Given two arrays of numbers a₁,......,a_n and b₁,......, b_n where each number is 0 or 1, the fastest algorithm to find the largest span (i, j) such that a_i+a_i+1......a_j = b_i+b_i+1......b_j or report that there is not such span,

Suppose there are $$\lceil \log n \rceil$$ sorted lists of $$\left\lfloor {{n \over {\log n}}} \right\rfloor $$ elements each. The time complexity of producing a sorted list of all these elements is :
(Hint : Use a heap data structure)

Let G(V, E) an undirected graph with positive edge weights. Dijkstra's single-source shortest path algorithm can be implemented using the binary heap data structure with time complexity:

The elements 32, 15, 20, 30, 12, 25, 16, are inserted one by one in the given order into a max Heap. The resultant max Heap is