7.1: Compute the extreme value
- Page ID
- 49310
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We will prove that array[1] is the minimum element in the heap. We prove it by seeing a contradiction if some other element is less than the first element. Suppose array[i] is the first instance of the minimum, with array[j] > array[i] for all j < i, and i >= 2. But by the heap invariant array, array[floor(i/2)] <= array[i]: this is a contradiction.
Therefore, it is easy to compute MIN(heap):
MIN(heap)
return heap.array[1];