Quiz 81: Print prime numbers upto N where 1<=N<=1000000

Problem:

Given a positive integer N, print all prime numbers upto N

Input Format: 

positive integer N

Output Format: 

prime numbers from 0 to N in new line

Constraints: 

1<=N<=1000000

Sample Input

20

Sample Output:

2
3
5
7
11
13
17
19

Explanations:

Prime numbers upto 20

---

Solution:

use strict;
use warnings;

chomp(my $n=<>);
if($n>1)
{
print "2\n";
}
my @arr=(2);
for (my $i=3; $i<=$n;$i+=2) {
    my $isprime = 1;
    my $c = sqrt($i) + 1;
    foreach my $p (@arr) {
        if ($p >= $c) {
            last;
        }
        if ($i % $p == 0) {
            $isprime = 0;
            last;
        }
    }
    if ($isprime == 1) {
print "$i\n";
push(@arr, $i);
    }
}

---

Tips:

This algorithms is fastest method to print prime numbers upto 1000000

Quiz 80: Remove leading zeros from an array of positive integers

Problem:

Given an array of positive integers, display an array after removing all the leading zeros from original array.

Input Format: 

array having elements separated by "space"

Output Format: 

array having elements separated by "space" after removing leading zeros

Constraints: 
Each element of array is < 1000000

Sample Input

007 70 01022 0000000001 00200 20000 0012300

Sample Output:

7 70 1022 1 200 20000 12300

Explanations:

Simple, removed all zeros before first non-zero character

---

Solution:

use strict;
use warnings;

chomp(my $line=<>);
my @arr=split(" ",$line);
@arr=map{$_%1000000}@arr;
print "@arr";

---

Tips:

Use mod of maximum value ie 1000000 in our case.

Quiz 79: Print a square matrix in anti-clockwise direction

Problem:

Given a positive integer(n), print square matrix(n x n) in anticlockwise direction.
Check sample input/output for better understanding

Input Format: 

N=a positive integer

Output Format: 

square matrix in anti-clockwise direction

Constraints: 
None

Sample Input

4

Sample Output:

1 12 11 10
2 13 16 9
3 14 15 8
4 5 6 7

Explanations:

in a matrix, 4 x 4, starting printing numbers from 1 in anticlockwise direction ie down,right,up,left.

---

Solution:

use strict;
use warnings;

my $n=<STDIN>;
my $m=$n;
my @arr=();
my $ans=1;
my $row=0;
my $col=$n-1;
my $i=0;
my $j=0;
while($n>=1)
{
for($i=$row;$i<=$col;$i++)
{
$arr[$i][$row]=$ans;
$ans++;
}
for($i=$row+1;$i<=$col;$i++)
{
$arr[$col][$i]=$ans;
$ans++;
}
for($i=$col-1;$i>=$row;$i--)
{
$arr[$i][$col]=$ans;
$ans++;
}
for($i=$col-1;$i>=$row+1;$i--)
{
$arr[$row][$i]=$ans;
$ans++;
}
$n=$n-2;
$row=$row+1;
$col=$col-1;
}
for($i=0;$i<$m;$i++)
{
for($j=0;$j<$m;$j++)
{
print "$arr[$i][$j] ";
}
print "\n";
}

---

Tips:

On completing 1 full anticlockwise cycle, the dimension of matrix will change by 2, so i used $n=$n-2