Algorithms: Graph Algorithms Tutorials and Code Examples - Page 10

Warshall Transitive Closure in C

Transitive closure records whether every vertex can reach every other vertex.

c

int transitive_closure(int *graph, size_t graph_length, int n) {
    int alg_error = 0;
    int alg_result = INT_MIN;
    errno = 0;
    if (graph_length > 1000000 || (graph_length && !graph)) { errno = EINVAL; 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)graph_length == alg_mul(n, n, &alg_error)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int i = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int j = 0;

Nov 15, 2026 C

Algorithms: Graph Algorithms

Warshall Transitive Closure in Python

Transitive closure records whether every vertex can reach every other vertex.

python

def transitive_closure(graph: list[int], n: int) -> int:
    alg_require(isinstance(graph, list) and len(graph) <= 1000000)
    alg_require(type(n) is int and -2147483648 <= n <= 2147483647)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(graph) == n * n)
    i: int = 0
    j: int = 0
    k: int = 0
    while i < n:
        graph[i * n + i] = 1
        i += 1
    while k < n:

Nov 15, 2026 python

Algorithms: Graph Algorithms

Warshall Transitive Closure in JavaScript

Transitive closure records whether every vertex can reach every other vertex.

javascript

function transitive_closure(graph, n) {
    alg_require(graph instanceof Int32Array);
    alg_require(Number.isInteger(n) && n >= -2147483648 && n <= 2147483647);
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((graph.length == alg_mul(n, n)));
    let i = 0;
    let j = 0;
    let k = 0;
    while ((i < n)) {
        graph[alg_add(alg_mul(i, n), i)] = 1;
        i = alg_add(i, 1);
    }

Nov 15, 2026 javascript

Algorithms: Graph Algorithms

Warshall Transitive Closure in Java

Transitive closure records whether every vertex can reach every other vertex.

java

    static int transitive_closure(int[] graph, int n) {
        java.util.Objects.requireNonNull(graph, "graph");
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((graph.length == Math.multiplyExact(n, n)));
        int i = 0;
        int j = 0;
        int k = 0;
        while ((i < n)) {
            graph[Math.addExact(Math.multiplyExact(i, n), i)] = 1;
            i = Math.addExact(i, 1);
        }
        while ((k < n)) {

Nov 15, 2026 Java

Algorithms: Graph Algorithms

Bellman Ford Shortest Path in PHP

Bellman-Ford permits negative edge weights and detects negative cycles reachable from the source.

php

function bellman_ford(array $from_vertex, array $to_vertex, array $weight, int $n, int $source, int $target): int {
    alg_require(array_is_list($from_vertex));
    alg_require(array_is_list($to_vertex));
    alg_require(array_is_list($weight));
    $m = count($from_vertex);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((($m >= 0) && ($m <= 1000000)));
    alg_require((count($from_vertex) == $m));
    alg_require((count($to_vertex) == $m));
    alg_require((count($weight) == $m));
    alg_require((($n >= 1) && ($source >= 0) && ($source < $n)));
    alg_require((($target >= 0) && ($target < $n)));

Nov 15, 2026 PHP