334 Increasing Triplet Subsequence
1. Question
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]
,
returntrue
.
Given[5, 4, 3, 2, 1]
,
returnfalse
.
2. Implementation
(1) DP
思路: 直接用Longest Increasing Subsequence的做法,如果最长的递增子序列长度大于等于3,则return true。如果遍历整个数组后,最长递增子序列都小于3,则返回false
class Solution {
public boolean increasingTriplet(int[] nums) {
if (nums == null || nums.length <= 2) {
return false;
}
int n = nums.length;
int[] dp = new int[n];
Arrays.fill(dp, 1);
int maxLen = 1;
for (int i = 1; i < n; i++) {
for (int j = 0; j < i; j++) {
if (nums[j] < nums[i] && dp[j] + 1 > dp[i]) {
dp[i] = dp[j] + 1;
}
maxLen = Math.max(maxLen, dp[i]);
if (maxLen >= 3) {
return true;
}
}
}
return false;
}
}
(2) Linear Search
思路: 因为问题只问是否存在长度为3的increasing subsequence,我们可以维护两个变量min1, min2,min1表示当前在数组i的位置上最小的数,min2表示当前数组i的位置上次小的数,当我们从左向右扫描数组时,如果当前的数num符合min1 < min2 < num,则返回true
class Solution {
public boolean increasingTriplet(int[] nums) {
if (nums == null || nums.length < 3) {
return false;
}
int min1 = Integer.MAX_VALUE;
int min2 = Integer.MAX_VALUE;
for (int num : nums) {
if (num <= min1) {
min1 = num;
}
else if (num <= min2) {
min2 = num;
}
else {
return true;
}
}
return false;
}
}
3. Time & Space Complexity
DP: 时间复杂度O(n^2), 空间复杂度O(n)
Linear Search: 时间复杂度O(n), 空间复杂度O(1)
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