Algorithms: Tree Algorithms

Algorithms: Tree Algorithms

Explore algorithms: tree algorithms code snippets and tutorials

Algorithms: Tree Algorithms

Binary Search Tree Lookup in Java

A binary search tree chooses a branch by comparing the target with the current node key..

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// Binary Search Tree Lookup in Java
//
// PURPOSE
// A binary search tree chooses a branch by comparing the target with the current node key.
//
// METHOD
// At each node return on equality, otherwise follow the left child for a smaller target or
// the right child for a larger target.
//
// COMPLEXITY
// O(height) time and O(1) auxiliary space; height is O(log n) only when the tree is
// balanced.
//
// CONTRACT
// keys,left_child,right_child have n entries; -1 means absent. Must be a valid BST. Returns
// node ID or -1.
// 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: 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 bst_lookup(int[] keys, int[] left_child, int[] right_child, int root, int target) {
        java.util.Objects.requireNonNull(keys, "keys");
        java.util.Objects.requireNonNull(left_child, "left_child");
        java.util.Objects.requireNonNull(right_child, "right_child");
        int n = keys.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((keys.length == n));
        alg_require((left_child.length == n));
        alg_require((right_child.length == n));
        alg_require(((root >= Math.negateExact(1)) && (root < n)));
        for (int alg_i = 0; alg_i < left_child.length; alg_i++) {
            int alg_value = left_child[alg_i];
            alg_require(((alg_value >= Math.negateExact(1)) && (alg_value < n)));
        }
        for (int alg_i = 0; alg_i < right_child.length; alg_i++) {
            int alg_value = right_child[alg_i];
            alg_require(((alg_value >= Math.negateExact(1)) && (alg_value < n)));
        }
        while ((root != Math.negateExact(1))) {
            if ((keys[root] == target)) {
                return root;
            }
            if ((target < keys[root])) {
                root = left_child[root];
            } else {
                root = right_child[root];
            }
        }
        return Math.negateExact(1);
    }

    public static void main(String[] args) {
        int[] keys = new int[] {4, 2, 6};
        int[] left_child = new int[] {1, -1, -1};
        int[] right_child = new int[] {2, -1, -1};
        int root = 0;
        int target = 6;
        int result = bst_lookup(keys, left_child, right_child, root, target);
        System.out.println(result);
    }
}
Nov 15, 2026 Java
Algorithms: Tree Algorithms

Binary Search Tree Lookup in JavaScript

A binary search tree chooses a branch by comparing the target with the current node key..

javascript 
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"use strict";
// Binary Search Tree Lookup in JavaScript
//
// PURPOSE
// A binary search tree chooses a branch by comparing the target with the current node key.
//
// METHOD
// At each node return on equality, otherwise follow the left child for a smaller target or
// the right child for a larger target.
//
// COMPLEXITY
// O(height) time and O(1) auxiliary space; height is O(log n) only when the tree is
// balanced.
//
// CONTRACT
// keys,left_child,right_child have n entries; -1 means absent. Must be a valid BST. Returns
// node ID or -1.
// 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: 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 bst_lookup(keys, left_child, right_child, root, target) {
    alg_require(keys instanceof Int32Array);
    alg_require(left_child instanceof Int32Array);
    alg_require(right_child instanceof Int32Array);
    alg_require(Number.isInteger(root) && root >= -2147483648 && root <= 2147483647);
    alg_require(Number.isInteger(target) && target >= -2147483648 && target <= 2147483647);
    let n = keys.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((keys.length == n));
    alg_require((left_child.length == n));
    alg_require((right_child.length == n));
    alg_require(((root >= alg_sub(0, 1)) && (root < n)));
    for (let alg_i = 0; alg_i < left_child.length; alg_i++) {
        let alg_value = left_child[alg_i];
        alg_require(((alg_value >= alg_sub(0, 1)) && (alg_value < n)));
    }
    for (let alg_i = 0; alg_i < right_child.length; alg_i++) {
        let alg_value = right_child[alg_i];
        alg_require(((alg_value >= alg_sub(0, 1)) && (alg_value < n)));
    }
    while ((root != alg_sub(0, 1))) {
        if ((keys[root] == target)) {
            return root;
        }
        if ((target < keys[root])) {
            root = left_child[root];
        } else {
            root = right_child[root];
        }
    }
    return alg_sub(0, 1);
}

