Arithmetic Slices

题目地址：
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.

解题思路：
这道题也是可以借鉴之前的动态规划的思想来解决。

代码：

public int numberOfArithmeticSlices(int[] A) {
    if(A == null || A.length <= 2){
        return 0;
    }
    boolean[][] dp = new boolean[A.length][A.length];
    int len = A.length;
    for(int i = 0; i <= len - 1; i++){
        for(int j = i; j <= len - 1; j++){
            if(j == i || j - i == 1){
                dp[i][j] = true;
            }
            else if(dp[i][j - 1] && (A[j] - A[j - 1] == A[j - 1] - A[j - 2])){
                dp[i][j] = true;
            }
            else{
                dp[i][j] = false;
            }
        }
    }
    int rst = 0;
    for(int i = 0; i <= len - 3; i++){
        for(int j = i + 2; j <= len - 1; j++){
            if(dp[i][j]){
                rst++;
            }
        }
    }
    return rst;
}