We have an N*N matrix, can we achieve better than transposing the matrix into an array, and then sorting it?
I did some online searching and found that quickselect eliminates the log factor, how can we extend quickselect to 2 dimensions?
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Convert the matrix to an array first, then use
nth_element(x,x+n/2,x+n). The overall complexity is the same as the input complexity, which has reached the lower bound.nth_element is $$$\Theta(n)$$$.
nth_element is $$$O(n) $$$, not $$$\Theta(n)$$$
You're wrong, it's $$$\Theta(n)$$$, because it takes at least a linear perusal of all the elements to determine the value of the nth.
Just use the Thanos algorithm: among $$$n^2$$$ elements of the matrix, select random $$$n$$$ and find their median with
nth_element;-)How can we efficiently select n random elements from the matrix without iterating over the full matrix?
And let's we want to extend the program, and find the smallest median among every submatrix of size K*K, how can we solve this?
binary search
With binary search wouldnt it be N^2*K*logK, but can we achieve N^2*K or better?
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