PHP Program to Check Whether All Rotations of a Given Number is Greater than or Equal to the Given Number or Not

Given an integer x, the task is to find if every k-cycle shift on the element produces a number greater than or equal to the same element. 

A k-cyclic shift of an integer x is a function that removes the last k digits of x and inserts them in its beginning. For example, the k-cyclic shifts of 123 are 312 for k=1 and 231 for k=2. Print Yes if the given condition is satisfied else print No.

Examples: 

Input: x = 123 
Output : Yes 
Explanations: The k-cyclic shifts of 123 are 312 for k = 1 and 231 for k = 2. 
Both 312 and 231 are greater than 123.

Input: 2214 
Output: No 
Explanations: The k-cyclic shift of 2214 when k = 2 is 1422 which is smaller than 2214 

Simple Approach

Find all the possible k-cyclic shifts of the number and check if all are greater than the given number or not.

Below is the implementation of the above approach:

<?php
// PHP program to implement above approach

function CheckKCycles($n, $s) {
    $ff = true;
    $x = 0;
    for ($i = 1; $i < $n; $i++) {

        // Splitting the number at index i 
        // and adding to the front 
        $x = strlen(substr($s, $i).substr($s, 0, $i));

        // Checking if the value is greater than 
        // or equal to the given value 
        if ($x >= strlen($s)) {
            continue;
        }
        $ff = false;
        break;
    }
    if ($ff) {
        print("Yes");
    }
    else {
        print("No");
    }
}

// Driver code
$n = 3;
$s = "123";

CheckKCycles($n, $s);

?>

Yes

Time Complexity: O(N²), where N is the length of the given string. First it runs a loop for traversing the string and inside that substring function is used. So, the code will run in O(N²) time.

Auxiliary Space: O(1), no extra space required, so it is a constant.

Please refer complete article on Check whether all the rotations of a given number is greater than or equal to the given number or not for more details!