A Latin Square is a n x n grid filled by n distinct numbers each appearing exactly once in each row and column. Given an input n, we have to print a n x n matrix consisting of numbers from 1 to n each appearing exactly once in each row and each column.
Examples :
Input: 3
Output: 1 2 3
3 1 2
2 3 1
Input: 5
Output: 1 2 3 4 5
5 1 2 3 4
4 5 1 2 3
3 4 5 1 2
2 3 4 5 1
Did you find any pattern in which the number is stored in a Latin Square?
- In the first row, the numbers are stored from 1 to n serially.
- In the second row, the numbers are shifted to the right by one column. i.e, 1 is stored at 2nd column now and so on.
- In the third row, the numbers are shifted to the right by two columns. i.e, 1 is stored at 3rd column now and so on.
- We continue the same way for the remaining rows.
Note: There may be more than one possible configuration of a n x n Latin square.
Implementation:
C++
// C++ program to print Latin Square
#include <iostream>
using namespace std;
// Function to print n x n Latin Square
void printLatin(int n)
{
// A variable to control the rotation
// point.
int k = n+1;
// Loop to print rows
for (int i=1; i<=n; i++)
{
// This loops runs only after first
// iteration of outer loop. It prints
// numbers from n to k
int temp = k;
while (temp <= n)
{
cout << temp << " ";
temp++;
}
// This loop prints numbers from 1 to k-1.
for (int j=1; j<k; j++)
cout << j << " ";
k--;
cout << endl;
}
}
// Driver program to test above function
int main(void)
{
int n = 5;
// Invoking printLatin function
printLatin(n);
return 0;
}
// This code is contributed by kothavvsaakash.
// C program to print Latin Square
#include<stdio.h>
// Function to print n x n Latin Square
void printLatin(int n)
{
// A variable to control the rotation
// point.
int k = n+1;
// Loop to print rows
for (int i=1; i<=n; i++)
{
// This loops runs only after first
// iteration of outer loop. It prints
// numbers from n to k
int temp = k;
while (temp <= n)
{
printf("%d ", temp);
temp++;
}
// This loop prints numbers from 1 to k-1.
for (int j=1; j<k; j++)
printf("%d ", j);
k--;
printf("\n");
}
}
// Driver program to test above function
int main(void)
{
int n = 5;
// Invoking printLatin function
printLatin(n);
return 0;
}
// Java program to print Latin Square
class GFG {
// Function to print n x n Latin Square
static void printLatin(int n)
{
// A variable to control the
// rotation point.
int k = n+1;
// Loop to print rows
for (int i = 1; i <= n; i++)
{
// This loops runs only after
// first iteration of outer
// loop. It prints
// numbers from n to k
int temp = k;
while (temp <= n)
{
System.out.print(temp + " ");
temp++;
}
// This loop prints numbers from
// 1 to k-1.
for (int j = 1; j < k; j++)
System.out.print(j + " ");
k--;
System.out.println();
}
}
// Driver code
public static void main (String[] args)
{
int n = 5;
// Invoking printLatin function
printLatin(n);
}
}
// This code is contributed by Anant Agarwal.
# Python 3 program to print Latin Square
# Function to print n x n Latin Square
def printLatin(n):
# A variable to control the
# rotation point.
k = n + 1
# Loop to print rows
for i in range(1, n + 1, 1):
# This loops runs only after first
# iteration of outer loop. It prints
# numbers from n to k
temp = k
while (temp <= n) :
print(temp, end = " ")
temp += 1
# This loop prints numbers
# from 1 to k-1.
for j in range(1, k):
print(j, end = " ")
k -= 1
print()
# Driver Code
n = 5
# Invoking printLatin function
printLatin(n)
# This code is contributed by R_Raj
// C# program to print Latin Square
using System;
class GFG {
// Function to print n x n
// Latin Square
static void printLatin(int n)
{
// A variable to control the
// rotation point.
int k = n + 1;
// Loop to print rows
for (int i = 1; i <= n; i++)
{
// This loops runs only after
// first iteration of outer
// loop. It prints numbers
// from n to k
int temp = k;
while (temp <= n)
{
Console.Write(temp + " ");
temp++;
}
// This loop prints numbers from
// 1 to k-1.
for (int j = 1; j < k; j++)
Console.Write(j + " ");
k--;
Console.WriteLine();
}
}
// Driver code
public static void Main ()
{
int n = 5;
// Invoking printLatin function
printLatin(n);
}
}
// This code is contributed by KRV.
<?php
// PHP program to print Latin Square
// Function to print n x n Latin Square
function printLatin( $n)
{
// A variable to control
// the rotation point.
$k = $n + 1;
// Loop to print rows
for ( $i = 1; $i <= $n; $i++)
{
// This loops runs only after
// first iteration of outer loop.
// It prints numbers from n to k
$temp = $k;
while ($temp <= $n)
{
echo $temp," ";
$temp++;
}
// This loop prints numbers
// from 1 to k-1.
for ($j = 1; $j < $k; $j++)
echo $j, " ";
$k--;
echo "\n";
}
}
// Driver Code
$n = 5;
// Invoking printLatin function
printLatin($n);
// This code is contributed by anuj_67.
?>
<script>
// Javascript program to print Latin Square
// Function to print n x n
// Latin Square
function printLatin(n)
{
// A variable to control the
// rotation point.
let k = n + 1;
// Loop to print rows
for (let i = 1; i <= n; i++)
{
// This loops runs only after
// first iteration of outer
// loop. It prints numbers
// from n to k
let temp = k;
while (temp <= n)
{
document.write(temp + " ");
temp++;
}
// This loop prints numbers from
// 1 to k-1.
for (let j = 1; j < k; j++)
document.write(j + " ");
k--;
document.write("</br>");
}
}
let n = 5;
// Invoking printLatin function
printLatin(n);
</script>
Output1 2 3 4 5
5 1 2 3 4
4 5 1 2 3
3 4 5 1 2
2 3 4 5 1
Time Complexity: O(n*n)
Auxiliary Space: O(1)
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