(java)Increasing Triplet Subsequence

Given an unsorted array return whether an increasing subsequence of length 3 exists or not in the array.

Formally the function should:

Return true if there exists i, j, k

such that arr[i] < arr[j] < arr[k] given 0 ≤ i < j < k ≤ n-1 else return false.

Your algorithm should run in O(n) time complexity and O(1) space complexity.

Examples:

Given

[1, 2, 3, 4, 5]

,

return

true

.

Given

[5, 4, 3, 2, 1]

,

return

false

.

思路:这是一个典型的动态规划的题目，递推式是dp[i]=max(dp[i],dp[j]+1) nums[i]>nums[j], j<i;

代码如下(已通过leetcode)

public class Solution {

public boolean increasingTriplet(int[] nums) {

int[] dp=new int[nums.length];

Arrays.fill(dp, 1);

for(int i=0;i<nums.length;i++) {

for(int j=0;j<i;j++) {

if(nums[i]>nums[j]) dp[i]=Math.max(dp[i], dp[j]+1);

if(dp[i]>=3) return true;

}

}

return false;

}

}