let keys = new Int32Array([4, 2, 6]);
let left_child = new Int32Array([1, -1, -1]);
let right_child = new Int32Array([2, -1, -1]);
let root = 0;
let target = 6;
let result = bst_lookup(keys, left_child, right_child, root, target);
console.log(result);
Nov 15, 2026 javascript
Algorithms: Tree Algorithms

Binary Search Tree Lookup in Python

A binary search tree chooses a branch by comparing the target with the current node key..

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from bisect import bisect_left

# Binary Search Tree Lookup in Python
#
# PURPOSE
# A binary search tree chooses a branch by comparing the target with the current node key.
#
# METHOD
# At each node return on equality, otherwise follow the left child for a smaller target or
# the right child for a larger target.
#
# COMPLEXITY
# O(height) time and O(1) auxiliary space; height is O(log n) only when the tree is
# balanced.
#
# CONTRACT
# keys,left_child,right_child have n entries; -1 means absent. Must be a valid BST. Returns
# node ID or -1.
# 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: 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 bst_lookup(keys: list[int], left_child: list[int], right_child: list[int], root: int, target: int) -> int:
    alg_require(isinstance(keys, (list, tuple)) and len(keys) <= 1000000)
    alg_require(isinstance(left_child, (list, tuple)) and len(left_child) <= 1000000)
    alg_require(isinstance(right_child, (list, tuple)) and len(right_child) <= 1000000)
    alg_require(type(root) is int and -2147483648 <= root <= 2147483647)
    alg_require(type(target) is int and -2147483648 <= target <= 2147483647)
    n: int = len(keys)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(keys) == n)
    alg_require(len(left_child) == n)
    alg_require(len(right_child) == n)
    alg_require(root >= -1 and root < n)
    for value in left_child:
        alg_require(value >= -1 and value < n)
    for value in right_child:
        alg_require(value >= -1 and value < n)
    while root != -1:
        if keys[root] == target:
            return root
        if target < keys[root]:
            root = left_child[root]
        else:
            root = right_child[root]
    return -1

keys = [4, 2, 6]
left_child = [1, -1, -1]
right_child = [2, -1, -1]
root = 0
target = 6
result = bst_lookup(keys, left_child, right_child, root, target)
print(result)
Nov 15, 2026 python
Algorithms: Tree Algorithms

Binary Search Tree Lookup in C

A binary search tree chooses a branch by comparing the target with the current node key..

