Kahn Topological Cycle Detection in C++

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Kahn Topological Cycle Detection in C++
//
// PURPOSE
// Kahn algorithm repeatedly removes vertices with no incoming edges. A directed graph has a
// topological ordering exactly when all vertices can be removed this way.
//
// METHOD
// Compute indegrees, queue every zero-indegree vertex, then remove its outgoing edges.
// Enqueue a neighbor when its indegree becomes zero. Compare the number removed with n.
//
// COMPLEXITY
// O(n squared) time with an adjacency matrix and O(n) auxiliary space. Adjacency lists give
// O(V+E).
//
// CONTRACT
// Flattened n by n 0/1 directed matrix. Returns 1 for a DAG and 0 for a cycle. Empty graph
// is a DAG. This variant reports existence rather than returning an ordering.
// 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 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;
        while ((v < n)) {
            if ((graph[alg_add(alg_mul(u, n), v)] != 0)) {
                indegree[v] = alg_add(indegree[v], 1);
            }
            v = alg_add(v, 1);
        }
        u = alg_add(u, 1);
    }
    v = 0;
    while ((v < n)) {
        if ((indegree[v] == 0)) {
            queue[tail] = v;
            tail = alg_add(tail, 1);
        }
        v = alg_add(v, 1);
    }
    while ((head < tail)) {
        u = queue[head];
        head = alg_add(head, 1);
        v = 0;
        while ((v < n)) {
            if ((graph[alg_add(alg_mul(u, n), v)] != 0)) {
                indegree[v] = alg_sub(indegree[v], 1);
                if ((indegree[v] == 0)) {
                    queue[tail] = v;
                    tail = alg_add(tail, 1);
                }
            }
            v = alg_add(v, 1);
        }
    }
    if ((tail == n)) {
        return 1;
    }
    return 0;
}

int main(void) {
    std::vector<int> graph = {0, 1, 0, 0, 0, 1, 0, 0, 0};
    int n = 3;
    int result = is_dag(graph, n);
    printf("%d\n", result);
    return 0;
}