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Program to find length of longest increasing subsequence with at least k odd values in Python
Suppose we have a list of numbers called nums and another value k, we have to find the size of the longest increasing subsequence with at least k odd elements.
So, if the input is like nums = [12, 14, 16, 5, 7, 8] k = 2, then the output will be 3, as the longest increasing subsequence with at least 2 odd values is [5, 7, 8].
To solve this, we will follow these steps −
best := 0
Define a function dp() . This will take i, j, odd, taken
if odd >= k, then
best := maximum of best and taken
if j is same as size of nums , then
return
if nums[j] > nums[i], then
dp(j, j + 1, odd +(nums[j] AND 1) , taken + 1)
dp(i, j + 1, odd, taken)
From the main method do the following −
for i in range 0 to size of nums, do
dp(i, i + 1, nums[i] AND 1, 1)
return best
Example
Let us see the following implementation to get better understanding −
class Solution: def solve(self, nums, k): best = 0 def dp(i, j, odd, taken): nonlocal best if odd >= k: best = max(best, taken) if j == len(nums): return if nums[j] > nums[i]: dp(j, j + 1, odd + (nums[j] & 1), taken + 1) dp(i, j + 1, odd, taken) for i in range(len(nums)): dp(i, i + 1, nums[i] & 1, 1) return best ob = Solution() nums = [12, 14, 16, 5, 7, 8] k = 2 print(ob.solve(nums, k))
Input
[12, 14, 16, 5, 7, 8], 2
Output
3
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