A palindrome reads the same in both directions.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 | from bisect import bisect_left # Two Pointer Palindrome Check in Python # # PURPOSE # A palindrome reads the same in both directions. Symmetric comparisons detect the first # disagreement without reversing or copying the sequence. # # METHOD # Compare the two ends, reject on a mismatch, and move inward after a match. Passing every # symmetric pair proves the sequence is a palindrome. # # COMPLEXITY # O(n) time and O(1) auxiliary space. # # CONTRACT # Input is an integer sequence, so token and character encoding are outside this example. # Returns 1 or 0; empty input is a palindrome. # Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex # counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers. # Sorted order, correct tree topology, and caller-owned data-structure invariants are # preconditions; checking them on every query would change query complexity. # Scalar and shape checks are included. Value-range checks are included where needed to # prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000 # workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python # uses arbitrary precision. Native allocation failures propagate. In-place outputs may be # partly updated after arithmetic failure. These are single-threaded, in-memory # implementations. # # LANGUAGE DETAILS # Python 3.9+: automatic lengths, native lists, arbitrary-precision arithmetic, and # bisect_left for LIS. Invalid scalar/shape inputs raise ValueError. Integer element types # and sorted/tree invariants remain caller preconditions. # # EXAMPLE # Expected return: 1. # Run: python example.py # Tests for this exact source artifact run before publication. The accompanying source # archive includes unit cases, runtime results, and source hashes. def alg_require(condition): if not condition: raise ValueError("invalid algorithm input; see contract") def alg_size(n): alg_require(0 <= n <= 4000000) return n def is_palindrome(a: list[int]) -> int: alg_require(isinstance(a, (list, tuple)) and len(a) <= 1000000) n: int = len(a) alg_require(n >= 0 and n <= 1000000) alg_require(len(a) == n) left: int = 0 right: int = n - 1 while left < right: if a[left] != a[right]: return 0 left += 1 right -= 1 return 1 a = [1, 2, 1] result = is_palindrome(a) print(result) |