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

Quiz 78: Smallest positive integer not in list

Problem:

Given an array of positive numbers. Find the smallest positive integer which is not present in list

Input Format: 

T=number of test cases
Array(integers separated by space in new line for each test case)

Output Format: 

smallest positive integer in each line for each test case

Constraints: 
None

Sample Input

3
1 6 4 2 5 3
1 6 5 4 3 7
2 3 4 5 6 7

Sample Output:

7
2
1

Explanations:

For case 1, smallest positive integer not in list is 7, 1-6 are present, so ans is 7.

---

Solution:

use strict;
use warnings;

chomp(my $t=<>);
for(my $j=0;$j<$t;$j++)
{
chomp(my $line=<>);
my @arr=split(" ",$line);
@arr=sort{$a<=>$b}@arr;
my $i=1;
my $c=0;
foreach(@arr)
{
if($_==$i)
{
if($_+1!=$i+1)
{
my $tmp=$i;
$tmp++;
print "$tmp\n";
$c++;
last;
}
}
else
{
print "$i\n";
$c++;
last;
}
$i++;
}
if($c==0)
{
print "$i\n";
}
}

---

Tips:

Use sort function so that question could be solved in very less iterations

Quiz 77: Shortest path of directed Graph

Problem:

Given distances between different vertices, find the shortest path from vertex i to vertex j

Input Format: 

N ie no of direct path from one vertex to another
Next N lines have format- vertexA vertexB distance
vertexI vertexJ

Output Format: 

shortest path
length of shortest path

Constraints: 
None

Sample Input

11
a b 5
c a 5
a d 10
e c 12
d f 13
f d 1
a e 2
e a 4
f e 2
e f 1
b d 3
a d

Sample Output:

a e f d
4

Explanations:

shortest path from a to d is a-e-f-d

---

Solution:

#!/usr/bin/perl
use warnings;
use strict;

use Graph;
use Graph::Directed;

my $g = 'Graph::Directed'->new;

chomp(my $n=<>);
for(my $i=0;$i<$n;$i++)
{
my $tmp=<>;
my @arr=split(" ",$tmp);
$g->add_weighted_edges(@arr);
}

my $APSP = $g->APSP_Floyd_Warshall;

chomp(my $in=<>);
(my $u,my $v)=split(" ",$in);
        my $w = $APSP->path_length($u, $v);

        if ($w) {
            my @p = $APSP->path_vertices($u, $v);
    foreach(@p)
{
print "$_ ";
}
    print "\n$w";
        }

---

Tips:

Use module Graph for such problems

Quiz 76: Find all continuous substrings of all lengths

Problem:

Given a string, you have to all continuous substrings of different lengths
Ex for abc, print a,ab,abc,b,bc,c

Input Format: 

A String

Output Format: 

Different substrings in each line

Constraints: 
None

Sample Input

perl

Sample Output:

p
pe
per
perl
e
er
erl
r
rl
l

Explanations:

all continuous substrings of length 1 to 4

---

Solution:

use strict;
use warnings;

chomp(my $a=<STDIN>);
for (my $i=0; $i<=length($a);$i++) 
{
for (my $j = $i+1;$j<=length($a);$j++) 
{
        print substr($a, $i, $j - $i) . "\n";
}
}

---

Tips:

Length can give length of string directly

Quiz 75: Change array to have unique elements only

Problem:

Given an array, you have to print another array containing only unique elements ie removing duplicate elements

Input Format: 

Array->Each element separated by space

Output Format: 

Unique Array->Each element separated by space

Constraints: 

None

Sample Input

1 3 4 2 3 5 7 7 7 4 9 0 0 2

Sample Output:

1 3 4 2 5 7 9 0

Explanations:

removed duplicate elements from original array

---

Solution:

use strict;
use warnings;

sub unique {
    my %found;
    grep !$found{$_}++, @_;
}

chomp(my $in=<STDIN>);
my @array = split(" ",$in);
@array = unique(@array);
foreach(@array)
{
print "$_ ";
}

---

Tips:

Learn use of Hash and Grep