F004A. Layers of onion P88060


Statement
 

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[r] Given a matrix, all the elements which are in the first row, in the first column, in the last row and the last column, form the first layer of the matrix. Equally, the elements which are in the second row, in the second column, in the penultimate row and the penultimate column (but that are not in the first layer), form the second layer. The concept of layer becomes generalized in the same way for all the elements of the matrix.

For instance, for a matrix with 8 rows and 9 columns, the next diagram shows in which layer is each element of the matrix:

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111111111
122222221
123333321
123444321
123444321
123333321
122222221
111111111

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Your task is to write a program that, given different integer matrices, calculates, for each one, the values of the minimum and the maximum of all their layers. For instance, for the matrix

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1519292821519292
46311333246321313
1533222216123414
2317331223173221
1363562211362664
43985211439864
5396642176399614
9994551219994551

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The minimum and the maximum of the first layer are 1 and 99, the minimum and the maximum of the second layer are 3 and 99, the minimum and the maximum of the third layer are 2 and 62, and the minimum and the maximum of the fourth layer are 1 and 23. We represent this information with a vector of pairs:

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1,993,992,621,23

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The main program is already done; do not modify it. Using the types

int min, max; }; typedef vector<vector<int> > Matrix;

You must implement the function

that, given a rectangular matrix |mat| (with, at least, a row and a column), returns a vector with as many positions as layers has the matrix, where the position i of the vector contains the minimum and the maximum values of the layer i+1 of |mat|.

Public test cases
  • Input

    8 9
    15  1 92 92 82 15  1 92 92 
    46 31 13  3 32 46 32 13 13 
    15  3 32  2 22 16 12 34 14 
    23 17 33  1  2 23 17 32 21 
    13 63 56  2 21 13 62 66  4 
    43  9  8 52 11 43  9  8 64 
    53 96  6 42 17 63 99  6 14 
    99 94  5 51 21 99 94  5 51 
    
    10 10
    1 1 1 1 1 1 1 1 1 1
    1 2 2 2 2 2 2 2 2 1
    1 2 3 3 3 3 3 3 2 1
    1 2 3 4 4 4 4 3 2 1
    1 2 3 4 5 5 4 3 2 1
    1 2 3 4 5 5 4 3 2 1
    1 2 3 4 4 4 4 3 2 1
    1 2 3 3 3 3 3 3 2 1
    1 2 2 2 2 2 2 2 2 1
    1 1 1 1 1 1 1 1 1 1
    
    5 4
     1  2  3  4
     5  6  7  8
     9  1 11 12
    13 14 15 16
    17 28 29 20
    
    3 5
    11 21 31 74 85  
    17 18 69 10 11 
    13 14 15 16 17 
    
    1 1
    -666
    
    3 1
    10000001
    -10000001
    0
    
    1 9
    6 6 6 8 8 8 9 9 9
    
    

    Output

    matriu 1: 1,99 3,99 2,62 1,23
    matriu 2: 1,1 2,2 3,3 4,4 5,5
    matriu 3: 1,29 1,15
    matriu 4: 11,85 10,69
    matriu 5: -666,-666
    matriu 6: -10000001,10000001
    matriu 7: 6,9
    
  • Information
    Author
    Professorat de P1
    Language
    English
    Translator
    Carlos Molina
    Original language
    Catalan
    Other languages
    Catalan
    Official solutions
    C++
    User solutions
    C++