Kruskal Minimum Spanning Tree in C++

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Kruskal Minimum Spanning Tree in C++
//
// PURPOSE
// Kruskal adds edges in ascending weight order whenever they join different components.
//
// METHOD
// Sort edge indices by weight using a stable bottom-up merge. Use union by size and path
// halving to accept edges joining different roots. Stop after n-1 accepted edges.
//
// COMPLEXITY
// O(E log E + V) time and O(V+E) auxiliary space.
//
// CONTRACT
// n>=1, parallel edge arrays have m entries and valid vertex IDs. Weights nonnegative; total
// fits signed 32-bit. Returns -1 for a disconnected graph.
// 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: 6.
// 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 kruskal(const std::vector<int>& from_vertex, const std::vector<int>& to_vertex, const std::vector<int>& weight, int n) {
    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));
    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> order(alg_size(alg_add(m, 1)), 0);
    std::vector<int> buffer(alg_size(alg_add(m, 1)), 0);
    std::vector<int> parent(alg_size(n), 0);
    std::vector<int> size(alg_size(n), 0);
    int i = 0;
    int j = 0;
    int k = 0;
    int width = 1;
    int left = 0;
    int mid = 0;
    int right = 0;
    int edge = 0;
    int u = 0;
    int v = 0;
    int temp = 0;
    int accepted = 0;
    int total = 0;
    while ((i < m)) {
        order[i] = i;
        i = alg_add(i, 1);
    }
    while ((width < m)) {
        left = 0;
        while ((left < m)) {
            mid = alg_min(alg_add(left, width), m);
            right = alg_min(alg_add(left, alg_mul(2, width)), m);
            i = left;
            j = mid;
            k = left;
            while ((k < right)) {
                if (((i < mid) && ((j >= right) || (weight[order[i]] <= weight[order[j]])))) {
                    buffer[k] = order[i];
                    i = alg_add(i, 1);
                } else {
                    buffer[k] = order[j];
                    j = alg_add(j, 1);
                }
                k = alg_add(k, 1);
            }
            left = alg_add(left, alg_mul(2, width));
        }
        i = 0;
        while ((i < m)) {
            order[i] = buffer[i];
            i = alg_add(i, 1);
        }
        width = alg_mul(width, 2);
    }
    i = 0;
    while ((i < n)) {
        parent[i] = i;
        size[i] = 1;
        i = alg_add(i, 1);
    }
    while (((edge < m) && (accepted < alg_sub(n, 1)))) {
        u = from_vertex[order[edge]];
        v = to_vertex[order[edge]];
        while ((parent[u] != u)) {
            parent[u] = parent[parent[u]];
            u = parent[u];
        }
        while ((parent[v] != v)) {
            parent[v] = parent[parent[v]];
            v = parent[v];
        }
        if ((u != v)) {
            if ((size[u] < size[v])) {
                temp = u;
                u = v;
                v = temp;
            }
            parent[v] = u;
            size[u] = alg_add(size[u], size[v]);
            accepted = alg_add(accepted, 1);
            total = alg_add(total, weight[order[edge]]);
        }
        edge = alg_add(edge, 1);
    }
    if ((accepted != alg_sub(n, 1))) {
        return alg_sub(0, 1);
    }
    return total;
}

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, 10};
    int n = 3;
    int result = kruskal(from_vertex, to_vertex, weight, n);
    printf("%d\n", result);
    return 0;
}