How do you solve Maximize Score of Numbers in Ranges on LeetCode?

Maximize Score of Numbers in Ranges (LeetCode #3281) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log(max(start) + d)) time complexity and O(1) space complexity. Key insight: Sorting the start array helps in efficiently checking the feasibility of choosing integers.

What is the time complexity of Maximize Score of Numbers in Ranges?

The optimal solution for Maximize Score of Numbers in Ranges runs in O(n log(max(start) + d)) time and uses O(1) space. The binary search runs in logarithmic time relative to the maximum possible score, and for each mid value, we check the feasibility in linear time.

What is the brute force solution for Maximize Score of Numbers in Ranges?

The brute force approach for Maximize Score of Numbers in Ranges is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves generating all possible combinations of integers within the given ranges and calculating the minimum absolute difference for each combination. This is straightforward but inefficient for larger inputs. The optimal Optimal Solution approach improves this to O(n log(max(start) + d)).

What algorithm or data structure is used to solve Maximize Score of Numbers in Ranges?

Maximize Score of Numbers in Ranges uses the following concepts: Array, Binary Search, Greedy, Sorting. The recommended patterns to study are: Binary Search, Greedy Algorithms.

What are the interview tips for Maximize Score of Numbers in Ranges?

Always think about edge cases, such as when d is 0. Explain your thought process clearly while coding; it helps the interviewer understand your approach. Practice binary search problems to become comfortable with the technique.

What are common mistakes when solving Maximize Score of Numbers in Ranges?

Failing to sort the start array before applying the binary search. Not correctly implementing the feasibility check for chosen integers.

#3281

Maximize Score of Numbers in Ranges

Medium

ArrayBinary SearchGreedySortingBinary SearchGreedy Algorithms

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log(max(start) + d))
Space	O(1)	O(1)

💡

Intuition

Time O(n log(max(start) + d))Space O(1)

The optimal approach uses binary search to maximize the minimum absolute difference between chosen integers. By sorting the start array and strategically selecting integers within their ranges, we can efficiently find the best configuration.

⚙️

Algorithm

3 steps

1Step 1: Sort the start array.
2Step 2: Use binary search to find the maximum possible score (x).
3Step 3: For each mid value in the binary search, check if it's possible to select integers such that the minimum difference is at least mid.

solution.py20 lines

1# Full working Python code
2def canChoose(start, d, x):
3    last_chosen = start[0]
4    for i in range(1, len(start)):
5        next_chosen = last_chosen + x
6        if next_chosen > start[i] + d:
7            return False
8        last_chosen = max(start[i], next_chosen)
9    return True
10
11def maxScore(start, d):
12    start.sort()
13    left, right = 0, 10**9 + 1
14    while left < right:
15        mid = (left + right + 1) // 2
16        if canChoose(start, d, mid):
17            left = mid
18        else:
19            right = mid - 1
20    return left

ℹ

Complexity note: The binary search runs in logarithmic time relative to the maximum possible score, and for each mid value, we check the feasibility in linear time.

1Sorting the start array helps in efficiently checking the feasibility of choosing integers.
2Binary search allows us to systematically explore potential scores without generating all combinations.

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