Lituo Brushing Questions: Maximum Subarray Sum Problem

overview

The maximum subarray sum problem is a classic algorithmic problem when it comes to working with arrays. In this blog post, we will discuss the maximum subarray sum problem, and provide a problem prototype, C++ code solution, and problem-solving ideas.

topic prototype

Given an integer array nums, find a contiguous subarray with the maximum sum (the subarray contains at least one element), and return its maximum sum.

problem solving ideas

The maximum subarray sum problem can be solved using the idea of ​​dynamic programming. We define a variable maxSum to record the current maximum sub-array sum, the initial value is nums[0]. At the same time, we define a variable curSum to record the current sub-array sum, and the initial value is also nums[0].

Then, we start traversing from the second element of the array, and for each element nums[i], we have two options:

Add nums[i] to the current subarray, ie curSum += nums[i].
Start a new subarray with nums[i] as a new starting point, ie curSum = nums[i].
Each time we choose the larger of curSum and nums[i] as the new curSum, and then update maxSum to the larger of curSum and maxSum. In this way, during the traversal process, maxSum will record the current maximum sub-array sum.

Finally, after traversing the entire array, maxSum is the maximum sum of sub-arrays sought.

C++ code implementation

The following is the C++ code implementation to solve the maximum subarray sum problem of
a[i] = max(a[i], a[i]+lastmax) using dynamic programming ideas :

class Solution {
    
    
public:
    int maxSubArray(vector<int>& nums) {
    
    
        int maxSum = nums[0];
        int curSum = nums[0];
        
        for (int i = 1; i < nums.size(); ++i) {
    
    
            curSum = max(nums[i], curSum + nums[i]);
            maxSum = max(maxSum, curSum);
        }
        
        return maxSum;
    }
};

Summarize

The maximum subarray sum problem can be solved by a dynamic programming method. We use two variables maxSum and curSum to record the current maximum subarray sum and the current subarray sum respectively. By traversing the array, update curSum according to the value of the current element, and compare it with maxSum. Finally, maxSum is the desired maximum subarray sum. The above is the problem-solving ideas and C++ code implementation of the largest sub-array and problem. Hope it helps you!

Hope this blog post helps you understand the maximum subarray and problem. If you have any questions or suggestions, please feel free to leave a message. Thanks!