Code14 maximum suborder sum

topic

leetcode53. Maximum sub-order sum
Given an integer array nums, find a continuous sub-array with the largest sum (the sub-array contains at least one element), and return the largest sum.

Example:
Input: [-2,1,-3,4,-1,2,1,-5,4]
Output: 6
Explanation: The sum of consecutive subarrays [4,-1,2,1] is the largest, which is 6.

Code

• Ideas
  • Dynamic programming
    • Assuming that the maximum sub-order sum of the following element i as the ending is max_ending_here[i], the relationship is as follows:

      max_ending_here[i] = max(max_ending_here[i-1] + nums[i], nums[i])   (i > 0)
      

• Code

// C
int maxSubArray(int* nums, int numsSize) {
    
    
  int max_ending_here = nums[0];
  int max_so_for = nums[0];
  for (int i = 1; i < numsSize; ++i) {
    
    
    max_ending_here = (max_ending_here + nums[i]) > nums[i]
                      ? (max_ending_here + nums[i]): nums[i];
    max_so_for = max_ending_here > max_so_for ? max_ending_here : max_so_for;
  }

  return max_so_for;
}

// C++
#include <algorithm>
#include <vector>
using namespace std;

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

    return max_so_for;
  }
};

• note

// 以下语句可换一种写法
max_ending_here = std::max(max_ending_here + nums[i], nums[i]);
// 如下:
if (max_ending_here > 0){
    
      // max_ending_here + nums[i] > nums[i]
   max_ending_here = max_ending_here + nums[i];
}else{
    
    
   max_ending_here = nums[i];
}

test

#include <iostream>

int main() {
    
    
  {
    
    
    // C
    int nums[] = {
    
    -2, 1, -3, 4, -1, 2, 1, -5, 4};
    int n = sizeof(nums) / sizeof(nums[0]);
    cout << maxSubArray(nums, n) << endl;
  }
  {
    
    
    // C++
    vector<int> nums{
    
    -2, 1, -3, 4, -1, 2, 1, -5, 4};
    Solution s;
    cout << s.maxSubArray(nums) << endl;
  }

  cin.get();
  return 0;
}

• result

6
6