二分法-最长上升子序列

思路:使用一个栈来求最长上升子序列的长度,当栈为空或者待插入元素大于栈顶元素时就入栈,否则替换栈中小于等于待插入元素的数并替换,最终栈的长度即为最长上升子序列的长度.
优点:使用二分查找,时间复杂度为O(nlogn).

#include<iostream>
#include<vector>
using namespace std;
vector<int> v;
int solution(int arr[], int length)
{
    for(int i = 0; i < length; i++)
    {
        if(v.size() == 0 || arr[i] > v[v.size() - 1])  //如果栈空或者大于栈顶就入栈 
            v.push_back(arr[i]);
        else    //查找栈中小于等于arr[i]的元素并替换 
        {
            int begin = 0, end = v.size() - 1;
            int index = -1;
            while(begin <= end)
            {
                int mid = (end - begin) / 2 + begin;
                if(arr[mid] < arr[i])
                    begin = mid + 1;
                else
                    {
                        index = mid;
                        end = mid - 1;
                    }
            }
            v[index] = arr[i];
        }
    }
}
int main()
{
    int arr[] = {1,-1,2,-3,4,-5,6,-7};
    int res = solution(arr,8);
    for(int i = 0; i < v.size(); i++)
    cout<<v[i]<<" ";
    cout<<endl;
    cout<<v.size()<<" ";   
    return 0;
}

运行结果: