Grid Path Counting in Java

// Grid Path Counting in Java
//
// PURPOSE
// Grid path counting counts ways to reach a cell when each step moves only right or down.
// Every path arrives from the cell above or the cell to the left.
//
// METHOD
// Initialize one path along the first row. Update a single row left to right, adding the
// path count from the left to the retained count from above.
//
// COMPLEXITY
// O(rows * cols) time and O(cols) auxiliary space.
//
// CONTRACT
// rows and cols are at least one. Grid has no obstacles. Counts must fit the integer type.
// 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
// Java 17+: primitive int arrays, Arrays.binarySearch for LIS, and Math exact arithmetic.
// Invalid input throws IllegalArgumentException; arithmetic overflow throws
// ArithmeticException.
//
// EXAMPLE
// Expected return: 6.
// Run: javac AlgorithmExample.java && java AlgorithmExample
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

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

    static int grid_paths(int rows, int cols) {
        alg_require(((rows >= 1) && (cols >= 1) && (rows <= 1000000) && (cols <= 1000000)));
        int[] dp = new int[alg_size(cols)];
        int c = 0;
        int r = 1;
        while ((c < cols)) {
            dp[c] = 1;
            c = Math.addExact(c, 1);
        }
        while ((r < rows)) {
            c = 1;
            while ((c < cols)) {
                dp[c] = Math.addExact(dp[c], dp[Math.subtractExact(c, 1)]);
                c = Math.addExact(c, 1);
            }
            r = Math.addExact(r, 1);
        }
        return dp[Math.subtractExact(cols, 1)];
    }

    public static void main(String[] args) {
        int rows = 3;
        int cols = 3;
        int result = grid_paths(rows, cols);
        System.out.println(result);
    }
}