Minimum Grid Path Sum in C

#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <limits.h>
#include <errno.h>
// Minimum Grid Path Sum in C
//
// PURPOSE
// A minimum path through a cost grid combines optimal results from above and left when
// movement is restricted to right or down.
//
// METHOD
// Use one row of cumulative costs. Initialize the first row and column, then add each cell
// cost to the cheaper predecessor.
//
// COMPLEXITY
// O(rows * cols) time, O(cols) auxiliary space.
//
// CONTRACT
// rows,cols>=1. grid is a flattened matrix of nonnegative costs. All sums must fit signed
// 32-bit.
// 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: 7.
// 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 minimum_path_sum(const int *grid, size_t grid_length, int rows, int cols) {
    int alg_error = 0;
    int alg_result = INT_MIN;
    errno = 0;
    int *dp = NULL;
    if (grid_length > 1000000 || (grid_length && !grid)) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (!(((int)grid_length == alg_mul(rows, cols, &alg_error)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    if (!(((rows >= 1) && (cols >= 1) && (rows <= 1000000) && (cols <= 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 = cols;
        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; }
        dp = calloc((size_t)(alg_length ? alg_length : 1), sizeof(*dp));
        if (!dp) { errno = ENOMEM; alg_result = INT_MIN; goto alg_cleanup; }
    }
    int r = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int c = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    while (1) {
        int alg_condition = (r < rows);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (!alg_condition) break;
        c = 0;
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        while (1) {
            int alg_condition = (c < cols);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            if (!alg_condition) break;
            int alg_condition_1 = ((r == 0) && (c == 0));
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            if (alg_condition_1) {
                dp[c] = grid[0];
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            } else {
                int alg_condition_2 = (r == 0);
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                if (alg_condition_2) {
                    dp[c] = alg_add(dp[alg_sub(c, 1, &alg_error)], grid[c], &alg_error);
                    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                } else {
                    int alg_condition_3 = (c == 0);
                    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                    if (alg_condition_3) {
                        dp[c] = alg_add(dp[c], grid[alg_mul(r, cols, &alg_error)], &alg_error);
                        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                    } else {
                        dp[c] = alg_add(alg_min(dp[c], dp[alg_sub(c, 1, &alg_error)]), grid[alg_add(alg_mul(r, cols, &alg_error), c, &alg_error)], &alg_error);
                        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                    }
                }
            }
            c = alg_add(c, 1, &alg_error);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        }
        r = alg_add(r, 1, &alg_error);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    }
    alg_result = dp[alg_sub(cols, 1, &alg_error)];
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    goto alg_cleanup;
alg_cleanup:
    free(dp);
    return alg_result;
}

int main(void) {
    int grid[] = {1, 3, 1, 1, 5, 1, 4, 2, 1};
    int rows = 3;
    int cols = 3;
    int result = minimum_path_sum(grid, 9, rows, cols);
    printf("%d\n", result);
    if (errno) { perror("algorithm"); return 1; }
    return 0;
}