Leetcode #1966: Binary Searchable Numbers in an Unsorted Array
In this guide, we solve Leetcode #1966 Binary Searchable Numbers in an Unsorted Array in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Consider a function that implements an algorithm similar to Binary Search. The function has two input parameters: sequence is a sequence of integers, and target is an integer value.
Quick Facts
- Difficulty: Medium
- Premium: Yes
- Tags: Array, Binary Search
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
func(sequence, target)
while sequence is not empty
randomly choose an element from sequence as the pivot
if pivot = target, return true
else if pivot < target, remove pivot and all elements to its left from the sequence
else, remove pivot and all elements to its right from the sequence
end while
return false
Python Solution
class Solution:
def binarySearchableNumbers(self, nums: List[int]) -> int:
n = len(nums)
ok = [1] * n
mx, mi = -1000000, 1000000
for i, x in enumerate(nums):
if x < mx:
ok[i] = 0
else:
mx = x
for i in range(n - 1, -1, -1):
if nums[i] > mi:
ok[i] = 0
else:
mi = nums[i]
return sum(ok)
Complexity
The time complexity is O(log n) or O(n log n). The space complexity is O(1).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.