Longest Increasing Subsequence

• Lintcode : 76 / Leetcode : 300
• Level : Medium

Problem

Given a sequence of integers, find the longest increasing subsequence (LIS).

You code should return the length of the LIS.

Example
Example 1:
    Input:  [5,4,1,2,3]
    Output:  3

    Explanation:
    LIS is [1,2,3]

Example 2:
    Input: [4,2,4,5,3,7]
    Output:  4

    Explanation: 
    LIS is [2,4,5,7]
Challenge
Time complexity O(n^2) or O(nlogn)

Clarification
What's the definition of longest increasing subsequence?

The longest increasing subsequence problem is to find a subsequence of a given sequence in which the subsequence's elements are in sorted order, lowest to highest, and in which the subsequence is as long as possible. This subsequence is not necessarily contiguous, or unique.

Concept & Algorithm

筆記

Time Complexity & Space Complexity

time : O(n ^ 2)
space: O(n)

Answer

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

tags: DP

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