二分法-最長上升子序列

思路:使用一個棧來求最長上升子序列的長度,當棧爲空或者待插入元素大於棧頂元素時就入棧,否則替換棧中小於等於待插入元素的數並替換,最終棧的長度即爲最長上升子序列的長度.
優點:使用二分查找,時間複雜度爲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])  //如果棧空或者大於棧頂就入棧 
            v.push_back(arr[i]);
        else    //查找棧中小於等於arr[i]的元素並替換 
        {
            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;
}

運行結果: