Algorithms: Array Techniques

from bisect import bisect_left

# Dutch National Flag Partition in Python
#
# PURPOSE
# Three-way partition groups zeros, ones, and twos in one pass. The same idea is useful for
# grouping values around a pivot.
#
# METHOD
# Keep a zero prefix, a one middle, an unknown interval, and a two suffix. Swap a zero left,
# advance past a one, or swap a two right and re-examine the incoming unknown value.
#
# COMPLEXITY
# O(n) time and O(1) auxiliary space. Not stable.
#
# CONTRACT
# Every value must be 0, 1, or 2. Mutates the array into sorted order and 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, 0, 1, 2, 2].
# 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 dutch_flag(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 and value <= 2)
    low: int = 0
    mid: int = 0
    high: int = n - 1
    temp: int = 0
    while mid <= high:
        if a[mid] == 0:
            temp = a[low]
            a[low] = a[mid]
            a[mid] = temp
            low += 1
            mid += 1
        elif a[mid] == 1:
            mid += 1
        else:
            temp = a[mid]
            a[mid] = a[high]
            a[high] = temp
            high -= 1
    return 0

a = [2, 0, 1, 2, 0]
result = dutch_flag(a)
print(result)
print(a)
# Expected a: [0, 0, 1, 2, 2]

"use strict";
// Dutch National Flag Partition in JavaScript
//
// PURPOSE
// Three-way partition groups zeros, ones, and twos in one pass. The same idea is useful for
// grouping values around a pivot.
//
// METHOD
// Keep a zero prefix, a one middle, an unknown interval, and a two suffix. Swap a zero left,
// advance past a one, or swap a two right and re-examine the incoming unknown value.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space. Not stable.
//
// CONTRACT
// Every value must be 0, 1, or 2. Mutates the array into sorted order and 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, 0, 1, 2, 2].
// 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 dutch_flag(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) && (alg_value <= 2)));
    }
    let low = 0;
    let mid = 0;
    let high = alg_sub(n, 1);
    let temp = 0;
    while ((mid <= high)) {
        if ((a[mid] == 0)) {
            temp = a[low];
            a[low] = a[mid];
            a[mid] = temp;
            low = alg_add(low, 1);
            mid = alg_add(mid, 1);
        } else {
            if ((a[mid] == 1)) {
                mid = alg_add(mid, 1);
            } else {
                temp = a[mid];
                a[mid] = a[high];
                a[high] = temp;
                high = alg_sub(high, 1);
            }
        }
    }
    return 0;
}

let a = new Int32Array([2, 0, 1, 2, 0]);
let result = dutch_flag(a);
console.log(result);
console.log(a);
// Expected a: [0, 0, 1, 2, 2]

// Dutch National Flag Partition in Java
//
// PURPOSE
// Three-way partition groups zeros, ones, and twos in one pass. The same idea is useful for
// grouping values around a pivot.
//
// METHOD
// Keep a zero prefix, a one middle, an unknown interval, and a two suffix. Swap a zero left,
// advance past a one, or swap a two right and re-examine the incoming unknown value.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space. Not stable.
//
// CONTRACT
// Every value must be 0, 1, or 2. Mutates the array into sorted order and 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, 0, 1, 2, 2].
// 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 dutch_flag(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) && (alg_value <= 2)));
        }
        int low = 0;
        int mid = 0;
        int high = Math.subtractExact(n, 1);
        int temp = 0;
        while ((mid <= high)) {
            if ((a[mid] == 0)) {
                temp = a[low];
                a[low] = a[mid];
                a[mid] = temp;
                low = Math.addExact(low, 1);
                mid = Math.addExact(mid, 1);
            } else {
                if ((a[mid] == 1)) {
                    mid = Math.addExact(mid, 1);
                } else {
                    temp = a[mid];
                    a[mid] = a[high];
                    a[high] = temp;
                    high = Math.subtractExact(high, 1);
                }
            }
        }
        return 0;
    }

    public static void main(String[] args) {
        int[] a = new int[] {2, 0, 1, 2, 0};
        int result = dutch_flag(a);
        System.out.println(result);
        System.out.println(java.util.Arrays.toString(a));
        // Expected a: [0, 0, 1, 2, 2]
    }
}