Question

446. Arithmetic Slices II - Subsequence

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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

Solution 1

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

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;
  }
};

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;
}