# leetcode413. Arithmetic Slices

## 题目要求

```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.```

## 思路一：动态规划

```    public int numberOfArithmeticSlices(int[] A) {
int[] dp = new int[A.length];
int count = 0;
for(int i = 2 ; i<A.length ; i++) {
if(A[i] - A[i-1] == A[i-1] - A[i-2]) {
dp[i] = dp[i-1] + 1;
count += dp[i];
}
}
return count;
}```

## 思路二：算数方法

```    public int numberOfArithmeticSlices2(int[] A) {
if(A.length <3) return 0;
int diff = A-A;
int left = 0;
int right = 2;
int count = 0;
while(right < A.length) {
if(A[right] - A[right-1] != diff) {
count += (right-left-1) * (right-left-2) / 2;
diff = A[right] - A[right-1];
left = right-1;
}
right++;
}
count += (right-left-1) * (right-left-2) / 2;
return count;
}```

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