GATE CS 2015 Set 2 — Question 48
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Programming & Data Structures → Arrays & Strings → Array Operations (1D, 2D)
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Question
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.
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 ______.
| 1 | 2 | 5 | 14 |
|---|---|---|---|
| 3 | 4 | 6 | 23 |
| 10 | 12 | 18 | 25 |
| 31 |
Correct answer
5 to 5
Solution
To remove the element 1 at position , we replace it with the smaller of its neighbors (right or down) to maintain the sorted property. We repeat this process until we reach an or the boundary.
1.Start at (value 1 removed). Compare neighbors and . Min is 2. Shift 2 to . Hole moves to .
2.At . Compare neighbors and . Min is 4. Shift 4 to . Hole moves to .
3.At . Compare neighbors and . Min is 6. Shift 6 to . Hole moves to .
4.At . Compare neighbors and . Min is 18. Shift 18 to . Hole moves to .
5.At . Compare neighbors and . Min is 25. Shift 25 to . Hole moves to .
6.At . Neighbors are (out of bounds/) and . Both are . Fill hole with . Stop.
The elements shifted are: 2, 4, 6, 18, 25. Total count = 5.Continue learning with Success Tracker
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