How do you solve Find a Peak Element II on LeetCode?

Find a Peak Element II (LeetCode #1901) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(m log(n)) time complexity and O(1) space complexity. Key insight: A peak can be found efficiently by reducing the search space using binary search.

What is the brute force solution for Find a Peak Element II?

The brute force approach for Find a Peak Element II is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach checks each element in the matrix to see if it is a peak by comparing it with its neighbors. This is straightforward but inefficient for larger matrices. The optimal Optimal Solution approach improves this to O(m log(n)).

What algorithm or data structure is used to solve Find a Peak Element II?

Find a Peak Element II uses the following concepts: Array, Binary Search, Matrix. The recommended patterns to study are: Binary Search, Divide and Conquer.

What are the interview tips for Find a Peak Element II?

Clearly explain your thought process and the reasoning behind each step. Practice identifying patterns in problems, as they often lead to optimal solutions. Be prepared to discuss the trade-offs between different approaches.

What are common mistakes when solving Find a Peak Element II?

Not considering edge cases where the peak is at the boundary of the matrix. Failing to properly implement the binary search logic, leading to infinite loops or incorrect results.

#1901

Find a Peak Element II

Medium

ArrayBinary SearchMatrixBinary SearchDivide and Conquer

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(m log(n))
Space	O(1)	O(1)

💡

Intuition

Time O(m log(n))Space O(1)

The optimal solution uses a binary search approach to efficiently find a peak by reducing the search space in half at each step. This is akin to finding a needle in a haystack by eliminating half of the haystack with each guess.

⚙️

Algorithm

4 steps

1Step 1: Start with the entire matrix and choose the middle column.
2Step 2: Find the maximum element in this column.
3Step 3: Check if this maximum element is a peak. If yes, return its coordinates.
4Step 4: If the maximum element has a neighbor that is greater, move to that neighbor's row and repeat the process.

solution.py20 lines

1# Full working Python code
2
3def findPeakGrid(mat):
4    m, n = len(mat), len(mat[0])
5    left, right = 0, n - 1
6    while left < right:
7        mid = (left + right) // 2
8        max_row = 0
9        for i in range(m):
10            if mat[i][mid] > mat[max_row][mid]:
11                max_row = i
12        if (mid == n - 1 or mat[max_row][mid] > mat[max_row][mid + 1]):
13            return [max_row, mid]
14        else:
15            left = mid + 1
16    max_row = 0
17    for i in range(m):
18        if mat[i][left] > mat[max_row][left]:
19            max_row = i
20    return [max_row, left]

ℹ

Complexity note: The time complexity is O(m log(n)) because we perform a binary search on the columns, and for each column, we scan through all rows to find the maximum element. The space complexity is O(1) since we only use a constant amount of extra space.

1A peak can be found efficiently by reducing the search space using binary search.
2The problem can be approached from either row or column perspectives, depending on the dimensions.

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