Algorithm
Problem Name: 446. Arithmetic Slices II - Subsequence
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
Code Examples
#1 Code Example with Javascript Programming
Code -
Javascript Programming
const numberOfArithmeticSlices = function(A) {
if (!A || A.length < 3) return 0;
let res = 0;
const dp = Array(A.length);
for (let i = 0; i < A.length; i++) {
dp[i] = new Map();
for (let j = 0; j < i; j++) {
const diff = A[i] - A[j];
const prevCount = dp[j].get(diff) || 0;
res += prevCount;
const currCount = (dp[i].get(diff) || 0) + 1;
dp[i].set(diff, prevCount + currCount);
}
}
return res;
};
Input
nums = [2,4,6,8,10]
Output
7
#2 Code Example with Python Programming
Code -
Python Programming
class Solution:
def numberOfArithmeticSlices(self, A):
dp, res = collections.defaultdict(dict), 0
for j in range(len(A)):
for i in range(j):
dp[j][A[j] - A[i]] = dp[j].get(A[j] - A[i], 0) + dp[i].get(A[j] - A[i], 1)
if A[j] - A[i] in dp[i]: res, dp[j][A[j] - A[i]] = res + dp[i][A[j] - A[i]], dp[j][A[j] - A[i]] + 1
return res
Input
nums = [2,4,6,8,10]
Output
7