Is Sum of Beauty in the Array easy or hard?

The problem is rated Medium because the rules themselves are simple but recognizing the prefix and suffix optimization is the key challenge. Candidates who attempt brute force first often realize the inefficiency and then improve it to an O(n) solution.

Sum of Beauty in the Array Python/Java solution

Most implementations build prefixMax and suffixMin arrays and then iterate once through the array to accumulate the beauty score. The same algorithm works across languages such as Python, Java, C++, and JavaScript because it relies only on array traversal and simple comparisons.

How to solve Sum of Beauty in the Array in O(n)?

Create a prefix array where prefixMax[i] stores the maximum value from index 0 to i, and a suffix array where suffixMin[i] stores the minimum value from i to the end. For each index i from 1 to n-2, check if prefixMax[i-1] < nums[i] < suffixMin[i+1] to add 2 beauty points. If that condition fails, check the local ordering nums[i-1] < nums[i] < nums[i+1] to add 1 point.

What is the best approach for Sum of Beauty in the Array?

The most efficient solution uses prefix maximum and suffix minimum arrays. Precompute the maximum value to the left of every index and the minimum value to the right, then evaluate each element in constant time. This reduces repeated scanning and gives an overall O(n) time complexity with O(n) extra space.

Is Sum of Beauty in the Array asked at Google/Amazon/Meta?

Array scanning and prefix-suffix precomputation patterns commonly appear in interviews at companies like Google, Amazon, and Meta. While the exact problem may vary, recognizing how to maintain left-side maximums and right-side minimums is a common interview expectation.

What data structure is used in Sum of Beauty in the Array?

The main data structures are arrays used for prefix maximum and suffix minimum precomputation. These helper arrays allow constant-time lookups of the largest value on the left and the smallest value on the right for each index.

What is the time complexity of Sum of Beauty in the Array?

The optimal solution runs in O(n) time by precomputing prefix maximum and suffix minimum arrays and then scanning the array once more to compute beauty values. A straightforward brute force implementation takes O(n^2) time because it scans the left and right sides for every index.

Description Hints 3 Solution Video 10:13

2012. Sum of Beauty in the Array

Q: What is the best approach for Sum of Beauty in the Array?

The most efficient solution uses prefix maximum and suffix minimum arrays. Precompute the maximum value to the left of every index and the minimum value to the right, then evaluate each element in constant time. This reduces repeated scanning and gives an overall O(n) time complexity with O(n) extra space.

Q: Is Sum of Beauty in the Array asked at Google/Amazon/Meta?

Array scanning and prefix-suffix precomputation patterns commonly appear in interviews at companies like Google, Amazon, and Meta. While the exact problem may vary, recognizing how to maintain left-side maximums and right-side minimums is a common interview expectation.

Q: What data structure is used in Sum of Beauty in the Array?

The main data structures are arrays used for prefix maximum and suffix minimum precomputation. These helper arrays allow constant-time lookups of the largest value on the left and the smallest value on the right for each index.

Q: What is the time complexity of Sum of Beauty in the Array?

The optimal solution runs in O(n) time by precomputing prefix maximum and suffix minimum arrays and then scanning the array once more to compute beauty values. A straightforward brute force implementation takes O(n^2) time because it scans the left and right sides for every index.

Medium51.8% acceptance1 company

You are given a 0-indexed integer array nums. For each index i (1 <= i <= nums.length - 2) the beauty of nums[i] equals:

2, if nums[j] < nums[i] < nums[k], for all 0 <= j < i and for all i < k <= nums.length - 1.
1, if nums[i - 1] < nums[i] < nums[i + 1], and the previous condition is not satisfied.
0, if none of the previous conditions holds.

Return the sum of beauty of all nums[i] where 1 <= i <= nums.length - 2.

Example 1:

Input: nums = [1,2,3]
Output: 2
Explanation: For each index i in the range 1 <= i <= 1:
- The beauty of nums[1] equals 2.

Example 2:

Input: nums = [2,4,6,4]
Output: 1
Explanation: For each index i in the range 1 <= i <= 2:
- The beauty of nums[1] equals 1.
- The beauty of nums[2] equals 0.

Example 3:

Input: nums = [3,2,1]
Output: 0
Explanation: For each index i in the range 1 <= i <= 1:
- The beauty of nums[1] equals 0.

Constraints:

3 <= nums.length <= 10⁵
1 <= nums[i] <= 10⁵

Asked at 1 company

Amazon

Topics

Array

Hints open one at a time

Hint 1

Use suffix/prefix arrays.

Hint 2

prefix[i] records the maximum value in range (0, i - 1) inclusive.

Hint 3

suffix[i] records the minimum value in range (i + 1, n - 1) inclusive.

10:13

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