To find the maximum sub-sequence

C++:

#include <stdint.h>
#include <string>
#include <iostream>
#include <vector>
using namespace Std;

int maxsubsum (const vector<int> &a) {
int maxsum = 0;
int thissum = 0;
for (int i = 0; i < a.size (); i++) {
Thissum + = A[i];
if (thissum>maxsum)
Maxsum = Thissum;
else if (Thissum < 0)
thissum = 0;
}
return maxsum;
}

int main () {
Vector<int> A = {4,-1, 3,-7,-4, 5, 6,-9, 8};
Cout<<maxsubsum (a) <<endl;
System ("pause");

}

Dynamic programming, online algorithms (on-line algorithm)

Online algorithm: At any time, the algorithm to the operation of the data read only (scan) once, once read into and processing, it does not need to be remembered. In this process, the algorithm can immediately give the correct answer to the corresponding sub-sequence problem for the data it has been read into. Algorithms with this feature are called online algorithms (on-line algorithm).

Algorithm complexity O (n)

Method 2:

Using the idea of recursion, the sequence is divided into the left half, the right half and the middle part, in which the left and the parts can be solved by recursion .

The middle part is the maximum value of the first half (which contains the last element of the left half) and the maximum value of the right half, which contains the right half of the value, and

Comparing these three values is the final result.

Algorithmic complexity: O (N*LOGN)

To find the maximum sub-sequence