Spiral Numbers: Solution¶
Problem setter’s solution: skip leading zeroes and compare opposite digits. Codex (GPT-6) refines boundary handling and implementation and adds arithmetic reversal.
Two pointers¶
Advance the left endpoint past leading zeroes while leaving at least one digit. An all-zero input becomes one zero, and every other input becomes its usual decimal representation. Compare the characters at both endpoints and move inward when they agree. A mismatch immediately means the number is not a palindrome.
The already-checked outer digit pairs are equal, while unchecked digits form a contiguous interval. A mismatch violates the definition. Otherwise, when at most one digit remains, every symmetric pair has been checked. The algorithm therefore recognizes exactly the required palindromes.
Complexity and choice¶
Let \(L\) be the input string length for one case. Time is \(O(L)\) . Storing the input requires \(O(L)\) space, and the additional state uses \(O(1)\) space. Cases are processed sequentially, so total time is the sum of their lengths.
The preferred std.cpp follows the digit definition directly and does not rely on the range of a machine integer. Arithmetic reversal uses a fixed number of integers within this problem's bounds. Both methods support the full input range.