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This approach involves using a 2D dynamic programming array to keep track of the lengths of arithmetic subsequences ending at different indices with various common differences. The outer loop iterates over end indices while the inner loop considers all pairs of start and end indices to update the subsequence lengths.
Time Complexity: O(n^2)
Space Complexity: O(n^2), where n is the size of the input array.
1function longestArithSeqLength(nums) {
2 if (nums.length <= 2) return nums.length;
3 let dp = Array.from({length: nums.length}, () => new Map());
4 let maxLength = 2;
5 for (let i = 0; i < nums.length; i++) {
6 for (let j = 0; j < i; j++) {
7 let diff = nums[i] - nums[j];
8 dp[i].set(diff, (dp[j].get(diff) || 1) + 1);
9 maxLength = Math.max(maxLength, dp[i].get(diff));
10 }
11 }
12 return maxLength;
13}
14
15// Example usage
16const nums = [3, 6, 9, 12];
17console.log(longestArithSeqLength(nums));The JavaScript solution uses an array of Maps to store the lengths of arithmetic subsequences keyed by their differences. It iterates through the array twice (nested loops), calculating differences and maintaining sequence lengths in the Maps.
This approach uses a simplified dynamic programming technique with HashMaps and tracks differences and their counts for each number. By leveraging HashMap structures, we manage subsequence lengths more efficiently and avoid using unnecessary space for non-existent differences.
Time Complexity: O(n^2)
Space Complexity: O(n^2) in the worst case but often much less due to sparse differences.
1
This C implementation uses custom HashMap structures for each position to track possible differences and their lengths efficiently. It avoids using a full 2D array of fixed size by dynamically storing only necessary computations.