims = [8 , 20 , 16 , 10 , 6]
matri× A = 8 × 20
matri× B = 20 × 16
matri× C = 16 × 10
matri× D = 10 × 6
A(B(CD)) = 3840
(16×10×6) + (20×16×6 ) + (8×20×6 ) = 3840
*/
task.matrixChainMultiplication(dims2, n);
}
main();Output
((A(BC))D)
(A(B(CD)))import sys
# Python 3 Program
# Printing brackets in matrix chain multiplication
class Multiplication :
def __init__(self) :
self.name = 'A'
self.count = 0
def showBrackets(self, i, j, brackets) :
if (i == j) :
if (self.count != 0) :
print(ord(self.name) + self.count, end = "")
else :
print(self.name, end = "")
if (self.name == 'Z') :
# Useful when dimension size is exceed A..Z
self.name = 'A'
self.count += 1
else :
# Change name
self.name = chr(ord(self.name) + 1)
else :
print("(", end = "")
self.showBrackets(i, brackets[i][j], brackets)
self.showBrackets(brackets[i][j] + 1, j, brackets)
print(")", end = "")
def matrixChainMultiplication(self, dims, size) :
n = size - 1
result = [[0] * (n) for _ in range(n) ]
brackets = [[0] * (n) for _ in range(n) ]
cost = 0
j = 0
len = 1
while (len < n) :
i = 0
while (i < n - len) :
j = i + len
result[i][j] = sys.maxsize
k = i
while (k < j) :
cost = result[i][k] + result[k + 1][j] + dims[i] * dims[k + 1] * dims[j + 1]
if (cost < result[i][j]) :
result[i][j] = cost
brackets[i][j] = k
k += 1
i += 1
len += 1
self.name = 'A'
self.count = 0
# Show Brackets
self.showBrackets(0, n - 1, brackets)
print(end = "\n")
def main() :
task = Multiplication()
dims1 = [10, 16, 12, 6, 14]
dims2 = [8, 20, 16, 10, 6]
# dims = [10 , 16 , 12 , 6 , 14]
# matri× A = 10 × 16
# matri× B = 16 × 12
# matri× C = 12 × 6
# matri× D = 6 × 14
# --------------------
# (A(BC))D
# (16×12×6) + (10×16×6) + (10×6×14)
# = 2952
n = len(dims1)
task.matrixChainMultiplication(dims1, n)
n = len(dims2)
# dims = [8 , 20 , 16 , 10 , 6]
# matri× A = 8 × 20
# matri× B = 20 × 16
# matri× C = 16 × 10
# matri× D = 10 × 6
# A(B(CD)) = 3840
# (16×10×6) + (20×16×6 ) + (8×20×6 ) = 3840
task.matrixChainMultiplication(dims2, n)
if __name__ == "__main__": main()Output
((A(BC))D)
(A(B(CD)))# Ruby Program
# Printing brackets in matrix chain multiplication
class Multiplication
# Define the accessor and reader of class Multiplication
attr_reader :name, :count
attr_accessor :name, :count
def initialize()
self.name = 'A'
self.count = 0
end
def showBrackets(i, j, brackets)
if (i == j)
if (self.count != 0)
print(self.name.ord + self.count)
else
print(self.name)
end
if (self.name == 'Z')
# Useful when dimension size is exceed A..Z
self.name = 'A'
self.count += 1
else
# Change name
self.name = (self.name.ord+1).chr
end
else
print("(")
self.showBrackets(i, brackets[i][j], brackets)
self.showBrackets(brackets[i][j] + 1, j, brackets)
print(")")
end
end
def matrixChainMultiplication(dims, size)
n = size - 1
result = Array.new(n) {Array.new(n) {0}}
brackets = Array.new(n) {Array.new(n) {0}}
cost = 0
j = 0
len = 1
while (len < n)
i = 0
while (i < n - len)
j = i + len
result[i][j] = (2 ** (0. size * 8 - 2))
k = i
while (k < j)
cost = result[i][k] + result[k + 1][j] + dims[i] *
dims[k + 1] * dims[j + 1]
if (cost < result[i][j])
result[i][j] = cost
brackets[i][j] = k
end
k += 1
end
i += 1
end
len += 1
end
self.name = 'A'
self.count = 0
# Show Brackets
self.showBrackets(0, n - 1, brackets)
