title

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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.

solution

DP

dp[i] 表示以 A[i] 为结尾的等差递增子区间的个数。

如果 A[i] - A[i - 1] == A[i - 1] - A[i - 2]，表示 [A[i - 2], A[i - 1], A[i]] 是一个等差递增子区间。如果 [A[i - 3], A[i - 2], A[i - 1]] 是一个等差递增子区间，那么 [A[i - 3], A[i - 2], A[i - 1], A[i]] 也是。因此在这个条件下，dp[i] = dp[i-1] + 1。

class Solution {
public:
	int numberOfArithmeticSlices(vector<int>& A) {
		if (A.size() == 0) {
			return 0;
		}
		int n = A.size();
		int *dp = new int[n];
		fill(dp, dp + n, 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;
			}
		}
		int total = 0;
		for (int i = 2; i < n; i++) {
			total += dp[i];
		}
		return total;
	}
};