Bellman Ford Shortest Path in C++

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Bellman Ford Shortest Path in C++
//
// PURPOSE
// Bellman-Ford permits negative edge weights and detects negative cycles reachable from the
// source. Repeated edge relaxation finds progressively longer optimal paths.
//
// METHOD
// Relax every edge up to n-1 times, stopping early if nothing changes. Perform one extra
// pass to detect a reachable negative cycle. Guard unreachable endpoints before adding
// weights.
//
// COMPLEXITY
// O(VE) time and O(V) auxiliary space.
//
// CONTRACT
// Edge arrays from_vertex, to_vertex, weight each have m entries; n >= 1. Finite distances
// and all relaxed sums stay strictly between -1,000,000,000 and 1,000,000,000. Returns
// distance, INF if unreachable, or -INF for any reachable negative cycle (even if it cannot
// reach target).
// 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: 2.
// 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 bellman_ford(const std::vector<int>& from_vertex, const std::vector<int>& to_vertex, const std::vector<int>& weight, int n, int source, int target) {
    alg_require(from_vertex.size() <= 1000000);
    alg_require(to_vertex.size() <= 1000000);
    alg_require(weight.size() <= 1000000);
    int m = (int)from_vertex.size();
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((m >= 0) && (m <= 1000000)));
    alg_require(((int)from_vertex.size() == m));
    alg_require(((int)to_vertex.size() == m));
    alg_require(((int)weight.size() == m));
    alg_require(((n >= 1) && (source >= 0) && (source < n)));
    alg_require(((target >= 0) && (target < n)));
    for (int alg_i = 0; alg_i < (int)from_vertex.size(); alg_i++) {
        int alg_value = from_vertex[alg_i];
        alg_require(((alg_value >= 0) && (alg_value < n)));
    }
    for (int alg_i = 0; alg_i < (int)to_vertex.size(); alg_i++) {
        int alg_value = to_vertex[alg_i];
        alg_require(((alg_value >= 0) && (alg_value < n)));
    }
    std::vector<int> distance(alg_size(n), 0);
    int i = 0;
    int edge = 0;
    int iteration = 0;
    int changed = 0;
    int u = 0;
    int v = 0;
    while ((i < n)) {
        distance[i] = 1000000000;
        i = alg_add(i, 1);
    }
    distance[source] = 0;
    while ((iteration < alg_sub(n, 1))) {
        changed = 0;
        edge = 0;
        while ((edge < m)) {
            u = from_vertex[edge];
            v = to_vertex[edge];
            if (((distance[u] != 1000000000) && (alg_add(distance[u], weight[edge]) < distance[v]))) {
                distance[v] = alg_add(distance[u], weight[edge]);
                changed = 1;
            }
            edge = alg_add(edge, 1);
        }
        if ((changed == 0)) {
            break;
        }
        iteration = alg_add(iteration, 1);
    }
    edge = 0;
    while ((edge < m)) {
        u = from_vertex[edge];
        v = to_vertex[edge];
        if (((distance[u] != 1000000000) && (alg_add(distance[u], weight[edge]) < distance[v]))) {
            return alg_sub(0, 1000000000);
        }
        edge = alg_add(edge, 1);
    }
    return distance[target];
}

int main(void) {
    std::vector<int> from_vertex = {0, 1, 0};
    std::vector<int> to_vertex = {1, 2, 2};
    std::vector<int> weight = {4, -2, 9};
    int n = 3;
    int source = 0;
    int target = 2;
    int result = bellman_ford(from_vertex, to_vertex, weight, n, source, target);
    printf("%d\n", result);
    return 0;
}