Levenshtein Edit Distance in C++

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Levenshtein Edit Distance in C++
//
// PURPOSE
// Edit distance counts the minimum unit-cost insertions, deletions, and substitutions needed
// to turn one token sequence into another.
//
// METHOD
// Retain one row and the previous diagonal. Equal tokens keep the diagonal distance.
// Different tokens add one to the cheapest deletion, insertion, or substitution.
//
// COMPLEXITY
// O(nm) time and O(min(n,m)) auxiliary space. The public function automatically orients the
// shorter input as its work row.
//
// CONTRACT
// Inputs are integer tokens. For text, tokenize consistently before calling; Unicode
// normalization and grapheme rules are separate concerns. Returns distance only.
// 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 edit_distance(const std::vector<int>& a, const std::vector<int>& b) {
    alg_require(a.size() <= 1000000);
    alg_require(b.size() <= 1000000);
    int n = (int)a.size();
    int m = (int)b.size();
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((m >= 0) && (m <= 1000000)));
    alg_require(((int)a.size() == n));
    alg_require(((int)b.size() == m));
    if (n < m) return edit_distance(b, a);
    std::vector<int> dp(alg_size(alg_add(m, 1)), 0);
    int i = 0;
    int j = 0;
    int diagonal = 0;
    int old = 0;
    while ((j <= m)) {
        dp[j] = j;
        j = alg_add(j, 1);
    }
    while ((i < n)) {
        diagonal = dp[0];
        dp[0] = alg_add(i, 1);
        j = 1;
        while ((j <= m)) {
            old = dp[j];
            if ((a[i] == b[alg_sub(j, 1)])) {
                dp[j] = diagonal;
            } else {
                dp[j] = alg_add(1, alg_min(dp[j], alg_min(dp[alg_sub(j, 1)], diagonal)));
            }
            diagonal = old;
            j = alg_add(j, 1);
        }
        i = alg_add(i, 1);
    }
    return dp[m];
}

int main(void) {
    std::vector<int> a = {1, 2, 3};
    std::vector<int> b = {1, 4, 3, 5};
    int result = edit_distance(a, b);
    printf("%d\n", result);
    return 0;
}