# (DP LIS) leetcode 300. Longest Increasing Subsequence

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

Example:

Input: [10,9,2,5,3,7,101,18]
Output: 4
Explanation: The longest increasing subsequence is [2,3,7,101], therefore the length is 4. 

Note:

• 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?

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C++代码:

class Solution {
public:
int lengthOfLIS(vector<int>& nums) {
if(nums.size() == 0) return 0;
int n = nums.size();
vector<int> dp(n,1);  //边界值就是1，因为无论如何LIS中的最小值就是1，否则就是0.
int res = 1;
for(int i = 1; i < n; i++){
for(int j = 0; j < i; j++){
if(nums[i] > nums[j] && dp[i] < dp[j] + 1)
dp[i] = dp[j] + 1;
}
res = max(res,dp[i]);
}
return res;
}
};

posted @ 2019-05-10 21:01  PJCK  阅读(32)  评论(0编辑  收藏