How do you solve K-Concatenation Maximum Sum on LeetCode?

K-Concatenation Maximum Sum (LeetCode #1191) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Kadane's algorithm is essential for efficiently finding the maximum sub-array sum.

What is the brute force solution for K-Concatenation Maximum Sum?

The brute force approach for K-Concatenation Maximum Sum is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves generating the k-concatenated array and then finding the maximum sub-array sum using a nested loop. This is simple but inefficient for large inputs. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve K-Concatenation Maximum Sum?

K-Concatenation Maximum Sum uses the following concepts: Array, Dynamic Programming. The recommended patterns to study are: Dynamic Programming, Kadane's Algorithm, Prefix/Suffix Sum.

What are the interview tips for K-Concatenation Maximum Sum?

Always start with a brute-force solution to understand the problem better. Explain your thought process clearly, especially when transitioning to the optimal solution. Practice Kadane's algorithm and related problems to become comfortable with dynamic programming.

What are common mistakes when solving K-Concatenation Maximum Sum?

Failing to consider the case where k = 1 separately. Not handling large sums properly, leading to overflow errors.

#1191

K-Concatenation Maximum Sum

Medium

ArrayDynamic ProgrammingDynamic ProgrammingKadane's AlgorithmPrefix/Suffix Sum

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(1)

Instead of creating a large array, we can leverage the properties of sub-arrays and the sum of the original array. The optimal approach uses Kadane's algorithm and considers the total sum of the array to determine the maximum sub-array sum efficiently.

⚙️

Algorithm

5 steps

1Step 1: Use Kadane's algorithm to find the maximum sub-array sum for k = 1.
2Step 2: Calculate the total sum of the array.
3Step 3: If k = 1, return the result from Kadane's algorithm.
4Step 4: If k > 1 and total sum > 0, consider the maximum sub-array sum from the first and last parts of the array, plus the total sum multiplied by (k-2).
5Step 5: Return the maximum value found, ensuring to take modulo 10^9 + 7.

solution.py25 lines

1def kConcatenationMaxSum(arr, k):
2    mod = 10**9 + 7
3    def kadane(arr):
4        max_sum = 0
5        current_sum = 0
6        for num in arr:
7            current_sum = max(num, current_sum + num)
8            max_sum = max(max_sum, current_sum)
9        return max_sum
10    max_k1 = kadane(arr)
11    total_sum = sum(arr)
12    if k == 1:
13        return max_k1 % mod
14    max_prefix = max_suffix = 0
15    current_sum = 0
16    for num in arr:
17        current_sum += num
18        max_suffix = max(max_suffix, current_sum)
19    current_sum = 0
20    for num in reversed(arr):
21        current_sum += num
22        max_prefix = max(max_prefix, current_sum)
23    if total_sum > 0:
24        return max(max_k1, max_prefix + max_suffix + total_sum * (k - 2)) % mod
25    return max(max_k1, max_prefix + max_suffix) % mod

ℹ

Complexity note: The optimal solution runs in O(n) time because we only traverse the array a few times (for Kadane's algorithm and to calculate prefix/suffix sums).

1Kadane's algorithm is essential for efficiently finding the maximum sub-array sum.
2Understanding the contribution of the total sum of the array helps optimize the solution for k > 1.

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