Directed Cycle Detection by DFS in C++

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Directed Cycle Detection by DFS in C++
//
// PURPOSE
// DFS detects a directed cycle when an edge points to a vertex still active in the current
// search path.
//
// METHOD
// Use an explicit stack and per-vertex next-neighbor positions. Mark vertices active on
// entry and finished on exit. An edge to an active vertex is a back edge.
//
// COMPLEXITY
// O(n squared) matrix traversal time and O(n) auxiliary space.
//
// CONTRACT
// Flattened n by n 0/1 directed adjacency matrix; returns 1 if a cycle exists, otherwise 0.
// 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: 1.
// 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 directed_cycle(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> color(alg_size(alg_add(n, 1)), 0);
    std::vector<int> stack(alg_size(alg_add(n, 1)), 0);
    std::vector<int> next_vertex(alg_size(alg_add(n, 1)), 0);
    int source = 0;
    int top = 0;
    int u = 0;
    int v = 0;
    while ((source < n)) {
        if ((color[source] == 0)) {
            top = 1;
            stack[0] = source;
            color[source] = 1;
            while ((top > 0)) {
                u = stack[alg_sub(top, 1)];
                if ((next_vertex[u] == n)) {
                    color[u] = 2;
                    top = alg_sub(top, 1);
                } else {
                    v = next_vertex[u];
                    next_vertex[u] = alg_add(next_vertex[u], 1);
                    if ((graph[alg_add(alg_mul(u, n), v)] != 0)) {
                        if ((color[v] == 1)) {
                            return 1;
                        }
                        if ((color[v] == 0)) {
                            color[v] = 1;
                            stack[top] = v;
                            top = alg_add(top, 1);
                        }
                    }
                }
            }
        }
        source = alg_add(source, 1);
    }
    return 0;
}

int main(void) {
    std::vector<int> graph = {0, 1, 1, 0};
    int n = 2;
    int result = directed_cycle(graph, n);
    printf("%d\n", result);
    return 0;
}