print("\n")
end
end
def main()
task = Multiplication.new()
dims1 = [10, 16, 12, 6, 14]
dims2 = [8, 20, 16, 10, 6]
# dims = [10 , 16 , 12 , 6 , 14]
# matri× A = 10 × 16
# matri× B = 16 × 12
# matri× C = 12 × 6
# matri× D = 6 × 14
# --------------------
# (A(BC))D
# (16×12×6) + (10×16×6) + (10×6×14)
# = 2952
n = dims1.length
task.matrixChainMultiplication(dims1, n)
n = dims2.length
# dims = [8 , 20 , 16 , 10 , 6]
# matri× A = 8 × 20
# matri× B = 20 × 16
# matri× C = 16 × 10
# matri× D = 10 × 6
# A(B(CD)) = 3840
# (16×10×6) + (20×16×6 ) + (8×20×6 ) = 3840
task.matrixChainMultiplication(dims2, n)
end
main()Output
((A(BC))D)
(A(B(CD)))
// Scala Program
// Printing brackets in matrix chain multiplication
class Multiplication(var name: Char,
var count: Int)
{
def this()
{
this('A', 0)
}
def showBrackets(i: Int, j: Int, brackets: Array[Array[Int]]): Unit = {
if (i == j)
{
if (count != 0)
{
print(name.toInt + count);
}
else
{
print(name);
}
if (name == 'Z')
{
// Useful when dimension size is exceed A..Z
name = 'A';
count += 1;
}
else
{
// Change name
name = (name.toInt + 1).toChar;
}
}
else
{
print("(");
showBrackets(i, brackets(i)(j), brackets);
showBrackets(brackets(i)(j) + 1, j, brackets);
print(")");
}
}
def matrixChainMultiplication(dims: Array[Int], size: Int): Unit = {
var n: Int = size - 1;
var result: Array[Array[Int]] = Array.fill[Int](n, n)(0);
var brackets: Array[Array[Int]] = Array.fill[Int](n, n)(0);
var cost: Int = 0;
var j: Int = 0;
var len: Int = 1;
while (len < n)
{
var i: Int = 0;
while (i < n - len)
{
j = i + len;
result(i)(j) = Int.MaxValue;
var k: Int = i;
while (k < j)
{
cost = result(i)(k) + result(k + 1)(j) + dims(i) *
dims(k + 1) * dims(j + 1);
if (cost < result(i)(j))
{
result(i)(j) = cost;
brackets(i)(j) = k;
}
k += 1;
}
i += 1;
}
len += 1;
}
this.name = 'A';
this.count = 0;
// Show Brackets
showBrackets(0, n - 1, brackets);
print("\n");
}
}
object Main
{
def main(args: Array[String]): Unit = {
var task: Multiplication = new Multiplication();
var dims1: Array[Int] = Array(10, 16, 12, 6, 14);
var dims2: Array[Int] = Array(8, 20, 16, 10, 6);
/*
dims = [10 , 16 , 12 , 6 , 14]
matri× A = 10 × 16
matri× B = 16 × 12
matri× C = 12 × 6
matri× D = 6 × 14
--------------------
(A(BC))D
(16×12×6) + (10×16×6) + (10×6×14)
= 2952
*/
var n: Int = dims1.length;
task.matrixChainMultiplication(dims1, n);
n = dims2.length;
/*
dims = [8 , 20 , 16 , 10 , 6]
matri× A = 8 × 20
matri× B = 20 × 16
matri× C = 16 × 10
matri× D = 10 × 6
A(B(CD)) = 3840
(16×10×6) + (20×16×6 ) + (8×20×6 ) = 3840
*/
task.matrixChainMultiplication(dims2, n);
}
}Output
((A(BC))D)
(A(B(CD)))import Foundation;
// Swift 4 Program
// Printing brackets in matrix chain multiplication
class Multiplication
{
var name: Character;
var count: Int;
init()
{
self.name = "A";
self.count = 0;
}
func showBrackets(_ i: Int, _ j: Int, _ brackets: [
[Int]
])
{
if (i == j)
{
if (self.count != 0)
{
print(Int(UnicodeScalar(String(self.name))!.value) + self.count, terminator: "");
}
else
{
print(self.name, terminator: "");
}
if (self.name == "Z")
{
// Useful when dimension size is exceed A..Z
self.name = "A";
self.count += 1 ;
}
else
{
// Change name
self.name = Character(UnicodeScalar(
Int(UnicodeScalar(String(self.name))!.value) + i)!)
