0413. Arithmetic Slices (M)

Arithmetic Slices (M)

题目

A sequence of numbers 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 sequences:

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 the 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.

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题意

求数组中所有等差数列的个数。

思路

每次都找到一个最长的等差数列，那么里面包含的所有子等差数列的个数可以直接计算出来。

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代码实现

Java

class Solution {
    public int numberOfArithmeticSlices(int[] A) {
        if (A.length < 3) {
            return 0;
        }

        int ans = 0;
        int len = 2, diff = A[1] - A[0];

        for (int i = 2; i < A.length; i++) {
            if (A[i] - A[i - 1] == diff) {
                len++;
            } else {
                if (len >= 3) ans += (len - 1) * (len - 2) / 2;
                len = 2;
                diff = A[i] - A[i - 1];
            }
        }

        if (len >= 3) ans += (len - 1) * (len - 2) / 2;

        return ans;
    }
}