Algorithms: Sorting

Algorithms: Sorting

Explore algorithms: sorting code snippets and tutorials

Algorithms: Sorting

LSD Radix Sort in Java

LSD radix sort orders bounded nonnegative integers one byte at a time using stable counting passes..

java 
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// LSD Radix Sort in Java
//
// PURPOSE
// LSD radix sort orders bounded nonnegative integers one byte at a time using stable
// counting passes.
//
// METHOD
// For each of four base-256 digits, count occurrences, compute cumulative positions, then
// distribute from right to left to preserve stability.
//
// COMPLEXITY
// O(4(n+256)) time and O(n+256) auxiliary space for 32-bit keys. Stable.
//
// CONTRACT
// Keys are nonnegative signed 32-bit integers. Sorts ascending in place, returns 0.
// 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: 0.
// Expected a after call: [0, 1, 255, 256, 65536].
// 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 radix_sort(int[] a) {
        java.util.Objects.requireNonNull(a, "a");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        for (int alg_i = 0; alg_i < a.length; alg_i++) {
            int alg_value = a[alg_i];
            alg_require((alg_value >= 0));
        }
        int[] output = new int[alg_size(Math.addExact(n, 1))];
        int[] count = new int[alg_size(256)];
        int divisor = 1;
        int digit = 0;
        int pass_index = 0;
        int i = 0;
        while ((pass_index < 4)) {
            i = 0;
            while ((i < 256)) {
                count[i] = 0;
                i = Math.addExact(i, 1);
            }
            i = 0;
            while ((i < n)) {
                digit = ((a[i] / divisor) % 256);
                count[digit] = Math.addExact(count[digit], 1);
                i = Math.addExact(i, 1);
            }
            i = 1;
            while ((i < 256)) {
                count[i] = Math.addExact(count[i], count[Math.subtractExact(i, 1)]);
                i = Math.addExact(i, 1);
            }
            i = Math.subtractExact(n, 1);
            while ((i >= 0)) {
                digit = ((a[i] / divisor) % 256);
                count[digit] = Math.subtractExact(count[digit], 1);
                output[count[digit]] = a[i];
                i = Math.subtractExact(i, 1);
            }
            i = 0;
            while ((i < n)) {
                a[i] = output[i];
                i = Math.addExact(i, 1);
            }
            pass_index = Math.addExact(pass_index, 1);
            if ((pass_index < 4)) {
                divisor = Math.multiplyExact(divisor, 256);
            }
        }
        return 0;
    }

    public static void main(String[] args) {
        int[] a = new int[] {256, 1, 65536, 0, 255};
        int result = radix_sort(a);
        System.out.println(result);
        // Expected a: [0, 1, 255, 256, 65536]
        System.out.println(java.util.Arrays.toString(a));
    }
}
Nov 15, 2026 Java
Algorithms: Sorting

LSD Radix Sort in JavaScript

LSD radix sort orders bounded nonnegative integers one byte at a time using stable counting passes..

javascript 
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"use strict";
// LSD Radix Sort in JavaScript
//
// PURPOSE
// LSD radix sort orders bounded nonnegative integers one byte at a time using stable
// counting passes.
//
// METHOD
// For each of four base-256 digits, count occurrences, compute cumulative positions, then
// distribute from right to left to preserve stability.
//
// COMPLEXITY
// O(4(n+256)) time and O(n+256) auxiliary space for 32-bit keys. Stable.
//
// CONTRACT
// Keys are nonnegative signed 32-bit integers. Sorts ascending in place, returns 0.
// 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: 0.
// Expected a after call: [0, 1, 255, 256, 65536].
// 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 radix_sort(a) {
    alg_require(a instanceof Int32Array);
    let n = a.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((a.length == n));
    for (let alg_i = 0; alg_i < a.length; alg_i++) {
        let alg_value = a[alg_i];
        alg_require((alg_value >= 0));
    }
    let output = new Int32Array(alg_size(alg_add(n, 1)));
    let count = new Int32Array(alg_size(256));
    let divisor = 1;
    let digit = 0;
    let pass_index = 0;
    let i = 0;
    while ((pass_index < 4)) {
        i = 0;
        while ((i < 256)) {
            count[i] = 0;
            i = alg_add(i, 1);
        }
        i = 0;
        while ((i < n)) {
            digit = (Math.floor(a[i] / divisor) % 256);
            count[digit] = alg_add(count[digit], 1);
            i = alg_add(i, 1);
        }
        i = 1;
        while ((i < 256)) {
            count[i] = alg_add(count[i], count[alg_sub(i, 1)]);
            i = alg_add(i, 1);
        }
        i = alg_sub(n, 1);
        while ((i >= 0)) {
            digit = (Math.floor(a[i] / divisor) % 256);
            count[digit] = alg_sub(count[digit], 1);
            output[count[digit]] = a[i];
            i = alg_sub(i, 1);
        }
        i = 0;
        while ((i < n)) {
            a[i] = output[i];
            i = alg_add(i, 1);
        }
        pass_index = alg_add(pass_index, 1);
        if ((pass_index < 4)) {
            divisor = alg_mul(divisor, 256);
        }
    }
    return 0;
}

