Greedy Interval Scheduling in C++

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Greedy Interval Scheduling in C++
//
// PURPOSE
// Earliest-finish-time scheduling selects a maximum-size collection of non-overlapping
// intervals.
//
// METHOD
// Process intervals sorted by finish time. Accept the next interval whenever its start is at
// least the finish of the last accepted interval.
//
// COMPLEXITY
// O(n) scan time and O(1) auxiliary space once sorted; sorting unsorted intervals first
// costs O(n log n).
//
// CONTRACT
// start and finish arrays have n entries; finish is nondecreasing and start[i]<finish[i].
// Half-open intervals allow touching endpoints. Returns selected count.
// 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: 4.
// 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 interval_schedule(const std::vector<int>& start, const std::vector<int>& finish) {
    alg_require(start.size() <= 1000000);
    alg_require(finish.size() <= 1000000);
    int n = (int)start.size();
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((int)start.size() == n));
    alg_require(((int)finish.size() == n));
    int count = 0;
    int end = 0;
    int i = 0;
    while ((i < n)) {
        if (((count == 0) || (start[i] >= end))) {
            count = alg_add(count, 1);
            end = finish[i];
        }
        i = alg_add(i, 1);
    }
    return count;
}

int main(void) {
    std::vector<int> start = {1, 3, 0, 5, 8, 5};
    std::vector<int> finish = {2, 4, 6, 7, 9, 9};
    int result = interval_schedule(start, finish);
    printf("%d\n", result);
    return 0;
}