Greedy Interval Scheduling in Java

// Greedy Interval Scheduling in Java
//
// PURPOSE
// Earliest-finish-time scheduling selects a maximum-size collection of non-overlapping
// intervals.
//
// METHOD
// Process intervals sorted by finish time. Accept the next interval whenever its start is at
// least the finish of the last accepted interval.
//
// COMPLEXITY
// O(n) scan time and O(1) auxiliary space once sorted; sorting unsorted intervals first
// costs O(n log n).
//
// CONTRACT
// start and finish arrays have n entries; finish is nondecreasing and start[i]<finish[i].
// Half-open intervals allow touching endpoints. Returns selected 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: 4.
// 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 interval_schedule(int[] start, int[] finish) {
        java.util.Objects.requireNonNull(start, "start");
        java.util.Objects.requireNonNull(finish, "finish");
        int n = start.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((start.length == n));
        alg_require((finish.length == n));
        int count = 0;
        int end = 0;
        int i = 0;
        while ((i < n)) {
            if (((count == 0) || (start[i] >= end))) {
                count = Math.addExact(count, 1);
                end = finish[i];
            }
            i = Math.addExact(i, 1);
        }
        return count;
    }

    public static void main(String[] args) {
        int[] start = new int[] {1, 3, 0, 5, 8, 5};
        int[] finish = new int[] {2, 4, 6, 7, 9, 9};
        int result = interval_schedule(start, finish);
        System.out.println(result);
    }
}