GATE | GATE-CS-2015 (Set 2) | Question 65
A Young tableau is a 2D array of integers increasing from left to right and from top to bottom. Any unfilled entries are marked with ∞, and hence there cannot be any entry to the right of, or below a ∞. The following Young tableau consists of unique entries.
1 2 5 14
3 4 6 23
10 12 18 25
31 ∞ ∞ ∞
When an element is removed from a Young tableau, other elements should be moved into its place so that the resulting table is still a Young tableau (unfilled entries may be filled in with a ∞). The minimum number of entries (other than 1) to be shifted, to remove 1 from the given Young tableau is ____________
(A) 2
(B) 5
(C) 6
(D) 18
Answer: (B)
Explanation: Initially
1 2 5 14
3 4 6 23
10 12 18 25
31 ∞ ∞ ∞
When 1 is removed, it is replaced by the smallest adjacent which is 2.
2 2 5 14
3 4 6 23
10 12 18 25
31 ∞ ∞ ∞
When 2 is moved in place of 1, it is replaced by smallest adjacent which is 4
2 4 5 14
3 4 6 23
10 12 18 25
31 ∞ ∞ ∞
When 4 is moved in place of 2, it is replaced by smallest adjacent which is 6
2 4 5 14
3 6 6 23
10 12 18 25
31 ∞ ∞ ∞
When 6 is moved in place of 4, it is replaced by smallest adjacent which is 18.
2 4 5 14
3 6 18 23
10 12 18 25
31 ∞ ∞ ∞
When 18 is moved in place of 6, it is replaced by smallest adjacent which is 25.
2 4 5 14
3 6 18 23
10 12 25 25
31 ∞ ∞ ∞
When 25 is moved in place of 18, it is replaced by smallest adjacent which is ∞.
2 4 5 14
3 6 18 23
10 12 25 ∞
31 ∞ ∞ ∞
Shifted numbers are 2, 4, 6, 18, 25
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Last Updated :
28 Jun, 2021
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