c 
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#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <limits.h>
#include <errno.h>
// Binary Search Tree Lookup in C
//
// PURPOSE
// A binary search tree chooses a branch by comparing the target with the current node key.
//
// METHOD
// At each node return on equality, otherwise follow the left child for a smaller target or
// the right child for a larger target.
//
// COMPLEXITY
// O(height) time and O(1) auxiliary space; height is O(log n) only when the tree is
// balanced.
//
// CONTRACT
// keys,left_child,right_child have n entries; -1 means absent. Must be a valid BST. Returns
// node ID or -1.
// 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: 2.
// 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 bst_lookup(const int *keys, size_t keys_length, const int *left_child, size_t left_child_length, const int *right_child, size_t right_child_length, int root, int target) {
    int alg_error = 0;
    int alg_result = INT_MIN;
    errno = 0;
    if (keys_length > 1000000 || (keys_length && !keys)) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (left_child_length > 1000000 || (left_child_length && !left_child)) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (right_child_length > 1000000 || (right_child_length && !right_child)) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    int n = (int)keys_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)keys_length == n))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    if (!(((int)left_child_length == n))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    if (!(((int)right_child_length == n))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    if (!(((root >= alg_sub(0, 1, &alg_error)) && (root < 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)left_child_length; alg_i++) {
        int alg_value = left_child[alg_i];
        if (!(((alg_value >= alg_sub(0, 1, &alg_error)) && (alg_value < 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)right_child_length; alg_i++) {
        int alg_value = right_child[alg_i];
        if (!(((alg_value >= alg_sub(0, 1, &alg_error)) && (alg_value < n)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    }
    while (1) {
        int alg_condition = (root != alg_sub(0, 1, &alg_error));
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (!alg_condition) break;
        int alg_condition_1 = (keys[root] == target);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_condition_1) {
            alg_result = root;
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            goto alg_cleanup;
        }
        int alg_condition_2 = (target < keys[root]);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_condition_2) {
            root = left_child[root];
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        } else {
            root = right_child[root];
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        }
    }
    alg_result = alg_sub(0, 1, &alg_error);
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    goto alg_cleanup;
alg_cleanup:
    return alg_result;
}

int main(void) {
    int keys[] = {4, 2, 6};
    int left_child[] = {1, -1, -1};
    int right_child[] = {2, -1, -1};
    int root = 0;
    int target = 6;
    int result = bst_lookup(keys, 3, left_child, 3, right_child, 3, root, target);
    printf("%d\n", result);
    if (errno) { perror("algorithm"); return 1; }
    return 0;
}
Nov 15, 2026 C
Algorithms: Tree Algorithms

Binary Search Tree Lookup in C++

A binary search tree chooses a branch by comparing the target with the current node key..

cpp 
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#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Binary Search Tree Lookup in C++
//
// PURPOSE
// A binary search tree chooses a branch by comparing the target with the current node key.
//
// METHOD
// At each node return on equality, otherwise follow the left child for a smaller target or
// the right child for a larger target.
//
// COMPLEXITY
// O(height) time and O(1) auxiliary space; height is O(log n) only when the tree is
// balanced.
//
// CONTRACT
// keys,left_child,right_child have n entries; -1 means absent. Must be a valid BST. Returns
// node ID or -1.
// 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: 2.
// 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 bst_lookup(const std::vector<int>& keys, const std::vector<int>& left_child, const std::vector<int>& right_child, int root, int target) {
    alg_require(keys.size() <= 1000000);
    alg_require(left_child.size() <= 1000000);
    alg_require(right_child.size() <= 1000000);
    int n = (int)keys.size();
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((int)keys.size() == n));
    alg_require(((int)left_child.size() == n));
    alg_require(((int)right_child.size() == n));
    alg_require(((root >= alg_sub(0, 1)) && (root < n)));
    for (int alg_i = 0; alg_i < (int)left_child.size(); alg_i++) {
        int alg_value = left_child[alg_i];
        alg_require(((alg_value >= alg_sub(0, 1)) && (alg_value < n)));
    }
    for (int alg_i = 0; alg_i < (int)right_child.size(); alg_i++) {
        int alg_value = right_child[alg_i];
        alg_require(((alg_value >= alg_sub(0, 1)) && (alg_value < n)));
    }
    while ((root != alg_sub(0, 1))) {
        if ((keys[root] == target)) {
            return root;
        }
        if ((target < keys[root])) {
            root = left_child[root];
        } else {
            root = right_child[root];
        }
    }
    return alg_sub(0, 1);
}

int main(void) {
    std::vector<int> keys = {4, 2, 6};
    std::vector<int> left_child = {1, -1, -1};
    std::vector<int> right_child = {2, -1, -1};
    int root = 0;
    int target = 6;
    int result = bst_lookup(keys, left_child, right_child, root, target);
    printf("%d\n", result);
    return 0;
}
Nov 15, 2026 C++