PHP Exercises: Create maximum number of regions obtained by drawing n given straight lines

PHP: Exercise-67 with Solution

If you draw a straight line on a plane, the plane is divided into two regions. For example, if you pull two straight lines in parallel, you get three areas, and if you draw vertically one to the other you get 4 areas.
Write a PHP program to create maximum number of regions obtained by drawing n given straight lines.

Input: (1 ≤ n ≤ 10,000)

Sample Solution:

PHP Code:

<?php
// Read input from standard input until an empty line is encountered
while (($line = trim(fgets(STDIN))) !== '') {
    // Convert the input to an integer
    $n = (int)$line;
    
    // Initialize the result with the minimum number of regions (2)
    $result = 2;

    // Calculate the maximum number of regions based on the formula
    for ($i = 2; $i <= $n; $i++) {
        $result += $i;
    }

    // Output the result
    echo 'Maximum number of regions: ';
    echo $result, PHP_EOL;
}

?>

Explanation:

• Input Loop:
• The code reads input continuously from standard input until an empty line is encountered.
• Convert Input to Integer:
• Each line of input is trimmed and converted to an integer, stored in variable $n.
• Initialize Result:
• The variable $result is initialized to 2, representing the minimum possible regions (with 0 or 1 cuts).
• Calculate Maximum Regions:
• A for loop iterates from 2 up to $n. For each value of $i, $result is incremented by i.
• This cumulative addition represents the number of regions formed when making n straight-line cuts in a plane.
• Output the Result:
• The code outputs the total maximum number of regions, prefixed with "Maximum number of regions:", followed by a newline.

Sample Input:
5

Sample Output:

Maximum number of regions: 16

Flowchart:

PHP Code Editor:

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