Algorithms: Range Queries

#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <limits.h>
#include <errno.h>
// Iterative Segment Tree Point Assignment in C
//
// PURPOSE
// A point assignment changes a leaf and recomputes only its ancestors.
//
// METHOD
// Write the new leaf value, move upward by dividing the index by two, and recompute each
// parent from its children.
//
// COMPLEXITY
// O(log n) time, O(1) auxiliary space.
//
// CONTRACT
// tree is an existing iterative sum tree of length 2*n; n>=1, 0<=index<n. Mutates tree;
// 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 tree after call: [0, 17, 10, 7, 1, 9, 3, 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 segment_set(int *tree, size_t tree_length, int index, int value) {
    int alg_error = 0;
    int alg_result = INT_MIN;
    errno = 0;
    if (tree_length > 1000000 || (tree_length && !tree)) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    int n = ((int)tree_length / 2);
    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)tree_length == alg_mul(2, n, &alg_error)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    if (!(((n >= 1) && (index >= 0) && (index < n)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    index = alg_add(index, n, &alg_error);
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    tree[index] = value;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    index = (index / 2);
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    while (1) {
        int alg_condition = (index > 0);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (!alg_condition) break;
        tree[index] = alg_add(tree[alg_mul(2, index, &alg_error)], tree[alg_add(alg_mul(2, index, &alg_error), 1, &alg_error)], &alg_error);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        index = (index / 2);
        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:
    return alg_result;
}

int main(void) {
    int tree[] = {0, 10, 3, 7, 1, 2, 3, 4};
    int index = 1;
    int value = 9;
    int result = segment_set(tree, 8, index, value);
    printf("%d\n", result);
    // Expected tree: [0, 17, 10, 7, 1, 9, 3, 4]
    for (int alg_print = 0; alg_print < 8; alg_print++) printf("%d ", tree[alg_print]);
    printf("\n");
    if (errno) { perror("algorithm"); return 1; }
    return 0;
}

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Iterative Segment Tree Point Assignment in C++
//
// PURPOSE
// A point assignment changes a leaf and recomputes only its ancestors.
//
// METHOD
// Write the new leaf value, move upward by dividing the index by two, and recompute each
// parent from its children.
//
// COMPLEXITY
// O(log n) time, O(1) auxiliary space.
//
// CONTRACT
// tree is an existing iterative sum tree of length 2*n; n>=1, 0<=index<n. Mutates tree;
// 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 tree after call: [0, 17, 10, 7, 1, 9, 3, 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 segment_set(std::vector<int>& tree, int index, int value) {
    alg_require(tree.size() <= 1000000);
    int n = ((int)tree.size() / 2);
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((int)tree.size() == alg_mul(2, n)));
    alg_require(((n >= 1) && (index >= 0) && (index < n)));
    index = alg_add(index, n);
    tree[index] = value;
    index = (index / 2);
    while ((index > 0)) {
        tree[index] = alg_add(tree[alg_mul(2, index)], tree[alg_add(alg_mul(2, index), 1)]);
        index = (index / 2);
    }
    return 0;
}

int main(void) {
    std::vector<int> tree = {0, 10, 3, 7, 1, 2, 3, 4};
    int index = 1;
    int value = 9;
    int result = segment_set(tree, index, value);
    printf("%d\n", result);
    // Expected tree: [0, 17, 10, 7, 1, 9, 3, 4]
    for (int alg_print = 0; alg_print < 8; alg_print++) printf("%d ", tree[alg_print]);
    printf("\n");
    return 0;
}

using System;
// Iterative Segment Tree Point Assignment in C#
//
// PURPOSE
// A point assignment changes a leaf and recomputes only its ancestors.
//
// METHOD
// Write the new leaf value, move upward by dividing the index by two, and recompute each
// parent from its children.
//
// COMPLEXITY
// O(log n) time, O(1) auxiliary space.
//
// CONTRACT
// tree is an existing iterative sum tree of length 2*n; n>=1, 0<=index<n. Mutates tree;
// 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# / .NET 10: ReadOnlySpan<int> inputs, Span<int> outputs, primitive workspace arrays,
// Array.BinarySearch for LIS, and checked integer arithmetic. Invalid arguments and overflow
// throw exceptions.
//
// EXAMPLE
// Expected return: 0.
// Expected tree after call: [0, 17, 10, 7, 1, 9, 3, 4].
// Run: Use Program.cs in a net10.0 console project; dotnet run.
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

