Algorithms: String Algorithms

Algorithms: String Algorithms

Explore algorithms: string algorithms code snippets and tutorials

Algorithms: String Algorithms

Manacher Longest Palindromic Substring in Java

Manacher reuses mirrored palindrome radii to find a longest contiguous palindrome in linear time..

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// Manacher Longest Palindromic Substring in Java
//
// PURPOSE
// Manacher reuses mirrored palindrome radii to find a longest contiguous palindrome in
// linear time.
//
// METHOD
// Compute odd and even center radii in separate passes. Reuse the mirror radius within the
// current rightmost palindrome, then expand only beyond its known boundary.
//
// COMPLEXITY
// O(n) time and O(n) auxiliary space.
//
// CONTRACT
// Integer tokens. Returns longest palindrome LENGTH; empty input returns zero.
// 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
// Java 17+: primitive int arrays, Arrays.binarySearch for LIS, and Math exact arithmetic.
// Invalid input throws IllegalArgumentException; arithmetic overflow throws
// ArithmeticException.
//
// EXAMPLE
// Expected return: 4.
// Run: javac AlgorithmExample.java && java AlgorithmExample
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

class AlgorithmExample {
    static void alg_require(boolean valid) { if (!valid) throw new IllegalArgumentException("invalid algorithm input"); }
    static int alg_size(int n) { alg_require(n>=0 && n<=4000000); return n; }

    static int manacher(int[] a) {
        java.util.Objects.requireNonNull(a, "a");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        int[] radius = new int[alg_size(Math.addExact(n, 1))];
        int parity = 0;
        int left = 0;
        int right = Math.negateExact(1);
        int i = 0;
        int k = 0;
        int best = 0;
        while ((parity < 2)) {
            left = 0;
            right = Math.negateExact(1);
            i = 0;
            while ((i < n)) {
                k = Math.subtractExact(1, parity);
                if ((i <= right)) {
                    k = Math.min(radius[Math.addExact(Math.subtractExact(Math.addExact(left, right), i), parity)], Math.addExact(Math.subtractExact(right, i), 1));
                }
                while (((Math.subtractExact(Math.subtractExact(i, k), parity) >= 0) && (Math.addExact(i, k) < n) && (a[Math.subtractExact(Math.subtractExact(i, k), parity)] == a[Math.addExact(i, k)]))) {
                    k = Math.addExact(k, 1);
                }
                radius[i] = k;
                best = Math.max(best, Math.addExact(Math.subtractExact(Math.multiplyExact(2, k), 1), parity));
                if ((Math.subtractExact(Math.addExact(i, k), 1) > right)) {
                    left = Math.addExact(Math.subtractExact(Math.subtractExact(i, k), parity), 1);
                    right = Math.subtractExact(Math.addExact(i, k), 1);
                }
                i = Math.addExact(i, 1);
            }
            parity = Math.addExact(parity, 1);
        }
        return best;
    }

    public static void main(String[] args) {
        int[] a = new int[] {1, 2, 2, 1};
        int result = manacher(a);
        System.out.println(result);
    }
}
Nov 15, 2026 Java
Algorithms: String Algorithms

Manacher Longest Palindromic Substring in JavaScript

Manacher reuses mirrored palindrome radii to find a longest contiguous palindrome in linear time..

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"use strict";
// Manacher Longest Palindromic Substring in JavaScript
//
// PURPOSE
// Manacher reuses mirrored palindrome radii to find a longest contiguous palindrome in
// linear time.
//
// METHOD
// Compute odd and even center radii in separate passes. Reuse the mirror radius within the
// current rightmost palindrome, then expand only beyond its known boundary.
//
// COMPLEXITY
// O(n) time and O(n) auxiliary space.
//
// CONTRACT
// Integer tokens. Returns longest palindrome LENGTH; empty input returns zero.
// 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
// Node.js 18+: Int32Array inputs and workspaces provide compact integer storage. Automatic
// lengths and checked arithmetic reject values outside signed 32-bit. Invalid inputs or
// overflow throw RangeError.
//
// EXAMPLE
// Expected return: 4.
// Run: node example.js
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

