LeetCode-413. Arithmetic Slices

LeetCode-413. Arithmetic Slices

​​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, 97, 7, 7, 73, -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.

题解：dp问题。dp[i-1]为i-1前的连续等差数列中长度为3的子数列个数，然后每当A[i]加入后，判断与前者是否为等差，动态更新dp[i]。而0-n的连续等差子数列为dp[0]-dp[n-1]之和。

class Solution {public: int numberOfArithmeticSlices(vector& A) { int n = A.size(), ans = 0; vector dp(n, 0); if (n < 3){ return 0; } for (int i = 2; i < n; i++){ if (A[i] - A[i - 1] == A[i - 1] - A[i - 2]){ dp[i] = dp[i - 1] + 1; } ans += dp[i]; } return ans; }};

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