446. Arithmetic Slices II - Subsequence

1. Question

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 answer is guaranteed to fit in 32-bit integer.

2. Example

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.


3. Constraints

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

5. Solutions

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

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