Algorithms: Graph Algorithms Tutorials and Code Examples - Page 5

DAG Shortest Path in PHP

A directed acyclic graph permits shortest-path relaxation in topological order even when weights are negative..

php

function dag_shortest_path(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)));
    $degree = array_fill(0, alg_size($n), 0);
    $distance = array_fill(0, alg_size($n), 0);
    $queue = array_fill(0, alg_size($n), 0);
    $head = 0;
    $tail = 0;
    $u = 0;

Nov 15, 2026 PHP

Algorithms: Graph Algorithms

Directed Cycle Detection by DFS in Java

DFS detects a directed cycle when an edge points to a vertex still active in the current search path..

java

    static int directed_cycle(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[] color = new int[alg_size(Math.addExact(n, 1))];
        int[] stack = new int[alg_size(Math.addExact(n, 1))];
        int[] next_vertex = new int[alg_size(Math.addExact(n, 1))];
        int source = 0;
        int top = 0;
        int u = 0;
        int v = 0;
        while ((source < n)) {

Nov 15, 2026 Java

Algorithms: Graph Algorithms

Directed Cycle Detection by DFS in JavaScript

DFS detects a directed cycle when an edge points to a vertex still active in the current search path..

javascript

function directed_cycle(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 color = new Int32Array(alg_size(alg_add(n, 1)));
    let stack = new Int32Array(alg_size(alg_add(n, 1)));
    let next_vertex = new Int32Array(alg_size(alg_add(n, 1)));
    let source = 0;
    let top = 0;
    let u = 0;
    let v = 0;

Nov 15, 2026 javascript

Algorithms: Graph Algorithms

Directed Cycle Detection by DFS in Python

DFS detects a directed cycle when an edge points to a vertex still active in the current search path..

python

def directed_cycle(graph: list[int], n: int) -> int:
    alg_require(isinstance(graph, (list, tuple)) 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)
    color: list[int] = [0] * alg_size(n + 1)
    stack: list[int] = [0] * alg_size(n + 1)
    next_vertex: list[int] = [0] * alg_size(n + 1)
    source: int = 0
    top: int = 0
    u: int = 0
    v: int = 0

Nov 15, 2026 python

Algorithms: Graph Algorithms

Directed Cycle Detection by DFS in C

DFS detects a directed cycle when an edge points to a vertex still active in the current search path..

c

int directed_cycle(const int *graph, size_t graph_length, int n) {
    int alg_error = 0;
    int alg_result = INT_MIN;
    errno = 0;
    int *color = NULL;
    int *stack = NULL;
    int *next_vertex = NULL;
    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; }

Nov 15, 2026 C