Introduction
The Problem Statement:
The problem statement for the Public Knowledge University Online Judge (PKU OJ) is to evaluate the performance of a program written in C++ for solving the following problem: given an array of integers, find the maximum sum of three non-overlapping subarrays.
The Algorithm
Naive Approach
The most straightforward approach is to iterate through all possible combinations of three non-overlapping subarrays and compute their sums. This approach has a time complexity of O(n^3).
Divide and Conquer
We can optimize the algorithm by dividing the array into smaller subarrays and then finding the maximum sum of three non-overlapping subarrays for each subarray. This approach has a time complexity of O(n^2).
Examples
Here are some examples of how to solve this problem using the divide and conquer approach:
Example Input
int arr[] = {1, 5, 3, 6, 2};
int k = 2;
Example Output
8
Example Input
int arr[] = {1, 10, 1, 3, 20};
int k = 3;
Example Output
41
##This problem is a classic dynamic programming problem that can be solved efficiently using either a naive or divide and conquer approach. The key to solving this problem is to identify the structure of the problem and break it down into smaller subproblems that can be solved recursively.
