How do you solve Maximize Alternating Sum Using Swaps on LeetCode?

Maximize Alternating Sum Using Swaps (LeetCode #3695) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: Swaps create connected components.

What is the time complexity of Maximize Alternating Sum Using Swaps?

The optimal solution for Maximize Alternating Sum Using Swaps runs in O(n log n) time and uses O(n) space. DSU operations are nearly constant time, and sorting the components takes linearithmic time.

What is the brute force solution for Maximize Alternating Sum Using Swaps?

The brute force approach for Maximize Alternating Sum Using Swaps is Brute Force, with O(n²) time complexity and O(1) space complexity. Try all possible swaps and calculate the alternating sum for each configuration. This approach guarantees finding the maximum sum but is inefficient. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Maximize Alternating Sum Using Swaps?

Maximize Alternating Sum Using Swaps uses the following concepts: Array, Greedy, Union-Find, Sorting. The recommended patterns to study are: Graph Theory, Sorting, Greedy Algorithms.

What are the interview tips for Maximize Alternating Sum Using Swaps?

Explain your thought process clearly. Discuss edge cases, like empty arrays. Practice explaining DSU concepts.

What are common mistakes when solving Maximize Alternating Sum Using Swaps?

Not using all possible swaps. Ignoring the order of indices when calculating sums.

#3695

Maximize Alternating Sum Using Swaps

Hard

ArrayGreedyUnion-FindSortingGraph TheorySortingGreedy Algorithms

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n log n)Space O(n)

Use a Disjoint Set Union (DSU) to group indices that can be swapped. For each group, sort the values and place the largest in even indices to maximize the alternating sum.

⚙️

Algorithm

3 steps

1Step 1: Build connected components using DSU based on the swaps.
2Step 2: For each component, collect values and sort them in descending order.
3Step 3: Assign the largest values to even indices and the rest to odd indices to maximize the alternating sum.

solution.py25 lines

1class DSU:
2    def __init__(self, n):
3        self.parent = list(range(n))
4    def find(self, x):
5        if self.parent[x] != x:
6            self.parent[x] = self.find(self.parent[x])
7        return self.parent[x]
8    def union(self, x, y):
9        self.parent[self.find(x)] = self.find(y)
10
11def maxAlternatingSum(nums, swaps):
12    dsu = DSU(len(nums))
13    for p, q in swaps:
14        dsu.union(p, q)
15    components = {}
16    for i in range(len(nums)):
17        root = dsu.find(i)
18        if root not in components:
19            components[root] = []
20        components[root].append(nums[i])
21    total_sum = 0
22    for comp in components.values():
23        comp.sort(reverse=True)
24        total_sum += sum(comp[i] if i % 2 == 0 else -comp[i] for i in range(len(comp)))
25    return total_sum

ℹ

Complexity note: DSU operations are nearly constant time, and sorting the components takes linearithmic time.

1Swaps create connected components.
2Maximize even indices with the largest values.

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