Description
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
2
31, 3, 5, 7, 9
7, 7, 7, 7
3, -1, -5, -9
The following sequence is not arithmetic.1
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
1 | A = [1, 2, 3, 4] |
Solution
Solution 1: Best solution1
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15class Solution {
public int numberOfArithmeticSlices(int[] A) {
int cur = 0;
int sum = 0;
for (int i = 2; i < A.length; i++){
if (A[i] - A[i - 1] == A[i - 1] - A[i - 2]){
cur++;
sum += cur;
}
else
cur = 0;
}
return sum;
}
}
Solution 2: Basic DP, O(N) space1
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16class Solution {
// Basic DP Solution, O(N) time O(N) space
public int numberOfArithmeticSlices(int[] A) {
if (A.length < 3) return 0;
int[] dp = new int[A.length];
int sum = 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;
else dp[i] = 0;
sum += dp[i];
}
return sum;
}
}