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Program to find minimum number of operations required to make lists strictly Increasing in python

Suppose we have two list of numbers called A and B, and they are of same length. Now consider we can perform an operation where we can swap numbers A[i] and B[i]. We have to find the number of operations required to make both lists strictly increasing.

So, if the input is like A = [2, 8, 7, 10] B = [2, 4, 9, 10], then the output will be 1, as we can swap 7 in A and 9 in B. Then the lists will be like A = [2, 8, 9, 10] and B = [2, 4, 7, 10] which are both strictly increasing lists.

To solve this, we will follow these steps:

  • Define a function dp() . This will take i, prev_swapped
  • if size of A is same as i, then
    • return 0
  • otherwise when i is same as 0, then
    • return minimum of dp(i + 1, False) and 1 + dp(i + 1, True)
  • otherwise,
    • prev_A := A[i - 1]
    • prev_B := B[i - 1]
    • if prev_swapped is True, then
      • swap prev_A and prev_B
    • if A[i] <= prev_A or B[i] <= prev_B, then
      • return 1 + dp(i + 1, True)
    • otherwise,
      • ans := dp(i + 1, False)
      • if A[i] > prev_B and B[i] > prev_A, then
        • ans := minimum of ans, 1 + dp(i + 1, True)
      • return ans
    • From the main method call the function dp(0, False) and return its value as result

Let us see the following implementation to get better understanding:

Example Code

class Solution:
   def solve(self, A, B):
      def dp(i=0, prev_swapped=False):
         if len(A) == i:
            return 0
         elif i == 0:
            return min(dp(i + 1), 1 + dp(i + 1, True))
         else:
            prev_A = A[i - 1]
            prev_B = B[i - 1]
            if prev_swapped:
               prev_A, prev_B = prev_B, prev_A
            if A[i] <= prev_A or B[i] <= prev_B:
               return 1 + dp(i + 1, True)
            else:
               ans = dp(i + 1)
            if A[i] > prev_B and B[i] > prev_A:
               ans = min(ans, 1 + dp(i + 1, True))
            return ans

         return dp()

ob = Solution()
A = [2, 8, 7, 10]
B = [2, 4, 9, 10]
print(ob.solve(A, B))

Input

[2, 8, 7, 10], [2, 4, 9, 10]

Output

1