leetcode 1218

问题

Given an integer array arr and an integer difference, return the length of the longest subsequence in arr which is an arithmetic sequence such that the difference between adjacent elements in the subsequence equals difference.

Example 1:

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Input: arr = [1,2,3,4], difference = 1
Output: 4
Explanation: The longest arithmetic subsequence is [1,2,3,4].

Example 2:

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Input: arr = [1,3,5,7], difference = 1
Output: 1
Explanation: The longest arithmetic subsequence is any single element.

Example 3:

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Input: arr = [1,5,7,8,5,3,4,2,1], difference = -2
Output: 4
Explanation: The longest arithmetic subsequence is [7,5,3,1].

Constraints:

  • 1 <= arr.length <= 10^5
  • -10^4 <= arr[i], difference <= 10^4

分析

$dp[i]$ 表示以 $i-10000$ 结尾的序列的长度。

代码

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class Solution {
public:
    int longestSubsequence(vector<int>& arr, int difference) {
        int dp[20001] = {};
        int ans = 1;
        for (int a: arr) {
            int b = a-difference+10000;
            if (b >= 0 && b <= 20000) {
                dp[a+10000] = dp[b] + 1;
            } else {
                dp[a+10000] = 1;
            }
            ans = max(ans, dp[a+10000]);
        }
        return ans;
    }
};