Iterative Binary Tree Postorder in Java

// Iterative Binary Tree Postorder in Java
//
// PURPOSE
// Postorder traversal visits each binary-tree node once without recursion.
//
// METHOD
// Keep a stack of nodes and visit states. State zero descends left, state one descends
// right, and state two exits. Emit the node at the traversal-specific state.
//
// COMPLEXITY
// O(n) time and O(n) allocated stack space; live stack usage is O(tree height).
//
// CONTRACT
// Parallel left_child and right_child arrays contain -1 or node IDs. root=-1 means empty.
// The structure must be a valid tree, not cyclic or shared. output has n entries; writes
// node IDs and returns visited 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
// Java 17+: primitive int arrays, Arrays.binarySearch for LIS, and Math exact arithmetic.
// Invalid input throws IllegalArgumentException; arithmetic overflow throws
// ArithmeticException.
//
// EXAMPLE
// Expected return: 3.
// Expected output after call: [1, 2, 0].
// 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 tree_postorder(int[] left_child, int[] right_child, int root, int[] output) {
        java.util.Objects.requireNonNull(left_child, "left_child");
        java.util.Objects.requireNonNull(right_child, "right_child");
        java.util.Objects.requireNonNull(output, "output");
        int n = left_child.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((left_child.length == n));
        alg_require((right_child.length == n));
        alg_require((output.length == n));
        alg_require(((root >= Math.negateExact(1)) && (root < n)));
        for (int alg_i = 0; alg_i < left_child.length; alg_i++) {
            int alg_value = left_child[alg_i];
            alg_require(((alg_value >= Math.negateExact(1)) && (alg_value < n)));
        }
        for (int alg_i = 0; alg_i < right_child.length; alg_i++) {
            int alg_value = right_child[alg_i];
            alg_require(((alg_value >= Math.negateExact(1)) && (alg_value < n)));
        }
        int[] stack = new int[alg_size(Math.addExact(n, 1))];
        int[] state = new int[alg_size(Math.addExact(n, 1))];
        int top = 0;
        int u = 0;
        int phase = 0;
        int count = 0;
        if ((root == Math.negateExact(1))) {
            return 0;
        }
        stack[0] = root;
        top = 1;
        while ((top > 0)) {
            u = stack[Math.subtractExact(top, 1)];
            phase = state[Math.subtractExact(top, 1)];
            if ((phase == 2)) {
                output[count] = u;
                count = Math.addExact(count, 1);
            }
            if ((phase == 0)) {
                state[Math.subtractExact(top, 1)] = 1;
                if ((left_child[u] != Math.negateExact(1))) {
                    stack[top] = left_child[u];
                    state[top] = 0;
                    top = Math.addExact(top, 1);
                }
            } else {
                if ((phase == 1)) {
                    state[Math.subtractExact(top, 1)] = 2;
                    if ((right_child[u] != Math.negateExact(1))) {
                        stack[top] = right_child[u];
                        state[top] = 0;
                        top = Math.addExact(top, 1);
                    }
                } else {
                    top = Math.subtractExact(top, 1);
                }
            }
        }
        return count;
    }

    public static void main(String[] args) {
        int[] left_child = new int[] {1, -1, -1};
        int[] right_child = new int[] {2, -1, -1};
        int root = 0;
        int[] output = new int[] {0, 0, 0};
        int result = tree_postorder(left_child, right_child, root, output);
        System.out.println(result);
        // Expected output: [1, 2, 0]
        System.out.println(java.util.Arrays.toString(output));
    }
}