What is the time complexity of Lexicographically Smallest Negated Permutation that Sums to Target?

The optimal solution for Lexicographically Smallest Negated Permutation that Sums to Target runs in O(n) time and uses O(n) space. Linear time to create the array and adjust the last element.

What is the brute force solution for Lexicographically Smallest Negated Permutation that Sums to Target?

The brute force approach for Lexicographically Smallest Negated Permutation that Sums to Target is Brute Force, with O(n!) time complexity and O(n) space complexity. Generate all permutations of numbers from 1 to n, check their sums, and find the smallest lexicographically. This is inefficient due to the factorial growth of permutations. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Lexicographically Smallest Negated Permutation that Sums to Target?

Lexicographically Smallest Negated Permutation that Sums to Target uses the following concepts: Array, Math, Two Pointers, Greedy, Sorting. The recommended patterns to study are: Greedy, Sorting.

What are the interview tips for Lexicographically Smallest Negated Permutation that Sums to Target?

Explain your thought process clearly. Discuss edge cases and constraints. Practice similar problems to build intuition.

What are common mistakes when solving Lexicographically Smallest Negated Permutation that Sums to Target?

Not checking if the target is within the valid range. Forgetting to handle the even condition for (S - target).

#3752

Lexicographically Smallest Negated Permutation that Sums to Target

Medium

ArrayMathTwo PointersGreedySortingGreedySorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n!)	O(n)
Space	O(n)	O(n)

💡

Intuition

Time O(n)Space O(n)

Start with the sum of the first n natural numbers. Adjust the largest number to meet the target while ensuring the absolute values remain a permutation.

⚙️

Algorithm

3 steps

1Step 1: Calculate S = n * (n + 1) / 2.
2Step 2: Check if target is within the bounds [-S, S] and if (S - target) is even.
3Step 3: Create the array [1, 2, ..., n] and adjust the largest element to match the target.

solution.py7 lines

1def smallest_permutation(n, target):
2    S = n * (n + 1) // 2
3    if target < -S or target > S or (S - target) % 2 != 0:
4        return []
5    arr = list(range(1, n + 1))
6    arr[-1] += target - S
7    return [-x if x == arr[-1] else x for x in arr]

ℹ

Complexity note: Linear time to create the array and adjust the last element.

1The sum of the first n natural numbers defines the limits for the target.
2Adjusting the largest number allows for flexibility in achieving the target sum.

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