}
}
else
{
print("(", terminator: "");
self.showBrackets(i, brackets[i][j], brackets);
self.showBrackets(brackets[i][j] + 1, j, brackets);
print(")", terminator: "");
}
}
func matrixChainMultiplication(_ dims: [Int], _ size: Int)
{
let n: Int = size - 1;
var result: [
[Int]
] = Array(repeating: Array(repeating: 0, count: n), count: n);
var brackets: [
[Int]
] = Array(repeating: Array(repeating: 0, count: n), count: n);
var cost: Int = 0;
var j: Int = 0;
var len: Int = 1;
while (len < n)
{
var i: Int = 0;
while (i < n - len)
{
j = i + len;
result[i][j] = Int.max;
var k: Int = i;
while (k < j)
{
cost = result[i][k] + result[k + 1][j] + dims[i] *
dims[k + 1] * dims[j + 1];
if (cost < result[i][j])
{
result[i][j] = cost;
brackets[i][j] = k;
}
k += 1;
}
i += 1;
}
len += 1;
}
self.name = "A";
self.count = 0;
// Show Brackets
self.showBrackets(0, n - 1, brackets);
print(terminator: "\n");
}
}
func main()
{
let task: Multiplication = Multiplication();
let dims1: [Int] = [10, 16, 12, 6, 14];
let dims2: [Int] = [8, 20, 16, 10, 6];
/*
dims = [10 , 16 , 12 , 6 , 14]
matri× A = 10 × 16
matri× B = 16 × 12
matri× C = 12 × 6
matri× D = 6 × 14
--------------------
(A(BC))D
(16×12×6) + (10×16×6) + (10×6×14)
= 2952
*/
var n: Int = dims1.count;
task.matrixChainMultiplication(dims1, n);
n = dims2.count;
/*
dims = [8 , 20 , 16 , 10 , 6]
matri× A = 8 × 20
matri× B = 20 × 16
matri× C = 16 × 10
matri× D = 10 × 6
A(B(CD)) = 3840
(16×10×6) + (20×16×6 ) + (8×20×6 ) = 3840
*/
task.matrixChainMultiplication(dims2, n);
}
main();Output
((A(AB))D)
(A(A(BD)))// Kotlin Program
// Printing brackets in matrix chain multiplication
class Multiplication
{
var name: Char;
var count: Int;
constructor()
{
this.name = 'A';
this.count = 0;
}
fun showBrackets(i: Int, j: Int,
brackets: Array < Array < Int >> ): Unit
{
if (i == j)
{
if (this.count != 0)
{
print(this.name.toInt() + this.count);
}
else
{
print(this.name);
}
if (this.name == 'Z')
{
// Useful when dimension size is exceed A..Z
this.name = 'A';
this.count += 1;
}
else
{
// Change name
this.name += 1;
}
}
else
{
print("(");
this.showBrackets(i, brackets[i][j], brackets);
this.showBrackets(brackets[i][j] + 1, j, brackets);
print(")");
}
}
fun matrixChainMultiplication(dims: Array < Int > , size: Int): Unit
{
var n: Int = size - 1;
val result: Array < Array < Int >> = Array(n)
{
Array(n)
{
0
}
};
val brackets: Array < Array < Int >> = Array(n)
{
Array(n)
{
0
}
};
var cost : Int;
var j : Int;
var len: Int = 1;
while (len < n)
{
var i: Int = 0;
while (i < n - len)
{
j = i + len;
result[i][j] = Int.MAX_VALUE;
var k: Int = i;
while (k < j)
{
cost = result[i][k] + result[k + 1][j] + dims[i] *
dims[k + 1] * dims[j + 1];
if (cost < result[i][j])
{
result[i][j] = cost;
brackets[i][j] = k;
}
k += 1;
}
i += 1;
}
len += 1;
}
this.name = 'A';
this.count = 0;
// Show Brackets
this.showBrackets(0, n - 1, brackets);
print("\n");
}
}
fun main(args: Array < String > ): Unit
{
val task: Multiplication = Multiplication();
val dims1: Array < Int > = arrayOf(10, 16, 12, 6, 14);
val dims2: Array < Int > = arrayOf(8, 20, 16, 10, 6);
/*
dims = [10 , 16 , 12 , 6 , 14]
matri× A = 10 × 16
matri× B = 16 × 12
matri× C = 12 × 6
matri× D = 6 × 14
--------------------
(A(BC))D
(16×12×6) + (10×16×6) + (10×6×14)
= 2952
*/
var n: Int = dims1.count();
task.matrixChainMultiplication(dims1, n);
n = dims2.count();
/*
dims = [8 , 20 , 16 , 10 , 6]
matri× A = 8 × 20
matri× B = 20 × 16
matri× C = 16 × 10
matri× D = 10 × 6
A(B(CD)) = 3840
(16×10×6) + (20×16×6 ) + (8×20×6 ) = 3840
*/
task.matrixChainMultiplication(dims2, n);
}Output
((A(BC))D)
(A(B(CD)))
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