AveragesOfThree
SRM 843 · 2023-01-03 · by misof
Problem Statement
There was a sequence A that had at least three elements.
The sequence B was obtained by writing down the average of each three consecutive elements of A, from left to right.
For example, if A = {a, b, c, d, e}, then the sequence B would have the form {f, g, h} where f = the average of a,b,c, g = the average of b,c,d, and h = the average of c,d,e.
You are given the sequence B. All its elements are integers. You are also given the information that the first two elements of A were zeros.
Reconstruct A and return it.
Notes
- The sequence A is always unique.
- For the given constraints it is guaranteed that all elements of A are integers that fit into signed 32-bit integer variables.
Constraints
- B will have between 1 and 10 elements, inclusive.
- Each element of B will be between 0 and 1000, inclusive.
{3}
Returns: {0, 0, 9 }
The original sequence was {0, 0, x}, and as the average of 0, 0, and x was 3, it is clear that x must have been 9.
{1, 3, 6, 5}
Returns: {0, 0, 3, 6, 9, 0 }
{3, 1, 4, 1, 5, 9, 2, 6}
Returns: {0, 0, 9, -6, 9, 0, 6, 21, -21, 18 }
As seen here, some elements of the original sequence may be negative integers.
{64, 440, 566, 464, 584, 351}
Returns: {0, 0, 192, 1128, 378, -114, 1488, -321 }
{524, 395, 401, 630, 41}
Returns: {0, 0, 1572, -387, 18, 2259, -2154 }
Submissions are judged against all 56 archived test cases, of which 5 are shown here. Case numbers match the judge’s.
Language: C++17 · define a public class AveragesOfThree with a public method vector<int> restore(vector<int> B) · 56 test cases · 2 s / 256 MB per case