Leetcode: Arithmetic Slices

Posted 2020-08-21 neverlandly

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.

A slice (P, Q)其实就是从P到Q的序列，（P，Q）是arithmetic slice要求是等差数列且至少有三个数，问array里面有多少个这样的（P, Q）

这道题难点在于想到用DP，一旦想到用DP，就迎刃而解

dp[i]表示以i结束的slice有多少个

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