Syntax error Find longest bitonic sequence such that increasing and decreasing parts are from two different arrays in Python

Find longest bitonic sequence such that increasing and decreasing parts are from two different arrays in Python

Suppose we have two arrays; we have to find the longest possible bitonic sequence so that the increasing part should be from first array and should be a subsequence of first array. similarly decreasing part of must be from second array and a subsequence of the second one.

So, if the input is like A = [2, 6, 3, 5, 4, 6], B = [9, 7, 5, 8, 4, 3], then the output will be [2, 3, 4, 6, 9, 7, 5, 4, 3]

To solve this, we will follow these steps −

  • Define a function index_ceiling() . This will take arr, T, left, right, key

  • while right - left > 1, do

    • mid := left +(right - left) / 2;

    • if arr[T[mid]] >= key, then

      • right := mid

    • otherwise,

      • left := mid

  • return right

  • Define a function long_inc_seq() . This will take A

  • n := size of A

  • tails_idx := an array of size n, fill with 0

  • prev_idx := an array of size n, fill with -1

  • length := 1

  • for i in range 1 to n, do

    • if A[i] < A[tails_idx[0]], then

      • tails_idx[0] := i

    • otherwise when A[i] > A[tails_idx[length - 1]], then

      • prev_idx[i] := tails_idx[length - 1]

      • tails_idx[length] := i

      • length := length + 1

    • otherwise,

      • pos := index_ceiling(A, tails_idx, -1, length - 1, A[i])

      • prev_idx[i] := tails_idx[pos - 1]

      • tails_idx[pos] := i

  • i := tails_idx[length - 1]

  • while i >= 0, do

    • insert A[i] at the end of answer

    • i := prev_idx[i]

  • From the main method, do the following −

  • n1 := size of A, n2 := size of B

  • long_inc_seq(A)

  • answer := reverse answer

  • B := reverse B

  • long_inc_seq(B)

  • return answer

Example

Let us see the following implementation to get better understanding −

answer = []
def index_ceiling(arr,T, left,right, key):
   while (right - left > 1):
      mid = left + (right - left) // 2;
      if (arr[T[mid]] >= key):
         right = mid
      else:
         left = mid
   return right
def long_inc_seq(A):
   n = len(A)
   tails_idx = [0]*(n)
   prev_idx = [-1]*(n)
   length = 1
   for i in range(1, n):
      if (A[i] < A[tails_idx[0]]):
         tails_idx[0] = i
      elif (A[i] > A[tails_idx[length - 1]]):
         prev_idx[i] = tails_idx[length - 1]
         tails_idx[length] = i
         length += 1
      else:
         pos = index_ceiling(A, tails_idx, -1, length - 1, A[i])
         prev_idx[i] = tails_idx[pos - 1]
         tails_idx[pos] = i
   i = tails_idx[length - 1]
   while(i >= 0):
      answer.append(A[i])
      i = prev_idx[i]
def long_bitonic(A,B):
   n1 = len(A)
   n2 = len(B)
   global answer
   long_inc_seq(A)
   answer = answer[::-1]
   B = B[::-1]
   long_inc_seq(B)
A = [2, 6, 3, 5, 4, 6]
B = [9, 7, 5, 8, 4, 3]
long_bitonic(A,B)
print(answer)

Input

[2, 6, 3, 5, 4, 6], [9, 7, 5, 8, 4, 3]

Output

[2, 3, 4, 6, 9, 7, 5, 4, 3]
Updated on: 2020-08-25T09:56:08+05:30

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