446. Arithmetic Slices Ii Subsequence¶

Difficulty: Hard

446. Arithmetic Slices II - Subsequence

Hard

Given an integer array nums, return the number of all the arithmetic subsequences of nums.

A sequence of numbers is called arithmetic if it consists of at least three elements and if the difference between any two consecutive elements is the same.

For example, [1, 3, 5, 7, 9], [7, 7, 7, 7], and [3, -1, -5, -9] are arithmetic sequences.
For example, [1, 1, 2, 5, 7] is not an arithmetic sequence.

A subsequence of an array is a sequence that can be formed by removing some elements (possibly none) of the array.

For example, [2,5,10] is a subsequence of [1,2,1,2,4,1,5,10].

The test cases are generated so that the answer fits in 32-bit integer.

Example 1:

Input: nums = [2,4,6,8,10]
Output: 7
Explanation: All arithmetic subsequence slices are:
[2,4,6]
[4,6,8]
[6,8,10]
[2,4,6,8]
[4,6,8,10]
[2,4,6,8,10]
[2,6,10]

Example 2:

Input: nums = [7,7,7,7,7]
Output: 16
Explanation: Any subsequence of this array is arithmetic.

Constraints:

1 <= nums.length <= 1000
-2³¹ <= nums[i] <= 2³¹ - 1

Solution¶

class Solution {
    public int numberOfArithmeticSlices(int[] nums) {
        int n = nums.length;
        HashMap<Long, Integer>[] dp = new HashMap[n + 1];
        int res = 0;
        for (int i = 0; i < n; i++) {
            dp[i] = new HashMap<>();
            for (int j = i - 1; j >= 0; j--) {
                long diff = (long)(nums[i] * 1L - nums[j] * 1L);
                res += dp[j].getOrDefault(diff, 0);
                dp[i].put(diff, dp[i].getOrDefault(diff, 0) + dp[j].getOrDefault(diff, 0) + 1);
            }
        }
        return res;
    }
}

Complexity Analysis¶

Time Complexity: O(?)
Space Complexity: O(?)

Approach¶

Detailed explanation of the approach will be added here