function alg_require(valid) { if (!valid) throw new RangeError("invalid algorithm input"); }
function alg_checked(v) { if (!Number.isInteger(v) || v < -2147483648 || v > 2147483647) throw new RangeError("32-bit result overflow"); return v; }
function alg_add(a,b) { return alg_checked(a+b); }
function alg_sub(a,b) { return alg_checked(a-b); }
function alg_mul(a,b) { return alg_checked(a*b); }
function alg_size(n) { alg_require(Number.isInteger(n) && n>=0 && n<=4000000); return n; }

function manacher(a) {
    alg_require(a instanceof Int32Array);
    let n = a.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((a.length == n));
    let radius = new Int32Array(alg_size(alg_add(n, 1)));
    let parity = 0;
    let left = 0;
    let right = alg_sub(0, 1);
    let i = 0;
    let k = 0;
    let best = 0;
    while ((parity < 2)) {
        left = 0;
        right = alg_sub(0, 1);
        i = 0;
        while ((i < n)) {
            k = alg_sub(1, parity);
            if ((i <= right)) {
                k = Math.min(radius[alg_add(alg_sub(alg_add(left, right), i), parity)], alg_add(alg_sub(right, i), 1));
            }
            while (((alg_sub(alg_sub(i, k), parity) >= 0) && (alg_add(i, k) < n) && (a[alg_sub(alg_sub(i, k), parity)] == a[alg_add(i, k)]))) {
                k = alg_add(k, 1);
            }
            radius[i] = k;
            best = Math.max(best, alg_add(alg_sub(alg_mul(2, k), 1), parity));
            if ((alg_sub(alg_add(i, k), 1) > right)) {
                left = alg_add(alg_sub(alg_sub(i, k), parity), 1);
                right = alg_sub(alg_add(i, k), 1);
            }
            i = alg_add(i, 1);
        }
        parity = alg_add(parity, 1);
    }
    return best;
}

let a = new Int32Array([1, 2, 2, 1]);
let result = manacher(a);
console.log(result);
Nov 15, 2026 javascript
Algorithms: String Algorithms

Manacher Longest Palindromic Substring in Python

Manacher reuses mirrored palindrome radii to find a longest contiguous palindrome in linear time..

python 
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from bisect import bisect_left

# Manacher Longest Palindromic Substring in Python
#
# PURPOSE
# Manacher reuses mirrored palindrome radii to find a longest contiguous palindrome in
# linear time.
#
# METHOD
# Compute odd and even center radii in separate passes. Reuse the mirror radius within the
# current rightmost palindrome, then expand only beyond its known boundary.
#
# COMPLEXITY
# O(n) time and O(n) auxiliary space.
#
# CONTRACT
# Integer tokens. Returns longest palindrome LENGTH; empty input returns zero.
# 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: 4.
# 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 manacher(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)
    radius: list[int] = [0] * alg_size(n + 1)
    parity: int = 0
    left: int = 0
    right: int = -1
    i: int = 0
    k: int = 0
    best: int = 0
    while parity < 2:
        left = 0
        right = -1
        i = 0
        while i < n:
            k = 1 - parity
            if i <= right:
                k = min(radius[left + right - i + parity], right - i + 1)
            while i - k - parity >= 0 and i + k < n and (a[i - k - parity] == a[i + k]):
                k += 1
            radius[i] = k
            best = max(best, 2 * k - 1 + parity)
            if i + k - 1 > right:
                left = i - k - parity + 1
                right = i + k - 1
            i += 1
        parity += 1
    return best

a = [1, 2, 2, 1]
result = manacher(a)
print(result)
Nov 15, 2026 python
Algorithms: String Algorithms

Manacher Longest Palindromic Substring in C

Manacher reuses mirrored palindrome radii to find a longest contiguous palindrome in linear time..

