LeetCode 413. Arithmetic Slices

原题链接在这里：https://leetcode.com/problems/arithmetic-slices/description/

题目：

A sequence of number 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, these are arithmetic sequence:

1, 3, 5, 7, 9
7, 7, 7, 7
3, -1, -5, -9

The following sequence is not arithmetic.

1, 1, 2, 5, 7

A zero-indexed array A consisting of N numbers is given. A slice of that array is any pair of integers (P, Q) such that 0 <= P < Q < N.

A slice (P, Q) of array A is called arithmetic if the sequence:
A[P], A[p + 1], ..., A[Q - 1], A[Q] is arithmetic. In particular, this means that P + 1 < Q.

The function should return the number of arithmetic slices in the array A.

Example:

A = [1, 2, 3, 4]

return: 3, for 3 arithmetic slices in A: [1, 2, 3], [2, 3, 4] and [1, 2, 3, 4] itself.

题解：

DP问题. 求有多少种arithmetic slices. 储存历史信息dp[i]表示A在[k, i]区间内本身是arithmetic slice, 以A[i]结尾有多少种arithmetic slices.

递推时dp[i] = dp[i-1]+1.

初始化都是0.

答案dp内元素的和.

简化空间用cur取代一维数组. 当不再是arithmetic时cur清0.

Time Complexity: O(A.length). 

Space: O(1).

AC Java:

class Solution {
    public int numberOfArithmeticSlices(int[] A) {
        if(A == null || A.length < 3){
            return 0;
        }
        
        int cur = 0;
        int sum = 0;
        for(int i = 2; i<A.length; i++){
            if(A[i] - A[i-1] == A[i-1] - A[i-2]){
                cur++;
                sum += cur;
            }else{
                cur = 0;
            }
        }
        return sum;
    }
}

跟上Arithmetic Slices II - Subsequence.