ITPEC FE Morning October 2022 Question 8
ITPEC FE Morning October 2022 — Question 8 of 80
Row-Major vs Column-Major Memory Mapping — count elements at the same address in both orderings.
For array A(5,5) with 1-based indexing, the position in a 1D array:
- •Row-major:
pos = (i-1)*5 + (j-1) - •Column-major:
pos = (j-1)*5 + (i-1)
Set them equal:
- •
(i-1)*5 + (j-1) = (j-1)*5 + (i-1) - •
4(i-1) = 4(j-1)→i = j
All main diagonal elements match: A(1,1), A(2,2), A(3,3), A(4,4), A(5,5) → 5 elements
Why not others:
- (a) 2, (b) 3, (c) 4 — the diagonal of an N×N matrix always has exactly N elements
Key rule: In an N×N array, row-major and column-major orderings place the same element at the same address only when i = j (the main diagonal), giving exactly N matches.
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