import heapq
from random import random, randrange

@test
def check_invariant(heap):
    # Check the heap invariant.
    for pos, item in enumerate(heap):
        if pos: # pos 0 has no parent
            parentpos = (pos-1) >> 1
            assert heap[parentpos] <= item

@test
def test_heapify():
    for size in list(range(30)) + [20000]:
        heap = [random() for dummy in range(size)]
        heapq.heapify(heap)
        check_invariant(heap)

@test
def test_naive_nbest():
    data = [randrange(2000) for i in range(1000)]
    heap = List[int]()
    for item in data:
        heapq.heappush(heap, item)
        if len(heap) > 10:
            heapq.heappop(heap)
    heap.sort()
    assert heap == sorted(data)[-10:]

def heapiter(heap):
    # An iterator returning a heap's elements, smallest-first.
    while heap:
        yield heapq.heappop(heap)

@test
def test_nbest():
    # Less-naive "N-best" algorithm, much faster (if len(data) is big
    # enough <wink>) than sorting all of data.  However, if we had a max
    # heap instead of a min heap, it could go faster still via
    # heapify'ing all of data (linear time), then doing 10 heappops
    # (10 log-time steps).
    data = [randrange(2000) for i in range(1000)]
    heap = data[:10]
    heapq.heapify(heap)
    for item in data[10:]:
        if item > heap[0]:  # this gets rarer the longer we run
            heapq.heapreplace(heap, item)
    assert list(heapiter(heap)) == sorted(data)[-10:]

@test
def test_nbest_with_pushpop():
    data = [randrange(2000) for i in range(1000)]
    heap = data[:10]
    heapq.heapify(heap)
    for item in data[10:]:
        heapq.heappushpop(heap, item)
    assert list(heapiter(heap)) == sorted(data)[-10:]
    assert heapq.heappushpop(List[str](), 'x') == 'x'

@test
def test_heappushpop():
    h = List[int]()
    x = heapq.heappushpop(h, 10)
    assert (h, x) == (List[int](), 10)

    h = [10]
    x = heapq.heappushpop(h, 9)
    assert (h, x) == ([10], 9)

    h = [10]
    x = heapq.heappushpop(h, 11)
    assert (h, x) == ([11], 10)

@test
def test_heappop_max():
    # _heapop_max has an optimization for one-item lists which isn't
    # covered in other tests, so test that case explicitly here
    h = [3, 2]
    assert heapq._heappop_max(h) == 3
    assert heapq._heappop_max(h) == 2

@test
def test_heapsort():
    # Exercise everything with repeated heapsort checks
    for trial in range(100):
        size = randrange(50)
        data = [randrange(25) for i in range(size)]
        heap = None
        if trial & 1:     # Half of the time, use heapify
            heap = data[:]
            heapq.heapify(heap)
        else:             # The rest of the time, use heappush
            heap = List[int]()
            for item in data:
                heapq.heappush(heap, item)
        heap_sorted = [heapq.heappop(heap) for i in range(size)]
        assert heap_sorted == sorted(data)

'''
def test_merge(self):
    inputs = []
    for i in range(randrange(25)):
        row = []
        for j in range(randrange(100)):
            tup = choice('ABC'), randrange(-500, 500)
            row.append(tup)
        inputs.append(row)

    for key in [None, itemgetter(0), itemgetter(1), itemgetter(1, 0)]:
        for reverse in [False, True]:
            seqs = []
            for seq in inputs:
                seqs.append(sorted(seq, key=key, reverse=reverse))
            self.assertEqual(sorted(chain(*inputs), key=key, reverse=reverse),
                             list(heapq.merge(*seqs, key=key, reverse=reverse)))
            self.assertEqual(list(heapq.merge()), [])

def test_empty_merges(self):
    # Merging two empty lists (with or without a key) should produce
    # another empty list.
    self.assertEqual(list(heapq.merge([], [])), [])
    self.assertEqual(list(heapq.merge([], [], key=lambda: 6)), [])

def test_merge_does_not_suppress_index_error(self):
    # Issue 19018: Heapq.merge suppresses IndexError from user generator
    def iterable():
        s = list(range(10))
        for i in range(20):
            yield s[i]       # IndexError when i > 10
    with self.assertRaises(IndexError):
        list(heapq.merge(iterable(), iterable()))

def test_merge_stability(self):
    class Int(int):
        pass
    inputs = [[], [], [], []]
    for i in range(20000):
        stream = randrange(4)
        x = randrange(500)
        obj = Int(x)
        obj.pair = (x, stream)
        inputs[stream].append(obj)
    for stream in inputs:
        stream.sort()
    result = [i.pair for i in heapq.merge(*inputs)]
    self.assertEqual(result, sorted(result))
'''

def mykey(x: Tuple[int,int]): return (x[0] * 547 % 2000, x[1] * 547 % 2000)

@test
def test_nsmallest():
    data = [(randrange(2000), i) for i in range(1000)]
    for n in (10,):
        assert list(heapq.nsmallest(n, data)) == sorted(data)[:min(n, len(data))]
        assert list(heapq.nsmallest(n, data, key=mykey)) == sorted(data, key=mykey)[:min(n, len(data))]
        assert list(heapq.nsmallest(n, data)) == sorted(data)[:min(n, len(data))]

@test
def test_nlargest():
    data = [(randrange(2000), i) for i in range(1000)]
    for n in (0, 1, 2, 10, 100, 400, 999, 1000, 1100):
        assert list(heapq.nlargest(n, data)) == sorted(data)[::-1][:min(n, len(data))]
        assert list(heapq.nlargest(n, data, key=mykey)) == sorted(data, key=mykey)[::-1][:min(n, len(data))]
        assert list(heapq.nlargest(n, data)) == sorted(data)[::-1][:min(n, len(data))]

@test
def test_comparison_operator():
    def hsort[T](data: List[float]):
        data2 = [T(x) for x in data]
        heapq.heapify(data2)
        return [heapq.heappop(data2).x for i in range(len(data))]
    class LT:
        x: float
        def __init__(self, x: float):
            self.x = x
        def __lt__(self, other: LT):
            return self.x > other.x
    data = [random() for i in range(100)]
    target = list(reversed(sorted(data)))
    assert hsort(data, LT) == target

test_heapify()
test_naive_nbest()
test_nsmallest()
test_nlargest()
test_nbest()
test_nbest_with_pushpop()
test_heappushpop()
test_heappop_max()
test_heapsort()
# test_comparison_operator()