LeetCode 413. Arithmetic Slices

原題連接在這裏：https://leetcode.com/problems/arithmetic-slices/description/

題目：

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.

題解：

DP問題. 求有多少種arithmetic slices. 儲存歷史信息dp[i]表示A在[k, i]區間內自己是arithmetic slice, 以A[i]結尾有多少種arithmetic slices.

遞推時dp[i] = dp[i-1]+1.

初始化都是0.

答案dp內元素的和.

簡化空間用cur取代一維數組. 當再也不是arithmetic時cur清0.

Time Complexity: O(A.length). 

Space: O(1).

AC Java:

 1 class Solution {
 2     public int numberOfArithmeticSlices(int[] A) {
 3         if(A == null || A.length < 3){
 4             return 0;
 5         }
 6         
 7         int cur = 0;
 8         int sum = 0;
 9         for(int i = 2; i<A.length; i++){
10             if(A[i] - A[i-1] == A[i-1] - A[i-2]){
11                 cur++;
12                 sum += cur;
13             }else{
14                 cur = 0;
15             }
16         }
17         return sum;
18     }
19 }

跟上Arithmetic Slices II - Subsequence.