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

Solution: Dynamic Programming

• Time complexity: O(n²)
• Space complexity: O(n²)

 

JavaScript

/**
 * @param {number[]} nums
 * @return {number}
 */
const numberOfArithmeticSlices = function (nums) {
  const n = nums.length;
  const dp = new Array(n)
    .fill('')
    .map(_ => new Map());
  let result = 0;

  const getCount = (map, diff) => map.get(diff) ?? 0;

  for (let a = 1; a < n; a++) {
    const numA = nums[a];

    for (let b = 0; b < a; b++) {
      const numB = nums[b];
      const diff = numA - numB;
      const count = getCount(dp[b], diff);

      result += count;
      dp[a].set(diff, getCount(dp[a], diff) + count + 1);
    }
  }
  return result;
};