Arithmetic Sequence

求等差数列的个数

Given an array, return the number of possible arithmetic sequence. 给一个数组，返回可能的等差数列个数。

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.

public int numberOfArithmeticSlices(int[] A) {
        if (A == null || A.length < 3) return 0;
        int sum = 0, curr = 0;

        for (int i = 2; i < A.length; i++) {
            if (A[i] - A[i - 1] == A[i - 1] - A[i - 2]) {
                curr++;
                sum += curr;
            } else {
                curr = 0;
            }
        }
        return sum;
    }