Data Structure Array: Longest Monotonically Increasing Subsequence Size

http://www.geeksforgeeks.org/longest-monotonically-increasing-subsequence-size-n-log-n/

#include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
#include <stack>
#include <string>
#include <fstream>
#include <map>
using namespace std;

int maxsum(int arr[], int n) {
    vector<int> tail;
    tail.push_back(arr[0]);
    for (int i = 1; i < n; i++) {
        if (arr[i] < tail[0]) tail[0] = arr[0];
        else if (arr[i] > tail[tail.size()-1]) tail.push_back(arr[i]);
        else {
            int mid;
            int left = 0;
            int right = tail.size() - 1;
            while (left < right) {
                mid = (left + right) / 2;
                if (tail[mid] < arr[i]) left = mid + 1;
                else right = mid - 1;
            }
            mid = (left + right) / 2;
            tail[mid] = arr[i];
            cout << "tail[" << mid << "] is arr[" << i << "] = " << arr[i] << endl;
        }
    }
    return tail.size();
}

int main() {
    int arr[9] = {2, 5, 3, 7, 11, 8, 10, 13, 6};
    cout << maxsum(arr, 9) << endl;
    return 0;
}