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:
