Warshall Transitive Closure in C++

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Warshall Transitive Closure in C++
//
// PURPOSE
// Transitive closure records whether every vertex can reach every other vertex. Warshall is
// the Boolean counterpart of Floyd-Warshall.
//
// METHOD
// Mark each vertex reachable from itself. For every intermediate k, mark i-to-j reachable
// whenever i reaches k and k reaches j. The matrix accumulates reachability through the
// processed intermediates.
//
// COMPLEXITY
// O(n cubed) time and O(1) auxiliary space beyond the caller-owned matrix.
//
// CONTRACT
// Mutates a flattened n by n 0/1 adjacency matrix to reflexive transitive closure. Returns
// 0. A vertex reaches itself via a path of zero edges.
// 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: 0.
// Expected graph after call: [1, 1, 1, 0, 1, 1, 0, 0, 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 transitive_closure(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)));
    int i = 0;
    int j = 0;
    int k = 0;
    while ((i < n)) {
        graph[alg_add(alg_mul(i, n), i)] = 1;
        i = alg_add(i, 1);
    }
    while ((k < n)) {
        i = 0;
        while ((i < n)) {
            j = 0;
            while ((j < n)) {
                if (((graph[alg_add(alg_mul(i, n), k)] != 0) && (graph[alg_add(alg_mul(k, n), j)] != 0))) {
                    graph[alg_add(alg_mul(i, n), j)] = 1;
                }
                j = alg_add(j, 1);
            }
            i = alg_add(i, 1);
        }
        k = alg_add(k, 1);
    }
    return 0;
}

int main(void) {
    std::vector<int> graph = {0, 1, 0, 0, 0, 1, 0, 0, 0};
    int n = 3;
    int result = transitive_closure(graph, n);
    printf("%d\n", result);
    for (int z = 0; z < 9; z++) printf("%d ", graph[z]);
    printf("\n");
    // Expected graph: [1, 1, 1, 0, 1, 1, 0, 0, 1]
    return 0;
}