第17周Arithmetic Slices

Arithmetic Slices

Leetcode algorithms problem 413：Arithmetic Slices

• 問題描述

  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.

• 例子

  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

  dp[i]設爲(k,i)範圍內的算術切片數量，k爲最小的可能索引
  if(A[i] - A[i-1] == A[i-1] - A[i-2]) dp[i] = d[i-1] + 1

代碼

class Solution {
public:
    int numberOfArithmeticSlices(vector<int>& A) {
        int *dp = new int[A.size()];
        fill_n(dp, A.size(), 0);
        int sum = 0;
        for(int i = 2; i < A.size(); i++){
            if((A[i] - A[i-1]) == (A[i-1] - A[i-2])){
                dp[i] = 1 + dp[i-1];
                sum += dp[i];
            }
        }
        return sum;     
    }
};

時間複雜度: O(n)
空間複雜度: O(n)

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