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#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <limits.h>
#include <errno.h>
// Manacher Longest Palindromic Substring in C
//
// PURPOSE
// Manacher reuses mirrored palindrome radii to find a longest contiguous palindrome in
// linear time.
//
// METHOD
// Compute odd and even center radii in separate passes. Reuse the mirror radius within the
// current rightmost palindrome, then expand only beyond its known boundary.
//
// COMPLEXITY
// O(n) time and O(n) auxiliary space.
//
// CONTRACT
// Integer tokens. Returns longest palindrome LENGTH; empty input returns zero.
// 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
// C99: checked calloc/free workspace, const input pointers, explicit size_t lengths. Errors
// return INT_MIN with errno=EINVAL, ERANGE, or ENOMEM. Check errno before using a result.
// Input/output arrays must not alias. No variable-length stack arrays.
//
// EXAMPLE
// Expected return: 4.
// Run: gcc -std=c99 -O2 example.c -o example && ./example
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

static int alg_min(int a, int b) { return a < b ? a : b; }
static int alg_max(int a, int b) { return a > b ? a : b; }
static int alg_checked(int64_t v, int *error) {
    if (v < INT_MIN || v > INT_MAX) { *error = 1; return 0; }
    return (int)v;
}
static int alg_add(int a, int b, int *e) { return alg_checked((int64_t)a+b,e); }
static int alg_sub(int a, int b, int *e) { return alg_checked((int64_t)a-b,e); }
static int alg_mul(int a, int b, int *e) { return alg_checked((int64_t)a*b,e); }

int manacher(const int *a, size_t a_length) {
    int alg_error = 0;
    int alg_result = INT_MIN;
    errno = 0;
    int *radius = NULL;
    if (a_length > 1000000 || (a_length && !a)) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    int n = (int)a_length;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    if (!(((n >= 0) && (n <= 1000000)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    if (!(((int)a_length == n))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    {
        int alg_length = alg_add(n, 1, &alg_error);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_length < 0 || alg_length > 4000000) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
        radius = calloc((size_t)(alg_length ? alg_length : 1), sizeof(*radius));
        if (!radius) { errno = ENOMEM; alg_result = INT_MIN; goto alg_cleanup; }
    }
    int parity = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int left = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int right = alg_sub(0, 1, &alg_error);
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int i = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int k = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int best = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    while (1) {
        int alg_condition = (parity < 2);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (!alg_condition) break;
        left = 0;
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        right = alg_sub(0, 1, &alg_error);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        i = 0;
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        while (1) {
            int alg_condition = (i < n);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            if (!alg_condition) break;
            k = alg_sub(1, parity, &alg_error);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            int alg_condition_1 = (i <= right);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            if (alg_condition_1) {
                k = alg_min(radius[alg_add(alg_sub(alg_add(left, right, &alg_error), i, &alg_error), parity, &alg_error)], alg_add(alg_sub(right, i, &alg_error), 1, &alg_error));
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            }
            while (1) {
                int alg_condition = ((alg_sub(alg_sub(i, k, &alg_error), parity, &alg_error) >= 0) && (alg_add(i, k, &alg_error) < n) && (a[alg_sub(alg_sub(i, k, &alg_error), parity, &alg_error)] == a[alg_add(i, k, &alg_error)]));
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                if (!alg_condition) break;
                k = alg_add(k, 1, &alg_error);
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            }
            radius[i] = k;
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            best = alg_max(best, alg_add(alg_sub(alg_mul(2, k, &alg_error), 1, &alg_error), parity, &alg_error));
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            int alg_condition_2 = (alg_sub(alg_add(i, k, &alg_error), 1, &alg_error) > right);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            if (alg_condition_2) {
                left = alg_add(alg_sub(alg_sub(i, k, &alg_error), parity, &alg_error), 1, &alg_error);
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                right = alg_sub(alg_add(i, k, &alg_error), 1, &alg_error);
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            }
            i = alg_add(i, 1, &alg_error);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        }
        parity = alg_add(parity, 1, &alg_error);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    }
    alg_result = best;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    goto alg_cleanup;
alg_cleanup:
    free(radius);
    return alg_result;
}

int main(void) {
    int a[] = {1, 2, 2, 1};
    int result = manacher(a, 4);
    printf("%d\n", result);
    if (errno) { perror("algorithm"); return 1; }
    return 0;
}
Nov 15, 2026 C
Algorithms: String Algorithms

