package LeetCode_1027
/**
* 1027. Longest Arithmetic Subsequence
* https://leetcode.com/problems/longest-arithmetic-subsequence/description/
*
* Given an array A of integers, return the length of the longest arithmetic subsequence in A.
Recall that a subsequence of A is a list A[i_1], A[i_2], ..., A[i_k] with 0 <= i_1 < i_2 < ... < i_k <= A.length - 1,
and that a sequence B is arithmetic if B[i+1] - B[i] are all the same value (for 0 <= i < B.length - 1).
Example 1:
Input: A = [3,6,9,12]
Output: 4
Explanation:
The whole array is an arithmetic sequence with steps of length = 3.
Example 2:
Input: A = [9,4,7,2,10]
Output: 3
Explanation:
The longest arithmetic subsequence is [4,7,10].
Example 3:
Input: A = [20,1,15,3,10,5,8]
Output: 4
Explanation:
The longest arithmetic subsequence is [20,15,10,5].
Constraints:
1. 2 <= A.length <= 1000
2. 0 <= A[i] <= 500
* */
class Solution {
/*
* solution 1: bruce force, 3 loop, Time complexity:O(n^3), Space complexity:O(1)
* */
fun longestArithSeqLength(A: IntArray): Int {
if (A.isEmpty()) {
return 0
}
var max = 0
val n = A.size
for (i in 0 until n) {
for (j in i + 1 until n) {
val diff = A[j] - A[i]
//for example: 1,2,3,4, A[j]=2, diff=1, so next should be 2+1
var next = A[j] + diff
var currentMax = 2
for (k in j + 1 until n) {
if (A[k] == next) {
currentMax++
next = A[k] + diff
}
max = Math.max(max, currentMax)
}
}
}
return max
}
}
