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Find bitonic point in given bitonic sequence in Python

Suppose we have a bitonic sequence, we have to find the Bitonic Point in it. As we know a Bitonic Sequence is a sequence of numbers which is first strictly increasing then after a certain point it is strictly decreasing. This point is bitonic point. For only increasing or only decreasing sequences, bitonic points are not available.

So, if the input is like [7, 8, 9, 12, 10, 6, 3, 2], then the output will be 12

To solve this, we will follow these steps −

  • define a function binary_search(array, l, r)
  • if l <= r, then −
    • m := (l + r) / /2
  • if array[m - 1] < array[m] and array[m] > array[m + 1], then −
    • return m
  • if array[m] < array[m + 1], then −
    • return binary_search(array, m + 1, r)
  • Otherwise
    • return binary_search(array, l, m - 1)
  • return -1

Example

Let us see the following implementation to get better understanding −

def binary_search(array, l, r):
   if (l <= r):
      m = (l + r) // 2;
      if (array[m - 1] < array[m] and array[m] > array[m + 1]):
         return m;
      if (array[m] < array[m + 1]):
         return binary_search(array, m + 1,r);
      else:
         return binary_search(array, l, m - 1);
   return -1;
array = [7, 8, 9, 12, 10, 6, 3, 2]
n = len(array);
index = binary_search(array, 1, n-2);
if (index != -1):
   print(array[index]);

Input

[7, 8, 9, 12, 10, 6, 3, 2]

Output

12