Minimum Grid Path Sum in C#

using System;
// 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
// C# / .NET 10: ReadOnlySpan<int> inputs, Span<int> outputs, primitive workspace arrays,
// Array.BinarySearch for LIS, and checked integer arithmetic. Invalid arguments and overflow
// throw exceptions.
//
// EXAMPLE
// Expected return: 7.
// Run: Use Program.cs in a net10.0 console project; dotnet run.
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

class Program {
    static void alg_require(bool valid) { if (!valid) throw new ArgumentException("invalid algorithm input"); }
    static int alg_size(int n) { alg_require(n>=0 && n<=4000000); return n; }

    static int minimum_path_sum(ReadOnlySpan<int> grid, int rows, int cols) {
        checked {
            alg_require((grid.Length == (rows * cols)));
            alg_require(((rows >= 1) && (cols >= 1) && (rows <= 1000000) && (cols <= 1000000)));
            int[] dp = new int[alg_size(cols)];
            int r = 0;
            int c = 0;
            while ((r < rows)) {
                c = 0;
                while ((c < cols)) {
                    if (((r == 0) && (c == 0))) {
                        dp[c] = grid[0];
                    } else {
                        if ((r == 0)) {
                            dp[c] = (dp[(c - 1)] + grid[c]);
                        } else {
                            if ((c == 0)) {
                                dp[c] = (dp[c] + grid[(r * cols)]);
                            } else {
                                dp[c] = (Math.Min(dp[c], dp[(c - 1)]) + grid[((r * cols) + c)]);
                            }
                        }
                    }
                    c = (c + 1);
                }
                r = (r + 1);
            }
            return dp[(cols - 1)];
        }
    }

    static void Main() {
        int[] grid = new int[] {1, 3, 1, 1, 5, 1, 4, 2, 1};
        int rows = 3;
        int cols = 3;
        int result = minimum_path_sum(grid, rows, cols);
        Console.WriteLine(result);
    }
}