Depth First Search Reachability in C++

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Depth First Search Reachability in C++
//
// PURPOSE
// DFS follows a branch deeply before returning to pending branches. An explicit stack avoids
// language recursion limits for reachability exploration.
//
// METHOD
// Push the source and mark it. Pop a vertex, count it, then mark and push each unseen
// neighbor. Marking when pushed bounds stack entries to at most n.
//
// COMPLEXITY
// O(n squared) time with a matrix and O(n) auxiliary space. Adjacency lists reduce traversal
// to O(V+E).
//
// CONTRACT
// Flattened n by n 0/1 matrix, n >= 1, valid source. Returns the number of reachable
// vertices INCLUDING source. Directed edges supported.
// 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: 3.
// 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 dfs_reachable(const std::vector<int>& graph, int n, int source) {
    alg_require(graph.size() <= 1000000);
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((int)graph.size() == alg_mul(n, n)));
    alg_require(((n >= 1) && (source >= 0) && (source < n)));
    std::vector<int> seen(alg_size(n), 0);
    std::vector<int> stack(alg_size(n), 0);
    int top = 1;
    int count = 0;
    int u = 0;
    int v = 0;
    stack[0] = source;
    seen[source] = 1;
    while ((top > 0)) {
        top = alg_sub(top, 1);
        u = stack[top];
        count = alg_add(count, 1);
        v = 0;
        while ((v < n)) {
            if (((graph[alg_add(alg_mul(u, n), v)] != 0) && (seen[v] == 0))) {
                seen[v] = 1;
                stack[top] = v;
                top = alg_add(top, 1);
            }
            v = alg_add(v, 1);
        }
    }
    return count;
}

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