Subset Sum Decision in C++

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Subset Sum Decision in C++
//
// PURPOSE
// Subset sum asks whether some selection of items totals an exact target. A reachability
// table records which sums can be formed.
//
// METHOD
// Mark zero reachable. For each item, scan sums downward and mark a sum reachable if it
// already was or if the sum minus the item was reachable before this item.
//
// COMPLEXITY
// O(n * target) time and O(target) auxiliary space; pseudo-polynomial.
//
// CONTRACT
// Items and target are nonnegative integers. Each input position can be used once. Returns 1
// if reachable, otherwise 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 subset_sum(const std::vector<int>& a, int target) {
    alg_require(a.size() <= 1000000);
    int n = (int)a.size();
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((int)a.size() == n));
    alg_require(((target >= 0) && (target <= 1000000)));
    for (int alg_i = 0; alg_i < (int)a.size(); alg_i++) {
        int alg_value = a[alg_i];
        alg_require((alg_value >= 0));
    }
    std::vector<int> dp(alg_size(alg_add(target, 1)), 0);
    dp[0] = 1;
    int i = 0;
    int s = 0;
    while ((i < n)) {
        s = target;
        while ((s >= a[i])) {
            if ((dp[alg_sub(s, a[i])] != 0)) {
                dp[s] = 1;
            }
            s = alg_sub(s, 1);
        }
        i = alg_add(i, 1);
    }
    return dp[target];
}

int main(void) {
    std::vector<int> a = {3, 4, 5};
    int target = 9;
    int result = subset_sum(a, target);
    printf("%d\n", result);
    return 0;
}