Problem 54730. Local Extrema

Created by Dyuman Joshi

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Given a 2D (m,n>1) matrix, replace an element if it is not a local extrema (minima/maxima), with 0 (zero).
The comparison criteria for an extrema should be strict (> or <). (See example #1)
Check the 3 neighbours of the corner points, 5 for elements on the edge and 8 for elements in the middle.
%Example #1
x=[1 2 3
   2 3 1
   3 1 2];
y=[1 0 0
   0 0 0
   0 0 0];
%Example #2
x=[1     4     7    33    12     6    17
  29     8    20    13     3    -1     2
  19    14    26    -8    22    20     4
   1     6     4    17    34    14     2
 -23    27    31     9    30     3    10];
y=[1     0     0    33     0     0    17
  29     0     0     0     0    -1     0
   0     0    26    -8     0     0     0
   0     0     0     0    34     0     2
 -23     0    31     0     0     0     0]
%Example #3
x=[-5   -31   -17    -3   -23   -11
   -2   -37   -19    -7   -13   -29];
y=[0     0     0    -3     0   -11
  -2   -37     0     0     0   -29];
More test cases might be added later.

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Last Solution submitted on Jul 18, 2024

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ChrisR on 10 Jun 2022

Dyuman, Test 5 is missing a parenthesis.

Dyuman Joshi on 11 Jun 2022

Fixed. It's always something with my test suite :')

William on 11 Jun 2022

Dyuman, Thanks for the problem. It might be good to add that what you mean by a local maximum is not only that the value is the largest value, but also that it is strictly greater than the second largest. Likewise for a local minimum.

Dyuman Joshi on 11 Jun 2022

William, thanks for the comment.

I thought the value of extrema was based on strict criteria. I stand corrected. The problem statement has been updated.

William on 12 Jun 2022

Yes, if this were a continuous function, an extremum would imply that the value was strictly the largest. In the case of a set of discrete values, though, it may be debatable whether two equally large neighbors should be considered as 2 maxima or not.

Dyuman Joshi on 13 Jun 2022

I see, thanks for the clarification!

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Problem 54730. Local Extrema

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