LeetCode 1191: K-Concatenation Maximum Sum Solution

Master LeetCode problem 1191 (K-Concatenation Maximum Sum), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

1191. K-Concatenation Maximum Sum

Medium

Array Dynamic Programming

Problem Explanation

Explanation

To solve this problem, we can use Kadane's algorithm to find the maximum subarray sum. We need to consider two cases:

The maximum subarray sum within a single array arr.
The maximum subarray sum that can include elements from multiple concatenated arrays.

We can calculate the maximum subarray sum within a single array using Kadane's algorithm. Then, we can calculate the sum of all elements in the array and find the maximum subarray sum that includes elements from multiple arrays. This sum can be calculated by considering the prefix sum and suffix sum of the array concatenated k times.

Solution Code

class Solution {
    public int kConcatenationMaxSum(int[] arr, int k) {
        int mod = 1000000007;
        
        int maxSingle = kadane(arr);
        
        if (k == 1) {
            return maxSingle;
        }
        
        int totalSum = 0;
        for (int num : arr) {
            totalSum = (totalSum + num) % mod;
        }
        
        int prefixSum = 0, maxPrefixSum = 0, suffixSum = 0, maxSuffixSum = 0;
        
        for (int i = 0; i < arr.length; i++) {
            prefixSum = (prefixSum + arr[i]) % mod;
            maxPrefixSum = Math.max(maxPrefixSum, prefixSum);
        }
        
        for (int i = arr.length - 1; i >= 0; i--) {
            suffixSum = (suffixSum + arr[i]) % mod;
            maxSuffixSum = Math.max(maxSuffixSum, suffixSum);
        }
        
        int maxMiddleSum = Math.max(0, totalSum * (k - 2) + maxPrefixSum + maxSuffixSum) % mod;
        
        return Math.max(maxSingle, maxMiddleSum);
    }
    
    private int kadane(int[] arr) {
        int maxSum = 0;
        int currentSum = 0;
        
        for (int num : arr) {
            currentSum = Math.max(num, currentSum + num);
            maxSum = Math.max(maxSum, currentSum);
        }
        
        return maxSum < 0 ? 0 : maxSum;
    }
}

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