Algorithms: Range Queries

using System;
// Iterative Segment Tree Range Sum in C#
//
// PURPOSE
// A segment tree range query combines the small number of disjoint nodes covering a half-
// open interval.
//
// METHOD
// Move both endpoints to leaves. Include a left endpoint when it is a right child and a
// right endpoint when it is about to cross a left child, then move both up.
//
// COMPLEXITY
// O(log n) time, O(1) auxiliary space.
//
// CONTRACT
// tree has 2*n entries; n>=1, 0<=left<=right<=n. Returns sum in [left,right). Empty range
// 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# / .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: 5.
// 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_sum(ReadOnlySpan<int> tree, int left, int right) {
        checked {
            int n = (tree.Length / 2);
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((tree.Length == (2 * n)));
            alg_require(((n >= 1) && (left >= 0) && (left <= right) && (right <= n)));
            left = (left + n);
            right = (right + n);
            int total = 0;
            while ((left < right)) {
                if (((left % 2) == 1)) {
                    total = (total + tree[left]);
                    left = (left + 1);
                }
                if (((right % 2) == 1)) {
                    right = (right - 1);
                    total = (total + tree[right]);
                }
                left = (left / 2);
                right = (right / 2);
            }
            return total;
        }
    }

    static void Main() {
        int[] tree = new int[] {0, 10, 3, 7, 1, 2, 3, 4};
        int left = 1;
        int right = 3;
        int result = segment_sum(tree, left, right);
        Console.WriteLine(result);
    }
}

<?php
declare(strict_types=1);
// Iterative Segment Tree Range Sum in PHP
//
// PURPOSE
// A segment tree range query combines the small number of disjoint nodes covering a half-
// open interval.
//
// METHOD
// Move both endpoints to leaves. Include a left endpoint when it is a right child and a
// right endpoint when it is about to cross a left child, then move both up.
//
// COMPLEXITY
// O(log n) time, O(1) auxiliary space.
//
// CONTRACT
// tree has 2*n entries; n>=1, 0<=left<=right<=n. Returns sum in [left,right). Empty range
// 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
// 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: 5.
// 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_sum(array $tree, int $left, int $right): int {
    alg_require(array_is_list($tree));
    $n = intdiv(count($tree), 2);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($tree) == alg_mul(2, $n)));
    alg_require((($n >= 1) && ($left >= 0) && ($left <= $right) && ($right <= $n)));
    $left = alg_add($left, $n);
    $right = alg_add($right, $n);
    $total = 0;
    while (($left < $right)) {
        if ((($left % 2) == 1)) {
            $total = alg_add($total, $tree[$left]);
            $left = alg_add($left, 1);
        }
        if ((($right % 2) == 1)) {
            $right = alg_sub($right, 1);
            $total = alg_add($total, $tree[$right]);
        }
        $left = intdiv($left, 2);
        $right = intdiv($right, 2);
    }
    return $total;
}

$tree = [0, 10, 3, 7, 1, 2, 3, 4];
$left = 1;
$right = 3;
$result = segment_sum($tree, $left, $right);
echo $result, PHP_EOL;

// Iterative Segment Tree Point Assignment in Java
//
// 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
// 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, 17, 10, 7, 1, 9, 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_set(int[] tree, int index, int value) {
        java.util.Objects.requireNonNull(tree, "tree");
        int n = (tree.length / 2);
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((tree.length == Math.multiplyExact(2, n)));
        alg_require(((n >= 1) && (index >= 0) && (index < n)));
        index = Math.addExact(index, n);
        tree[index] = value;
        index = (index / 2);
        while ((index > 0)) {
            tree[index] = Math.addExact(tree[Math.multiplyExact(2, index)], tree[Math.addExact(Math.multiplyExact(2, index), 1)]);
            index = (index / 2);
        }
        return 0;
    }

    public static void main(String[] args) {
        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);
        System.out.println(result);
        // Expected tree: [0, 17, 10, 7, 1, 9, 3, 4]
        System.out.println(java.util.Arrays.toString(tree));
    }
}

"use strict";
// Iterative Segment Tree Point Assignment in JavaScript
//
// 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
// 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 tree after call: [0, 17, 10, 7, 1, 9, 3, 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 segment_set(tree, index, value) {
    alg_require(tree instanceof Int32Array);
    alg_require(Number.isInteger(index) && index >= -2147483648 && index <= 2147483647);
    alg_require(Number.isInteger(value) && value >= -2147483648 && value <= 2147483647);
    let n = Math.floor(tree.length / 2);
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((tree.length == alg_mul(2, n)));
    alg_require(((n >= 1) && (index >= 0) && (index < n)));
    index = alg_add(index, n);
    tree[index] = value;
    index = Math.floor(index / 2);
    while ((index > 0)) {
        tree[index] = alg_add(tree[alg_mul(2, index)], tree[alg_add(alg_mul(2, index), 1)]);
        index = Math.floor(index / 2);
    }
    return 0;
}

let tree = new Int32Array([0, 10, 3, 7, 1, 2, 3, 4]);
let index = 1;
let value = 9;
let result = segment_set(tree, index, value);
console.log(result);
// Expected tree: [0, 17, 10, 7, 1, 9, 3, 4]
console.log(Array.from(tree));

from bisect import bisect_left

# Iterative Segment Tree Point Assignment in Python
#
# 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
# 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 tree after call: [0, 17, 10, 7, 1, 9, 3, 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 segment_set(tree: list[int], index: int, value: int) -> int:
    alg_require(isinstance(tree, list) and len(tree) <= 1000000)
    alg_require(type(index) is int and -2147483648 <= index <= 2147483647)
    alg_require(type(value) is int and -2147483648 <= value <= 2147483647)
    n: int = len(tree) // 2
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(tree) == 2 * n)
    alg_require(n >= 1 and index >= 0 and (index < n))
    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

tree = [0, 10, 3, 7, 1, 2, 3, 4]
index = 1
value = 9
result = segment_set(tree, index, value)
print(result)
# Expected tree: [0, 17, 10, 7, 1, 9, 3, 4]
print(tree)