Longest Increasing Subsequence

Longest Increasing Subsequence

Total Accepted: 9797 Total Submissions: 30801 Difficulty: Medium

Given an unsorted array of integers, find the length of longest increasing subsequence.

For example,
Given

[10, 9, 2, 5, 3, 7, 101, 18]

,
The longest increasing subsequence is

[2, 3, 7, 101]

, therefore the length is

4

. Note that there may be more than one LIS combination, it is only necessary for you to return the length.

Your algorithm should run in O(n2) complexity.

Follow up: Could you improve it to O(n log n) time complexity?

1.o(n*n)

class Solution {
public:
int lengthOfLIS(vector<int>& nums) {
int n = nums.size();
int res = n==0 ? 0 : 1;
vector<int> help(n,1);
for(int i=1;i<n;i++){
for(int j=0;j<i;j++){
if(nums[j] < nums[i]){
help[i] = max(help[i],help[j]+1);
res = max(res,help[i]);
}
}
}
return res;
}
};

2.o(n*lgn)

class Solution {
public:
int lengthOfLIS(vector<int>& nums) {
int n = nums.size();
vector<int> help;
for(int i=0;i<n;i++){
auto iter = lower_bound(help.begin(),help.end(),nums[i]);
if(iter == help.end()){
help.push_back(nums[i]);
}else{
*iter=nums[i];
}
}
return help.size();
}
};