Form coils in a matrix
Last Updated :
07 Jul, 2022
Given a positive integer n which represents the dimensions of a 4n x 4n matrix with values from 1 to n filled from left to right and top to bottom. Form two coils from the matrix and print the coils.
Examples:
Input : n = 1;
Output : Coil 1 : 10 6 2 3 4 8 12 16
Coil 2 : 7 11 15 14 13 9 5 1
Explanation : Matrix is
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
Input : n = 2;
Output : Coil 1 : 36 28 20 21 22 30 38 46 54
53 52 51 50 42 34 26 18 10
2 3 4 5 6 7 8 16 24 32 40
48 56 64
Coil 2 : 29 37 45 44 43 35 27 19 11 12
13 14 15 23 31 39 47 55 63 62
61 60 59 58 57 49 41 33 25 17
9 1
The total elements in the matrix are 16n2. All elements are divided into two coils. Every coil has 8n2 elements. We make two arrays of this size. We first fill elements in coil1 by traversing them in the given order. Once we have filled elements in coil1, we can get elements of other coil2 using formula coil2[i] = 16*n*n + 1 -coil1[i].
Implementation:
C++
#include<iostream>
using namespace std;
void printCoils( int n)
{
int m = 8*n*n;
int coil1[m];
coil1[0] = 8*n*n + 2*n;
int curr = coil1[0];
int nflg = 1, step = 2;
int index = 1;
while (index < m)
{
for ( int i=0; i<step; i++)
{
curr = coil1[index++] = (curr - 4*n*nflg);
if (index >= m)
break ;
}
if (index >= m)
break ;
for ( int i=0; i<step; i++)
{
curr = coil1[index++] = curr + nflg;
if (index >= m)
break ;
}
nflg = nflg*(-1);
step += 2;
}
int coil2[m];
for ( int i=0; i<8*n*n; i++)
coil2[i] = 16*n*n + 1 -coil1[i];
cout << "Coil 1 : " ;
for ( int i=0; i<8*n*n; i++)
cout << coil1[i] << " " ;
cout << "\nCoil 2 : " ;
for ( int i=0; i<8*n*n; i++)
cout << coil2[i] << " " ;
}
int main()
{
int n = 1;
printCoils(n);
return 0;
}
|
Java
class GFG {
static void printCoils( int n)
{
int m = 8 * n * n;
int coil1[] = new int [m];
coil1[ 0 ] = 8 * n * n + 2 * n;
int curr = coil1[ 0 ];
int nflg = 1 , step = 2 ;
int index = 1 ;
while (index < m)
{
for ( int i = 0 ; i < step; i++)
{
curr = coil1[index++] = (curr - 4 * n * nflg);
if (index >= m)
break ;
}
if (index >= m)
break ;
for ( int i = 0 ; i < step; i++)
{
curr = coil1[index++] = curr + nflg;
if (index >= m)
break ;
}
nflg = nflg * (- 1 );
step += 2 ;
}
int coil2[] = new int [m];
for ( int i = 0 ; i < 8 * n * n; i++)
coil2[i] = 16 * n * n + 1 - coil1[i];
System.out.print( "Coil 1 : " );
for ( int i = 0 ; i < 8 * n * n; i++)
System.out.print(coil1[i] + " " );
System.out.print( "\nCoil 2 : " );
for ( int i = 0 ; i < 8 * n * n; i++)
System.out.print(coil2[i] + " " );
}
public static void main(String[] args)
{
int n = 1 ;
printCoils(n);
}
}
|
Python3
def printCoils(n):
m = 8 * n * n
coil1 = [ 0 ] * m
coil1[ 0 ] = 8 * n * n + 2 * n
curr = coil1[ 0 ]
nflg = 1
step = 2
index = 1
while (index < m):
for i in range (step):
curr = coil1[index] = (curr - 4 * n * nflg)
index + = 1
if (index > = m):
break
if (index > = m):
break
for i in range (step):
curr = coil1[index] = curr + nflg
index + = 1
if (index > = m):
break
nflg = nflg * ( - 1 )
step + = 2
coil2 = [ 0 ] * m
i = 0
while (i < 8 * n * n):
coil2[i] = 16 * n * n + 1 - coil1[i]
i + = 1
print ( "Coil 1 :" , end = " " )
i = 0
while (i < 8 * n * n):
print (coil1[i], end = " " )
i + = 1
print ( "\nCoil 2 :" , end = " " )
i = 0
while (i < 8 * n * n):
print (coil2[i], end = " " )
i + = 1
n = 1
printCoils(n)
|
C#
using System;
class GFG {
static void printCoils( int n)
{
int m = 8 * n * n;
int [] coil1 = new int [m];
coil1[0] = 8 * n * n + 2 * n;
int curr = coil1[0];
int nflg = 1, step = 2;
int index = 1;
while (index < m)
{
for ( int i = 0; i < step; i++)
{
curr = coil1[index++]
= (curr - 4 * n * nflg);
if (index >= m)
break ;
}
if (index >= m)
break ;
for ( int i = 0; i < step; i++)
{
curr = coil1[index++] = curr
+ nflg;
if (index >= m)
break ;
}
nflg = nflg * (-1);
step += 2;
}
int [] coil2 = new int [m];
for ( int i = 0; i < 8 * n * n; i++)
coil2[i] = 16 * n * n + 1 - coil1[i];
Console.Write( "Coil 1 : " );
for ( int i = 0; i < 8 * n * n; i++)
Console.Write(coil1[i] + " " );
Console.Write( "\nCoil 2 : " );
for ( int i = 0; i < 8 * n * n; i++)
Console.Write(coil2[i] + " " );
}
public static void Main()
{
int n = 1;
printCoils(n);
}
}
|
PHP
<?php
function printCoils( $n )
{
$m = 8 * $n * $n ;
$coil1 = array ();
$coil1 [0] = 8 * $n * $n + 2 * $n ;
$curr = $coil1 [0];
$nflg = 1; $step = 2;
$index = 1;
while ( $index < $m )
{
for ( $i = 0; $i < $step ; $i ++)
{
$curr = $coil1 [ $index ++] =
( $curr - 4* $n * $nflg );
if ( $index >= $m )
break ;
}
if ( $index >= $m )
break ;
for ( $i =0; $i < $step ; $i ++)
{
$curr = $coil1 [ $index ++] =
$curr + $nflg ;
if ( $index >= $m )
break ;
}
$nflg = $nflg * (-1);
$step += 2;
}
$coil2 = array ();
for ( $i = 0; $i < 8 * $n * $n ; $i ++)
$coil2 [ $i ] = 16 * $n * $n + 1 - $coil1 [ $i ];
echo "Coil 1 : " ;
for ( $i = 0; $i < 8 * $n * $n ; $i ++)
echo $coil1 [ $i ] , " " ;
echo "\nCoil 2 : " ;
for ( $i = 0; $i < 8 * $n * $n ; $i ++)
echo $coil2 [ $i ] , " " ;
}
$n = 1;
printCoils( $n );
?>
|
Javascript
<script>
function printCoils(n)
{
let m = 8 * n * n;
let coil1 = new Array(m);
coil1.fill(0);
coil1[0] = 8 * n * n + 2 * n;
let curr = coil1[0];
let nflg = 1, step = 2;
let index = 1;
while (index < m)
{
for (let i = 0; i < step; i++)
{
curr = coil1[index++]
= (curr - 4 * n * nflg);
if (index >= m)
break ;
}
if (index >= m)
break ;
for (let i = 0; i < step; i++)
{
curr = coil1[index++] = curr
+ nflg;
if (index >= m)
break ;
}
nflg = nflg * (-1);
step += 2;
}
let coil2 = new Array(m);
coil2.fill(0);
for (let i = 0; i < 8 * n * n; i++)
coil2[i] = 16 * n * n + 1 - coil1[i];
document.write( "Coil 1 : " );
for (let i = 0; i < 8 * n * n; i++)
document.write(coil1[i] + " " );
document.write( "</br>" + "Coil 2 : " );
for (let i = 0; i < 8 * n * n; i++)
document.write(coil2[i] + " " );
}
let n = 1;
printCoils(n);
</script>
|
Output
Coil 1 : 10 6 2 3 4 8 12 16
Coil 2 : 7 11 15 14 13 9 5 1
Time Complexity: O(n2)
Auxiliary Space: O(n2)
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