Manacher Longest Palindromic Substring in C++

Manacher reuses mirrored palindrome radii to find a longest contiguous palindrome in linear time..

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#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Manacher Longest Palindromic Substring in C++
//
// PURPOSE
// Manacher reuses mirrored palindrome radii to find a longest contiguous palindrome in
// linear time.
//
// METHOD
// Compute odd and even center radii in separate passes. Reuse the mirror radius within the
// current rightmost palindrome, then expand only beyond its known boundary.
//
// COMPLEXITY
// O(n) time and O(n) auxiliary space.
//
// CONTRACT
// Integer tokens. Returns longest palindrome LENGTH; empty input returns zero.
// 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
// C++17: const vector references for inputs, mutable references for outputs, RAII workspace,
// standard lower_bound for LIS. Invalid inputs throw invalid_argument; overflow throws
// overflow_error; allocation failure propagates bad_alloc.
//
// EXAMPLE
// Expected return: 4.
// Run: g++ -std=c++17 -O2 example.cpp -o example && ./example
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

static int alg_min(int a, int b) { return a < b ? a : b; }
static int alg_max(int a, int b) { return a > b ? a : b; }
static void alg_require(bool valid) { if (!valid) throw std::invalid_argument("invalid algorithm input"); }
static int alg_checked(int64_t v) { if (v < INT32_MIN || v > INT32_MAX) throw std::overflow_error("32-bit result overflow"); return (int)v; }
static int alg_add(int a,int b) { return alg_checked((int64_t)a+b); }
static int alg_sub(int a,int b) { return alg_checked((int64_t)a-b); }
static int alg_mul(int a,int b) { return alg_checked((int64_t)a*b); }
static size_t alg_size(int n) { alg_require(n>=0 && n<=4000000); return (size_t)n; }

int manacher(const std::vector<int>& a) {
    alg_require(a.size() <= 1000000);
    int n = (int)a.size();
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((int)a.size() == n));
    std::vector<int> radius(alg_size(alg_add(n, 1)), 0);
    int parity = 0;
    int left = 0;
    int right = alg_sub(0, 1);
    int i = 0;
    int k = 0;
    int best = 0;
    while ((parity < 2)) {
        left = 0;
        right = alg_sub(0, 1);
        i = 0;
        while ((i < n)) {
            k = alg_sub(1, parity);
            if ((i <= right)) {
                k = alg_min(radius[alg_add(alg_sub(alg_add(left, right), i), parity)], alg_add(alg_sub(right, i), 1));
            }
            while (((alg_sub(alg_sub(i, k), parity) >= 0) && (alg_add(i, k) < n) && (a[alg_sub(alg_sub(i, k), parity)] == a[alg_add(i, k)]))) {
                k = alg_add(k, 1);
            }
            radius[i] = k;
            best = alg_max(best, alg_add(alg_sub(alg_mul(2, k), 1), parity));
            if ((alg_sub(alg_add(i, k), 1) > right)) {
                left = alg_add(alg_sub(alg_sub(i, k), parity), 1);
                right = alg_sub(alg_add(i, k), 1);
            }
            i = alg_add(i, 1);
        }
        parity = alg_add(parity, 1);
    }
    return best;
}

int main(void) {
    std::vector<int> a = {1, 2, 2, 1};
    int result = manacher(a);
    printf("%d\n", result);
    return 0;
}
Nov 15, 2026 C++