Egg Dropping by Number of Moves in C

#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <limits.h>
#include <errno.h>
// Egg Dropping by Number of Moves in C
//
// PURPOSE
// Instead of trying every floor, this DP counts how many floors can be distinguished with a
// given number of moves and eggs.
//
// METHOD
// For each move, update egg counts downward using
// reachable[e]=reachable[e]+reachable[e-1]+1. Stop when the available egg count covers all
// floors.
//
// COMPLEXITY
// O(eggs * moves) time and O(eggs) space, where moves is the answer.
//
// CONTRACT
// 1<=eggs<=30, 0<=floors<=1000000. Returns the minimum worst-case number of drops.
// Reachability is capped at floors to avoid unnecessary growth.
// 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
// C99: checked calloc/free workspace, const input pointers, explicit size_t lengths. Errors
// return INT_MIN with errno=EINVAL, ERANGE, or ENOMEM. Check errno before using a result.
// Input/output arrays must not alias. No variable-length stack arrays.
//
// EXAMPLE
// Expected return: 14.
// Run: gcc -std=c99 -O2 example.c -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 int alg_checked(int64_t v, int *error) {
    if (v < INT_MIN || v > INT_MAX) { *error = 1; return 0; }
    return (int)v;
}
static int alg_add(int a, int b, int *e) { return alg_checked((int64_t)a+b,e); }
static int alg_sub(int a, int b, int *e) { return alg_checked((int64_t)a-b,e); }
static int alg_mul(int a, int b, int *e) { return alg_checked((int64_t)a*b,e); }

int egg_drop(int eggs, int floors) {
    int alg_error = 0;
    int alg_result = INT_MIN;
    errno = 0;
    int *reachable = NULL;
    if (!(((eggs >= 1) && (eggs <= 30) && (floors >= 0) && (floors <= 1000000)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    {
        int alg_length = alg_add(eggs, 1, &alg_error);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (alg_length < 0 || alg_length > 4000000) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
        reachable = calloc((size_t)(alg_length ? alg_length : 1), sizeof(*reachable));
        if (!reachable) { errno = ENOMEM; alg_result = INT_MIN; goto alg_cleanup; }
    }
    int moves = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int e = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    while (1) {
        int alg_condition = (reachable[eggs] < floors);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (!alg_condition) break;
        moves = alg_add(moves, 1, &alg_error);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        e = eggs;
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        while (1) {
            int alg_condition = (e > 0);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            if (!alg_condition) break;
            reachable[e] = alg_min(floors, alg_add(alg_add(reachable[e], reachable[alg_sub(e, 1, &alg_error)], &alg_error), 1, &alg_error));
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            e = alg_sub(e, 1, &alg_error);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        }
    }
    alg_result = moves;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    goto alg_cleanup;
alg_cleanup:
    free(reachable);
    return alg_result;
}

int main(void) {
    int eggs = 2;
    int floors = 100;
    int result = egg_drop(eggs, floors);
    printf("%d\n", result);
    if (errno) { perror("algorithm"); return 1; }
    return 0;
}