How do you solve Find in Mountain Array on LeetCode?

Find in Mountain Array (LeetCode #1095) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(log n) time complexity and O(1) space complexity. Key insight: Understanding the mountain array structure helps in optimizing the search process.

What is the brute force solution for Find in Mountain Array?

The brute force approach for Find in Mountain Array is Brute Force, with O(n) time complexity and O(1) space complexity. The brute-force approach involves checking each element of the mountain array to see if it matches the target. This is straightforward but inefficient, especially for large arrays. The optimal Optimal Solution approach improves this to O(log n).

What algorithm or data structure is used to solve Find in Mountain Array?

Find in Mountain Array uses the following concepts: Array, Binary Search, Interactive. The recommended patterns to study are: Binary Search, Divide and Conquer.

What are the interview tips for Find in Mountain Array?

Always clarify the constraints and requirements of the problem before jumping into coding. Think about how the properties of the data structure can help optimize your solution. Practice explaining your thought process as you code; it helps in interviews.

What are common mistakes when solving Find in Mountain Array?

Not recognizing the need to find the peak before searching for the target. Exceeding the limit of 100 calls to mountainArr.get() by not optimizing the search.

#1095

Find in Mountain Array

Hard

ArrayBinary SearchInteractiveBinary SearchDivide and Conquer

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n)	O(log n)
Space	O(1)	O(1)

💡

Intuition

Time O(log n)Space O(1)

The optimal solution leverages the properties of the mountain array to efficiently locate the target using binary search. First, we find the peak of the mountain, then search both sides of the peak for the target.

⚙️

Algorithm

4 steps

1Step 1: Use binary search to find the peak index of the mountain array.
2Step 2: Perform binary search on the left side of the peak to find the target.
3Step 3: If not found, perform binary search on the right side of the peak.
4Step 4: Return the minimum index if found, otherwise return -1.

solution.py37 lines

1# Full working Python code
2class MountainArray:
3    def __init__(self, arr):
4        self.arr = arr
5    def get(self, index):
6        return self.arr[index]
7    def length(self):
8        return len(self.arr)
9
10def findPeak(mountainArr):
11    left, right = 0, mountainArr.length() - 1
12    while left < right:
13        mid = (left + right) // 2
14        if mountainArr.get(mid) < mountainArr.get(mid + 1):
15            left = mid + 1
16        else:
17            right = mid
18    return left
19
20def binarySearch(mountainArr, target, left, right, ascending):
21    while left <= right:
22        mid = (left + right) // 2
23        mid_val = mountainArr.get(mid)
24        if mid_val == target:
25            return mid
26        if (mid_val < target) == ascending:
27            left = mid + 1
28        else:
29            right = mid - 1
30    return -1
31
32def findInMountainArray(target, mountainArr):
33    peak = findPeak(mountainArr)
34    index = binarySearch(mountainArr, target, 0, peak, True)
35    if index != -1:
36        return index
37    return binarySearch(mountainArr, target, peak + 1, mountainArr.length() - 1, False)

ℹ

Complexity note: The time complexity is O(log n) due to the binary search for the peak and the subsequent searches, while the space complexity is O(1) since we are using a constant amount of extra space.

1Understanding the mountain array structure helps in optimizing the search process.
2Finding the peak is crucial as it divides the array into two sorted halves.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.