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

    static int segment_set(Span<int> tree, int index, int value) {
        checked {
            int n = (tree.Length / 2);
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((tree.Length == (2 * n)));
            alg_require(((n >= 1) && (index >= 0) && (index < n)));
            index = (index + n);
            tree[index] = value;
            index = (index / 2);
            while ((index > 0)) {
                tree[index] = (tree[(2 * index)] + tree[((2 * index) + 1)]);
                index = (index / 2);
            }
            return 0;
        }
    }

    static void Main() {
        int[] tree = new int[] {0, 10, 3, 7, 1, 2, 3, 4};
        int index = 1;
        int value = 9;
        int result = segment_set(tree, index, value);
        Console.WriteLine(result);
        // Expected tree: [0, 17, 10, 7, 1, 9, 3, 4]
        Console.WriteLine("[" + string.Join(", ", tree) + "]");
    }
}

<?php
declare(strict_types=1);
// Iterative Segment Tree Point Assignment in PHP
//
// PURPOSE
// A point assignment changes a leaf and recomputes only its ancestors.
//
// METHOD
// Write the new leaf value, move upward by dividing the index by two, and recompute each
// parent from its children.
//
// COMPLEXITY
// O(log n) time, O(1) auxiliary space.
//
// CONTRACT
// tree is an existing iterative sum tree of length 2*n; n>=1, 0<=index<n. Mutates tree;
// 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
// PHP 8.1+ on a 64-bit runtime: packed arrays, strict scalar types, read-only inputs by
// value using copy-on-write, references only for outputs, and checked 32-bit arithmetic.
// Invalid input and overflow throw exceptions. PHP arrays have higher overhead than native
// packed buffers in C/Java.
//
// EXAMPLE
// Expected return: 0.
// Expected tree after call: [0, 17, 10, 7, 1, 9, 3, 4].
// Run: php example.php
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

function alg_require(bool $valid): void { if (!$valid) throw new InvalidArgumentException("invalid algorithm input"); }
function alg_checked(int|float $v): int { if ($v < -2147483648 || $v > 2147483647 || floor($v) != $v) throw new OverflowException("32-bit result overflow"); return (int)$v; }
function alg_add(int $a,int $b): int { return alg_checked($a+$b); }
function alg_sub(int $a,int $b): int { return alg_checked($a-$b); }
function alg_mul(int $a,int $b): int { return alg_checked($a*$b); }
function alg_size(int $n): int { alg_require($n>=0 && $n<=4000000); return $n; }

function segment_set(array &$tree, int $index, int $value): int {
    alg_require(array_is_list($tree));
    $n = intdiv(count($tree), 2);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($tree) == alg_mul(2, $n)));
    alg_require((($n >= 1) && ($index >= 0) && ($index < $n)));
    $index = alg_add($index, $n);
    $tree[$index] = $value;
    $index = intdiv($index, 2);
    while (($index > 0)) {
        $tree[$index] = alg_add($tree[alg_mul(2, $index)], $tree[alg_add(alg_mul(2, $index), 1)]);
        $index = intdiv($index, 2);
    }
    return 0;
}

$tree = [0, 10, 3, 7, 1, 2, 3, 4];
$index = 1;
$value = 9;
$result = segment_set($tree, $index, $value);
echo $result, PHP_EOL;
// Expected tree: [0, 17, 10, 7, 1, 9, 3, 4]
echo json_encode($tree), PHP_EOL;

// Iterative Segment Tree Build in Java
//
// PURPOSE
// An iterative sum segment tree stores leaves in the second half of a flat array and parents
// in the first half.
//
// METHOD
// Copy values into tree[n+i], then compute every internal node from its two children in
// descending index order.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space beyond caller-owned tree.
//
// CONTRACT
// n>=1, tree length is 2*n. Build once and reuse for point assignments and half-open range
// queries. Sums must fit.
// 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 tree after call: [0, 10, 3, 7, 1, 2, 3, 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 segment_build(int[] a, int[] tree) {
        java.util.Objects.requireNonNull(a, "a");
        java.util.Objects.requireNonNull(tree, "tree");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        alg_require((tree.length == Math.multiplyExact(2, n)));
        alg_require((n >= 1));
        int i = 0;
        tree[0] = 0;
        while ((i < n)) {
            tree[Math.addExact(n, i)] = a[i];
            i = Math.addExact(i, 1);
        }
        i = Math.subtractExact(n, 1);
        while ((i > 0)) {
            tree[i] = Math.addExact(tree[Math.multiplyExact(2, i)], tree[Math.addExact(Math.multiplyExact(2, i), 1)]);
            i = Math.subtractExact(i, 1);
        }
        return 0;
    }

    public static void main(String[] args) {
        int[] a = new int[] {1, 2, 3, 4};
        int[] tree = new int[] {0, 0, 0, 0, 0, 0, 0, 0};
        int result = segment_build(a, tree);
        System.out.println(result);
        // Expected tree: [0, 10, 3, 7, 1, 2, 3, 4]
        System.out.println(java.util.Arrays.toString(tree));
    }
}