[LeetCode] 446. Arithmetic Slices II - Subsequence

[frdmu]

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.

 

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
• -2^31 <= nums[i] <= 2^31 - 1

 

解法：
动态规划，直接看答案，反正不会，举个例子：

代码如下：

class Solution {
public:
    int numberOfArithmeticSlices(vector<int>& nums) {
        int n = nums.size();
        int ans = 0;
        vector<unordered_map<long, int>> f(n);

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < i; j++) {
                long d = (long)nums[i] - nums[j];
                auto it = f[j].find(d);
                int cnt = it == f[j].end() ? 0 : it->second;
                ans += cnt;
                f[i][d] += cnt + 1;
            }
        }

        return ans;
    }
};