Dot Star Regular Expression Matching in C++

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Dot Star Regular Expression Matching in C++
//
// PURPOSE
// This small matcher supports whole-sequence matching with a wildcard token and repetition
// of the preceding token.
//
// METHOD
// Use a table of prefix matches. A star can omit its preceding token or consume another
// matching text token. A non-star token extends the previous diagonal.
//
// COMPLEXITY
// O(nm) time and O(nm) space. Only dot and star semantics are supported; this is not a full
// regex engine.
//
// CONTRACT
// Tokens >=0 are literal; -1 is dot and -2 is star in the pattern. Star must follow a
// literal or dot, never another star. Returns 1 or 0.
// 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: 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 regex_match(const std::vector<int>& text, const std::vector<int>& pattern) {
    alg_require(text.size() <= 1000000);
    alg_require(pattern.size() <= 1000000);
    int n = (int)text.size();
    int m = (int)pattern.size();
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((m >= 0) && (m <= 1000000)));
    alg_require(((int)pattern.size() == m));
    alg_require(((int)text.size() == n));
    for (int alg_i = 0; alg_i < m; alg_i++) {
        alg_require((pattern[alg_i] >= alg_sub(0, 2)));
        alg_require(((pattern[alg_i] != alg_sub(0, 2)) || ((alg_i > 0) && (pattern[alg_sub(alg_i, 1)] != alg_sub(0, 2)))));
    }
    std::vector<int> dp(alg_size(alg_mul(alg_add(n, 1), alg_add(m, 1))), 0);
    dp[0] = 1;
    int i = 0;
    int j = 2;
    while ((j <= m)) {
        if ((pattern[alg_sub(j, 1)] == alg_sub(0, 2))) {
            dp[j] = dp[alg_sub(j, 2)];
        }
        j = alg_add(j, 1);
    }
    i = 1;
    while ((i <= n)) {
        j = 1;
        while ((j <= m)) {
            if ((pattern[alg_sub(j, 1)] == alg_sub(0, 2))) {
                dp[alg_add(alg_mul(i, alg_add(m, 1)), j)] = dp[alg_sub(alg_add(alg_mul(i, alg_add(m, 1)), j), 2)];
                if (((pattern[alg_sub(j, 2)] == alg_sub(0, 1)) || (pattern[alg_sub(j, 2)] == text[alg_sub(i, 1)]))) {
                    dp[alg_add(alg_mul(i, alg_add(m, 1)), j)] = alg_max(dp[alg_add(alg_mul(i, alg_add(m, 1)), j)], dp[alg_add(alg_mul(alg_sub(i, 1), alg_add(m, 1)), j)]);
                }
            } else {
                if (((pattern[alg_sub(j, 1)] == alg_sub(0, 1)) || (pattern[alg_sub(j, 1)] == text[alg_sub(i, 1)]))) {
                    dp[alg_add(alg_mul(i, alg_add(m, 1)), j)] = dp[alg_sub(alg_add(alg_mul(alg_sub(i, 1), alg_add(m, 1)), j), 1)];
                }
            }
            j = alg_add(j, 1);
        }
        i = alg_add(i, 1);
    }
    return dp[alg_add(alg_mul(n, alg_add(m, 1)), m)];
}

int main(void) {
    std::vector<int> text = {1, 1, 2};
    std::vector<int> pattern = {1, -2, 2};
    int result = regex_match(text, pattern);
    printf("%d\n", result);
    return 0;
}