let a = new Int32Array([256, 1, 65536, 0, 255]);
let result = radix_sort(a);
console.log(result);
// Expected a: [0, 1, 255, 256, 65536]
console.log(Array.from(a));
Nov 15, 2026 javascript
Algorithms: Sorting

LSD Radix Sort in Python

LSD radix sort orders bounded nonnegative integers one byte at a time using stable counting passes..

python 
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from bisect import bisect_left

# LSD Radix Sort in Python
#
# PURPOSE
# LSD radix sort orders bounded nonnegative integers one byte at a time using stable
# counting passes.
#
# METHOD
# For each of four base-256 digits, count occurrences, compute cumulative positions, then
# distribute from right to left to preserve stability.
#
# COMPLEXITY
# O(4(n+256)) time and O(n+256) auxiliary space for 32-bit keys. Stable.
#
# CONTRACT
# Keys are nonnegative signed 32-bit integers. Sorts ascending in place, returns 0.
# 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: 0.
# Expected a after call: [0, 1, 255, 256, 65536].
# 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 radix_sort(a: list[int]) -> int:
    alg_require(isinstance(a, list) and len(a) <= 1000000)
    n: int = len(a)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(a) == n)
    for value in a:
        alg_require(value >= 0)
    output: list[int] = [0] * alg_size(n + 1)
    count: list[int] = [0] * alg_size(256)
    divisor: int = 1
    digit: int = 0
    pass_index: int = 0
    i: int = 0
    while pass_index < 4:
        i = 0
        while i < 256:
            count[i] = 0
            i += 1
        i = 0
        while i < n:
            digit = a[i] // divisor % 256
            count[digit] += 1
            i += 1
        i = 1
        while i < 256:
            count[i] += count[i - 1]
            i += 1
        i = n - 1
        while i >= 0:
            digit = a[i] // divisor % 256
            count[digit] -= 1
            output[count[digit]] = a[i]
            i -= 1
        i = 0
        while i < n:
            a[i] = output[i]
            i += 1
        pass_index += 1
        if pass_index < 4:
            divisor *= 256
    return 0

a = [256, 1, 65536, 0, 255]
result = radix_sort(a)
print(result)
# Expected a: [0, 1, 255, 256, 65536]
print(a)
Nov 15, 2026 python
Algorithms: Sorting

LSD Radix Sort in C

LSD radix sort orders bounded nonnegative integers one byte at a time using stable counting passes..

c 
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#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <limits.h>
#include <errno.h>
// LSD Radix Sort in C
//
// PURPOSE
// LSD radix sort orders bounded nonnegative integers one byte at a time using stable
// counting passes.
//
// METHOD
// For each of four base-256 digits, count occurrences, compute cumulative positions, then
// distribute from right to left to preserve stability.
//
// COMPLEXITY
// O(4(n+256)) time and O(n+256) auxiliary space for 32-bit keys. Stable.
//
// CONTRACT
// Keys are nonnegative signed 32-bit integers. Sorts ascending in place, returns 0.
// 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: 0.
// Expected a after call: [0, 1, 255, 256, 65536].
// 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 radix_sort(int *a, size_t a_length) {
    int alg_error = 0;
    int alg_result = INT_MIN;
    errno = 0;
    int *output = NULL;
    int *count = 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; }
    for (int alg_i = 0; alg_i < (int)a_length; alg_i++) {
        int alg_value = a[alg_i];
        if (!((alg_value >= 0))) { 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; }
        output = calloc((size_t)(alg_length ? alg_length : 1), sizeof(*output));
        if (!output) { errno = ENOMEM; alg_result = INT_MIN; goto alg_cleanup; }
    }
    {
        int alg_length = 256;
        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; }
        count = calloc((size_t)(alg_length ? alg_length : 1), sizeof(*count));
        if (!count) { errno = ENOMEM; alg_result = INT_MIN; goto alg_cleanup; }
    }
    int divisor = 1;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int digit = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int pass_index = 0;
    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; }
    while (1) {
        int alg_condition = (pass_index < 4);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (!alg_condition) break;
        i = 0;
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        while (1) {
            int alg_condition = (i < 256);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            if (!alg_condition) break;
            count[i] = 0;
            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; }
        }
        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;
            digit = ((a[i] / divisor) % 256);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            count[digit] = alg_add(count[digit], 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; }
        }
        i = 1;
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        while (1) {
            int alg_condition = (i < 256);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            if (!alg_condition) break;
            count[i] = alg_add(count[i], count[alg_sub(i, 1, &alg_error)], &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; }
        }
        i = alg_sub(n, 1, &alg_error);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        while (1) {
            int alg_condition = (i >= 0);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            if (!alg_condition) break;
            digit = ((a[i] / divisor) % 256);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            count[digit] = alg_sub(count[digit], 1, &alg_error);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            output[count[digit]] = a[i];
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            i = alg_sub(i, 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;
            a[i] = output[i];
            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; }
        }
        pass_index = alg_add(pass_index, 1, &alg_error);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        int alg_condition_1 = (pass_index < 4);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_condition_1) {
            divisor = alg_mul(divisor, 256, &alg_error);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        }
    }
    alg_result = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    goto alg_cleanup;
alg_cleanup:
    free(output);
    free(count);
    return alg_result;
}

