1.7 KiB
A peak in a 2D list of values is a value that is not smaller than its 4 neighbours. Assume all values are natural numbers.
For example, consider the following list of values a = [[10, 8, 10, 10], [14, 13, 12, 11], [15, 9, 11, 21], [16, 17, 19, 20]]
Here, 21 is the only peak.
Write a python program that uses recursion to find a peak (not all, just one peak) given a list of 2D values (m columns, n rows). Your function should return the list index as a tuple of the peak. To do so you must implement the following recursive algorithm that uses the same idea as binary search (i.e., divide and conquer). • Pick middle column j = m//2 • Find global max on column j at (i, j), if there are multiple global max, pick the smallest possible i • Compare (i, j-1), (i, j), (i, j+1) • Pick left columns if (i, j-1) > (i, j) ◦ Similar for right • (i, j) is a 2D-peak if neither conditions holds • Solve the new problem with half the number of columns • When you have a single column, find global max and you are done (again, if there are multiple global max, pick the smallest possible index)
Similar to Q4, this method will always find a specific peak among all the others that may exist in the list of 2D values. Your program must follow this behaviour.
Input specification: • n lines and m columns of numbers separated by space • follow by an empty line input to determine the end of the input
Output specification: • The index as a tuple of the peak
Sample testcases (The bolded text are user input, including the blank line)
Case 1: 10 8 10 10 14 13 12 11 15 9 11 21 16 17 19 20
(2, 3)
Case 2: 1 2 3 4 5 6 7 8 9 10 11 12
(3, 2)