Algorithms: Graph Algorithms Tutorials and Code Examples - Page 8

Kahn Topological Cycle Detection in C++

Kahn algorithm repeatedly removes vertices with no incoming edges.

cpp

int is_dag(const std::vector<int>& graph, int n) {
    alg_require(graph.size() <= 1000000);
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((int)graph.size() == alg_mul(n, n)));
    std::vector<int> indegree(alg_size(alg_add(n, 1)), 0);
    std::vector<int> queue(alg_size(alg_add(n, 1)), 0);
    int u = 0;
    int v = 0;
    int head = 0;
    int tail = 0;
    while ((u < n)) {
        v = 0;

Nov 15, 2026 C++

Algorithms: Graph Algorithms

Kahn Topological Cycle Detection in C#

Kahn algorithm repeatedly removes vertices with no incoming edges.

csharp

    static int is_dag(ReadOnlySpan<int> graph, int n) {
        checked {
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((graph.Length == (n * n)));
            int[] indegree = new int[alg_size((n + 1))];
            int[] queue = new int[alg_size((n + 1))];
            int u = 0;
            int v = 0;
            int head = 0;
            int tail = 0;
            while ((u < n)) {
                v = 0;

Nov 15, 2026 csharp

Algorithms: Graph Algorithms

Dijkstra Shortest Path in PHP

Dijkstra repeatedly settles the unsettled vertex with smallest tentative distance.

php

function dijkstra(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 < $n)));
    alg_require(($n >= 1));
    for ($alg_i = 0; $alg_i < count($graph); $alg_i++) {
        $alg_value = $graph[$alg_i];
        alg_require((($alg_value >= alg_sub(0, 1)) && ($alg_value < 1000000000)));
    }
    $distance = array_fill(0, alg_size($n), 0);

Nov 15, 2026 PHP

Algorithms: Graph Algorithms

Kahn Topological Cycle Detection in PHP

Kahn algorithm repeatedly removes vertices with no incoming edges.

php

function is_dag(array $graph, int $n): int {
    alg_require(array_is_list($graph));
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($graph) == alg_mul($n, $n)));
    $indegree = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $queue = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $u = 0;
    $v = 0;
    $head = 0;
    $tail = 0;
    while (($u < $n)) {
        $v = 0;

Nov 15, 2026 PHP

Algorithms: Graph Algorithms

Floyd Warshall All Pairs Shortest Paths in Java

Floyd-Warshall computes distances between every pair by gradually allowing more intermediate vertices.

java

    static int floyd_warshall(int[] distance, int n) {
        java.util.Objects.requireNonNull(distance, "distance");
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((distance.length == Math.multiplyExact(n, n)));
        int k = 0;
        int i = 0;
        int j = 0;
        while ((k < n)) {
            i = 0;
            while ((i < n)) {
                j = 0;
                while ((j < n)) {

Nov 15, 2026 Java