Can someone give some hints? I have absolutely no clue how heap or anything else fits into this? Thank you!
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I'm not completely sure, but this approach should work — binary search on the final answer.
Assume the answer is <=x. Now, mark arr[i][j]=1 if grid[i][j]<=x and 0 otherwise. Build connected components of 1's in arr. Now the answer is <=x if both the source and destination are 1 and lie in the same connected component of arr. Binary search on x to get your answer.