LeetCode 413. Arithmetic Slices

最新推荐文章于 2021-10-19 11:47:34 发布

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本文介绍了一种用于检测数组中是否存在等差序列的有效算法。该算法通过一次遍历即可找出所有长度至少为3的等差子序列，并返回这些子序列的数量。文中详细解释了算法的工作原理，并附带了一个具体的例子。

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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.

class Solution {
public:
    int numberOfArithmeticSlices(vector<int>& A) {
        int n = A.size();
        int pre = 0;
        int ans = 0;
        for (int i = 2; i < n; ++i) {
            if (A[i] + A[i - 2] == 2 * A[i - 1]) {
                pre += 1;
                ans += pre;
            }
            else {
                pre = 0;
            }
        }
        return ans;
    }
};