algorithm - Intersection of two maximum heaps -


i have 2 maximum-heaps (represented in arrays), h1 of size m , h2 of size n, n>m. have create third max-heap elements coming intersection of h1 , h2.

the elementary solution (scan 2 arrays) takes o(n*m) time, , doesn't take advantage of max-heap properties.

other ideas?

given 2 heaps, can compute intersection of elements in o(m log m + n log n) time, , result ordered. ordered array heap, no further time required.

python-syntax example:

# given arrays heap1, heap2.  intersection = [] while len(heap1) > 0 , len(heap2) > 0:     if heap1[0] == heap2[0]:         # common element, part of intersection.         intersection.append(heap1[0])         heap.heappop(heap1)         heap.heappop(heap2)     elif heap1[0] > heap2[0]:         heap.heappop(heap1)     else:         heap.heappop(heap2)  # intersection contains common elements of heap1 , heap2, # in max-to-min order, meets heap invariant.

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