# 446. Arithmetic Slices II - Subsequence

## Description

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

## Solutions

• class Solution {
public int numberOfArithmeticSlices(int[] nums) {
int n = nums.length;
Map<Long, Integer>[] f = new Map[n];
Arrays.setAll(f, k -> new HashMap<>());
int ans = 0;
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].merge(d, cnt + 1, Integer::sum);
}
}
return ans;
}
}

• class Solution {
public:
int numberOfArithmeticSlices(vector<int>& nums) {
int n = nums.size();
unordered_map<long long, int> f[n];
int ans = 0;
for (int i = 0; i < n; ++i) {
for (int j = 0; j < i; ++j) {
long long d = 1LL * nums[i] - nums[j];
int cnt = f[j][d];
ans += cnt;
f[i][d] += cnt + 1;
}
}
return ans;
}
};

• class Solution:
def numberOfArithmeticSlices(self, nums: List[int]) -> int:
f = [defaultdict(int) for _ in nums]
ans = 0
for i, x in enumerate(nums):
for j, y in enumerate(nums[:i]):
d = x - y
ans += f[j][d]
f[i][d] += f[j][d] + 1
return ans


• func numberOfArithmeticSlices(nums []int) (ans int) {
f := make([]map[int]int, len(nums))
for i := range f {
f[i] = map[int]int{}
}
for i, x := range nums {
for j, y := range nums[:i] {
d := x - y
cnt := f[j][d]
ans += cnt
f[i][d] += cnt + 1
}
}
return
}

• function numberOfArithmeticSlices(nums: number[]): number {
const n = nums.length;
const f: Map<number, number>[] = new Array(n).fill(0).map(() => new Map());
let ans = 0;
for (let i = 0; i < n; ++i) {
for (let j = 0; j < i; ++j) {
const d = nums[i] - nums[j];
const cnt = f[j].get(d) || 0;
ans += cnt;
f[i].set(d, (f[i].get(d) || 0) + cnt + 1);
}
}
return ans;
}