int main(void) {
    int a[] = {256, 1, 65536, 0, 255};
    int result = radix_sort(a, 5);
    printf("%d\n", result);
    // Expected a: [0, 1, 255, 256, 65536]
    for (int alg_print = 0; alg_print < 5; alg_print++) printf("%d ", a[alg_print]);
    printf("\n");
    if (errno) { perror("algorithm"); return 1; }
    return 0;
}
Nov 15, 2026 C
Algorithms: Sorting

LSD Radix Sort in C++

LSD radix sort orders bounded nonnegative integers one byte at a time using stable counting passes..

cpp 
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#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// LSD Radix Sort in C++
//
// PURPOSE
// LSD radix sort orders bounded nonnegative integers one byte at a time using stable
// counting passes.
//
// METHOD
// For each of four base-256 digits, count occurrences, compute cumulative positions, then
// distribute from right to left to preserve stability.
//
// COMPLEXITY
// O(4(n+256)) time and O(n+256) auxiliary space for 32-bit keys. Stable.
//
// CONTRACT
// Keys are nonnegative signed 32-bit integers. Sorts ascending in place, returns 0.
// 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: 0.
// Expected a after call: [0, 1, 255, 256, 65536].
// 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 radix_sort(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));
    for (int alg_i = 0; alg_i < (int)a.size(); alg_i++) {
        int alg_value = a[alg_i];
        alg_require((alg_value >= 0));
    }
    std::vector<int> output(alg_size(alg_add(n, 1)), 0);
    std::vector<int> count(alg_size(256), 0);
    int divisor = 1;
    int digit = 0;
    int pass_index = 0;
    int i = 0;
    while ((pass_index < 4)) {
        i = 0;
        while ((i < 256)) {
            count[i] = 0;
            i = alg_add(i, 1);
        }
        i = 0;
        while ((i < n)) {
            digit = ((a[i] / divisor) % 256);
            count[digit] = alg_add(count[digit], 1);
            i = alg_add(i, 1);
        }
        i = 1;
        while ((i < 256)) {
            count[i] = alg_add(count[i], count[alg_sub(i, 1)]);
            i = alg_add(i, 1);
        }
        i = alg_sub(n, 1);
        while ((i >= 0)) {
            digit = ((a[i] / divisor) % 256);
            count[digit] = alg_sub(count[digit], 1);
            output[count[digit]] = a[i];
            i = alg_sub(i, 1);
        }
        i = 0;
        while ((i < n)) {
            a[i] = output[i];
            i = alg_add(i, 1);
        }
        pass_index = alg_add(pass_index, 1);
        if ((pass_index < 4)) {
            divisor = alg_mul(divisor, 256);
        }
    }
    return 0;
}

int main(void) {
    std::vector<int> a = {256, 1, 65536, 0, 255};
    int result = radix_sort(a);
    printf("%d\n", result);
    // Expected a: [0, 1, 255, 256, 65536]
    for (int alg_print = 0; alg_print < 5; alg_print++) printf("%d ", a[alg_print]);
    printf("\n");
    return 0;
}
Nov 15, 2026 C++