/**
 * Priority queue for bidirectional BFS frontier management.
 *
 * Min-heap implementation that returns items with lowest priority first.
 * Includes duplicate prevention and iteration support.
 *
 * Time Complexity:
 * - push: O(log n)
 * - pop: O(log n)
 * - contains: O(1)
 * - length: O(1)
 *
 * Space Complexity: O(n) for heap array and item set
 *
 * @template T - Type of items stored in the queue
 * @example
 * ```typescript
 * const queue = new PriorityQueue<string>();
 * queue.push('nodeA', 10);  // Low-degree node (high priority)
 * queue.push('nodeB', 100); // High-degree node (low priority)
 *
 * const next = queue.pop(); // Returns 'nodeA' (lower degree = higher priority)
 * ```
 */
export declare class PriorityQueue<T> {
    private heap;
    private itemSet;
    /**
     * Add an item to the queue with given priority.
     * Silently ignores duplicates.
     *
     * @param item - Item to add
     * @param priority - Priority value (lower values = higher priority)
     */
    push(item: T, priority: number): void;
    /**
     * Remove and return the item with lowest priority.
     *
     * @returns Item with minimum priority, or undefined if queue is empty
     */
    pop(): T | undefined;
    /**
     * Get the number of items in the queue.
     */
    get length(): number;
    /**
     * Peek at the priority of the minimum item without removing it.
     *
     * @returns Priority of the item with minimum priority, or Infinity if queue is empty
     */
    peekPriority(): number;
    /**
     * Check if an item is in the queue.
     *
     * @param item - Item to check
     * @returns true if item is in queue
     */
    contains(item: T): boolean;
    /**
     * Make the queue iterable for checking connections.
     * Iterates over items in no particular order (not sorted by priority).
     */
    [Symbol.iterator](): Iterator<T>;
    /**
     * Bubble up an element to maintain min-heap property.
     * @param index
     * @internal
     */
    private bubbleUp;
    /**
     * Bubble down an element to maintain min-heap property.
     * @param index
     * @internal
     */
    private bubbleDown;
}
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