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GATE | GATE-CS-2015 (Set 2) | Question 65

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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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