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Longest Arithmetic Sequence

Longest Arithmetic Sequence

题目地址

题目描述

Given an array A of integers, return the length of the longest arithmetic subsequence in A.
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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).
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Example 1:
Input: [3,6,9,12]
Output: 4
Explanation:
The whole array is an arithmetic sequence with steps of length = 3.
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Example 2:
Input: [9,4,7,2,10]
Output: 3
Explanation:
The longest arithmetic subsequence is [4,7,10].
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Example 3:
Input: [20,1,15,3,10,5,8]
Output: 4
Explanation:
The longest arithmetic subsequence is [20,15,10,5].
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Note:
2 <= A.length <= 2000
0 <= A[i] <= 10000

代码

Approach #1 DP

dp[diff][index] equals to the length of arithmetic sequence at index with difference diff.
class Solution {
public int longestArithSeqLength(int[] A) {
int res = 2, n = A.length;
HashMap<Integer, Integer>[] dp = new HashMap[n];
for (int j = 0; j < A.length; j++) {
dp[j] = new HashMap();
for (int i = 0; i < j; i++) {
int d = A[j] - A[i];
dp[j].put(d, dp[i].getOrDefault(d, 1) + 1);
res = Math.max(res, dp[j].get(d));
}
}
return res;
}
}