leetcode -- 413. Arithmetic Slices

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.

来源：力扣（LeetCode）
链接：https://leetcode-cn.com/problems/arithmetic-slices
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我的思路：

1. dp[i][j]表示从i到j是否是等差数列

2. 再枚举长度，但是有个样例（1,2,3,8,9,10）算出来是6，我自己验算是2....头秃！

class Solution {
public:
    int numberOfArithmeticSlices(vector<int>& A) {
        int len = A.size();
        if(len == 0) return 0;
        vector<vector<int>> dp(len, vector<int>(len,0));
        int ans = 0;
        for(int i = 0; i < len-1; i++){ //每一行
            dp[i][i] = 1;
            int arth = A[i+1]- A[i];
            for(int j = i+1; j < len; j++){
                if(A[j]-A[j-1] == arth){
                    dp[i][j] = 1;
                }
            }
        }
        
        for(int l = 3; l <= len; l++){
            for(int i = 0; i+l-1 < len; i++){
                int j = i+l-1;
                if(dp[i][j] == 1) ans++;
            }
        }
        return ans;
    }
};

 

参考代码思路：

1. dp[i]表示以元素A[i]结尾的等差数列的个数

class Solution {
public:
	int numberOfArithmeticSlices(vector<int>& A) {
		int len = A.size(), result = 0;
		vector<int> dp(len, 0);//dp[i]用于保存以A[i]结尾的等差数列的个数
		for (int i = 2; i < len; ++i) {//等差数列长度需要大于2，所以前两个必定为0
            //判断步长
			if (A[i] - A[i - 1] == A[i - 1] - A[i - 2]) {
				dp[i] = dp[i - 1] + 1;//转移方程
				result += dp[i];//求和
			}
		}
		return result;
	}
};
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作者：hestyle 
来源：优快云 
原文：https://blog.youkuaiyun.com/qq_41855420/article/details/88721808 
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