## Algorithm

Problem Name: Mathematics - Restaurant

In this HackerRank in Mathematics - Restaurant solutions,

Martha is interviewing at Subway. One of the rounds of the interview requires her to cut a bread of size l * b into smaller identical pieces such that each piece is a square having maximum possible side length with no left over piece of bread.

Input Format

The first line contains an integer T.T lines follow. Each line contains two space separated integers l and b which denote length and breadth of the bread.

Constraints

• 1 <= T <= 1000
• 1 <= l,b <= 1000

Output Format

T lines, each containing an integer that denotes the number of squares of maximum size, when the bread is cut as per the given condition.

Sample Input 0

```2
2 2
6 9
```

Sample Output 0

```1
6
```

Explanation 0

The 1st testcase has a bread whose original dimensions are 2 * 2 , the bread is uncut and is a square. Hence the answer is 1.
The 2nd testcase has a bread of size 6 * 9 . We can cut it into 54 squares of size 1 * 1 , 6 of size 3 * 3 . For other sizes we will have leftovers. Hence, the number of squares of maximum size that can be cut is 6.

## Code Examples

### #1 Code Example with C Programming

```Code - C Programming```

``````
#include <stdio.h>
#include <string.h>
#include <math.h>
#include <stdlib.h>

int gcd ( int a, int b )
{
int c;
while ( a != 0 ) {
c = a; a = b%a;  b = c;
}
return b;
}

int main(){
int testcases;
scanf("%d", &testcases);
int i;
for(i = 0; i  <  testcases; i++){
int l;
int b;
scanf("%d %d", &l, &b);
printf("%d\n", (l/gcd(l,b)*b/gcd(l,b)));
}
return 0;
}

``````
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### #2 Code Example with C++ Programming

```Code - C++ Programming```

``````
#include <bits/stdc++.h>

using namespace std;

string ltrim(const string &);
string rtrim(const string &);
vector < string> split(const string &);

/*
* Complete the 'restaurant' function below.
*
* The function is expected to return an INTEGER.
* The function accepts following parameters:
*  1. INTEGER l
*  2. INTEGER b
*/

int gcd(int a, int b)
{
if(a == 0)
return b;
else
return gcd(b % a, a);
}
int restaurant(int l, int b) {
int area = l * b;
int bread = area / (gcd(l, b) * gcd(l, b));
}

int main()
{
ofstream fout(getenv("OUTPUT_PATH"));

string t_temp;
getline(cin, t_temp);

int t = stoi(ltrim(rtrim(t_temp)));

for (int t_itr = 0; t_itr < t; t_itr++) {
string first_multiple_input_temp;
getline(cin, first_multiple_input_temp>;

vector < string> first_multiple_input = split(rtrim(first_multiple_input_temp));

int l = stoi(first_multiple_input[0]);

int b = stoi(first_multiple_input[1]);

int result = restaurant(l, b);

fout << result << "\n";
}

fout.close();

return 0;
}

string ltrim(const string &str) {
string s(str);

s.erase(
s.begin(),
find_if(s.begin(), s.end(), not1(ptr_fun < int, int>(isspace)))
);

return s;
}

string rtrim(const string &str) {
string s(str);

s.erase(
find_if(s.rbegin(), s.rend(), not1(ptr_fun < int, int>(isspace))).base(),
s.end()
);

return s;
}

vector < string> split(const string &str) {
vector<string> tokens;

string::size_type start = 0;
string::size_type end = 0;

while ((end = str.find(" ", start)) != string::npos) {
tokens.push_back(str.substr(start, end - start));

start = end + 1;
}

tokens.push_back(str.substr(start));

}
``````
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### #3 Code Example with Java Programming

```Code - Java Programming```

``````
import java.io.*;
import java.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.function.*;
import java.util.regex.*;
import java.util.stream.*;
import static java.util.stream.Collectors.joining;
import static java.util.stream.Collectors.toList;

class Result {

/*
* Complete the 'restaurant' function below.
*
* The function is expected to return an INTEGER.
* The function accepts following parameters:
*  1. INTEGER l
*  2. INTEGER b
*/

public static int restaurant(int l, int b) {
for(int i=2;i < =Math.min(l,b);i++){
if(l==1||b==1)break;
if(l%i==0&&b%i==0){
l/=i; b/=i;
i--;
}
}
return l*b;
}

}

public class Solution {
public static void main(String[] args) throws IOException {
BufferedWriter bufferedWriter = new BufferedWriter(new FileWriter(System.getenv("OUTPUT_PATH")));

IntStream.range(0, t).forEach(tItr -> {
try {

int l = Integer.parseInt(firstMultipleInput[0]);

int b = Integer.parseInt(firstMultipleInput[1]);

int result = Result.restaurant(l, b);

bufferedWriter.write(String.valueOf(result));
bufferedWriter.newLine();
} catch (IOException ex) {
throw new RuntimeException(ex);
}
});

bufferedWriter.close();
}
}
``````
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### #4 Code Example with Python Programming

```Code - Python Programming```

``````
#!/bin/python3

import math
import os
import random
import re
import sys

#
# Complete the 'restaurant' function below.
#
# The function is expected to return an INTEGER.
# The function accepts following parameters:
#  1. INTEGER l
#  2. INTEGER b
#

def restaurant(l, b):
tot = l * b
m = min(l, b)
pl = []
i = 1
mid = m // i
while mid > 1:
if m % mid == 0:
pl.append(mid)
i += 1
while mid == m // i:
i += 1
mid = m // i
for i in pl:
if l % i == 0 and b % i == 0:
x = i ** 2
if tot % x == 0:

if __name__ == '__main__':
fptr = open(os.environ['OUTPUT_PATH'], 'w')

t = int(input().strip())

for t_itr in range(t):
first_multiple_input = input().rstrip().split()

l = int(first_multiple_input[0])

b = int(first_multiple_input[1])

result = restaurant(l, b)

fptr.write(str(result) + '\n')

fptr.close()

``````
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