algorithm - Combining integer vectors -

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i have vector of length k each element 2-by-m matrix mapping between indices. elements integers set {1,2,...,mn}, there no duplicates within given 2-by-m matrix, , know m , n are. want efficient way of finding n-1 of these 2-by-m matrices such combining these mappings gives me of elements in {1,2,...,mn}. make things more concrete, assume m=n=3 , vector is

4 3 6
2 7 5

4 6 3
1 9 8

9 1 8
6 2 7

7 8 3
2 1 4

i want algorithm output

4 3 6
2 7 5
1 8 9

which found combining first 2 mappings.


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