Algorithms: Graph Algorithms Tutorials and Code Examples - Page 13

Disjoint Set Union in Python

Disjoint set union maintains connected components as a forest of parent links.

python

def component_count(u_edges: list[int], v_edges: list[int], n: int) -> int:
    alg_require(isinstance(u_edges, (list, tuple)) and len(u_edges) <= 1000000)
    alg_require(isinstance(v_edges, (list, tuple)) and len(v_edges) <= 1000000)
    alg_require(type(n) is int and -2147483648 <= n <= 2147483647)
    m: int = len(u_edges)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(m >= 0 and m <= 1000000)
    alg_require(len(u_edges) == m)
    alg_require(len(v_edges) == m)
    for value in u_edges:
        alg_require(value >= 0 and value < n)
    for value in v_edges:

Nov 15, 2026 python

Algorithms: Graph Algorithms

Breadth First Search Shortest Path in PHP

BFS explores an unweighted graph one distance layer at a time.

php

function bfs_distance(array $graph, int $n, int $source, int $target): int {
    alg_require(array_is_list($graph));
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($graph) == alg_mul($n, $n)));
    alg_require((($n >= 1) && ($source >= 0) && ($source < $n)));
    alg_require((($target >= 0) && ($target < $n)));
    $distance = array_fill(0, alg_size($n), 0);
    $queue = array_fill(0, alg_size($n), 0);
    $v = 0;
    $u = 0;
    $head = 0;
    $tail = 1;

Nov 15, 2026 PHP

Algorithms: Graph Algorithms

Disjoint Set Union in Java

Disjoint set union maintains connected components as a forest of parent links.

java

    static int component_count(int[] u_edges, int[] v_edges, int n) {
        java.util.Objects.requireNonNull(u_edges, "u_edges");
        java.util.Objects.requireNonNull(v_edges, "v_edges");
        int m = u_edges.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require(((m >= 0) && (m <= 1000000)));
        alg_require((u_edges.length == m));
        alg_require((v_edges.length == m));
        for (int alg_i = 0; alg_i < u_edges.length; alg_i++) {
            int alg_value = u_edges[alg_i];
            alg_require(((alg_value >= 0) && (alg_value < n)));
        }

Nov 15, 2026 Java

Algorithms: Graph Algorithms

Disjoint Set Union in JavaScript

Disjoint set union maintains connected components as a forest of parent links.

javascript

function component_count(u_edges, v_edges, n) {
    alg_require(u_edges instanceof Int32Array);
    alg_require(v_edges instanceof Int32Array);
    alg_require(Number.isInteger(n) && n >= -2147483648 && n <= 2147483647);
    let m = u_edges.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((m >= 0) && (m <= 1000000)));
    alg_require((u_edges.length == m));
    alg_require((v_edges.length == m));
    for (let alg_i = 0; alg_i < u_edges.length; alg_i++) {
        let alg_value = u_edges[alg_i];
        alg_require(((alg_value >= 0) && (alg_value < n)));

Nov 15, 2026 javascript

Algorithms: Graph Algorithms

Breadth First Search Shortest Path in C#

BFS explores an unweighted graph one distance layer at a time.

csharp

    static int bfs_distance(ReadOnlySpan<int> graph, int n, int source, int target) {
        checked {
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((graph.Length == (n * n)));
            alg_require(((n >= 1) && (source >= 0) && (source < n)));
            alg_require(((target >= 0) && (target < n)));
            int[] distance = new int[alg_size(n)];
            int[] queue = new int[alg_size(n)];
            int v = 0;
            int u = 0;
            int head = 0;
            int tail = 1;

Nov 15, 2026 csharp