5192: Tape Equilibrium
[Creator : ]
Description
Minimize the value |(A[0] + ... + A[P-1]) - (A[P] + ... + A[N-1])|.
A non-empty array A consisting of N integers is given. Array A represents numbers on a tape.
Any integer P, such that 0 < P < N, splits this tape into two non-empty parts: A[0], A[1], ..., A[P − 1] and A[P], A[P + 1], ..., A[N − 1].
The difference between the two parts is the value of: |(A[0] + A[1] + ... + A[P − 1]) − (A[P] + A[P + 1] + ... + A[N − 1])|
In other words, it is the absolute difference between the sum of the first part and the sum of the second part.
For example, consider array A such that:
A[0] = 3 A[1] = 1 A[2] = 2 A[3] = 4 A[4] = 3 We can split this tape in four places:
Write an efficient algorithm for the following assumptions:
A non-empty array A consisting of N integers is given. Array A represents numbers on a tape.
Any integer P, such that 0 < P < N, splits this tape into two non-empty parts: A[0], A[1], ..., A[P − 1] and A[P], A[P + 1], ..., A[N − 1].
The difference between the two parts is the value of: |(A[0] + A[1] + ... + A[P − 1]) − (A[P] + A[P + 1] + ... + A[N − 1])|
In other words, it is the absolute difference between the sum of the first part and the sum of the second part.
For example, consider array A such that:
A[0] = 3 A[1] = 1 A[2] = 2 A[3] = 4 A[4] = 3 We can split this tape in four places:
-
P = 1, difference = |3 − 10| = 7
-
P = 2, difference = |4 − 9| = 5
-
P = 3, difference = |6 − 7| = 1
- P = 4, difference = |10 − 3| = 7
Write an efficient algorithm for the following assumptions:
- N is an integer within the range [2..100,000];
- each element of array A is an integer within the range [−1,000..1,000].
Input
Two lines.
First line: N
Second line: N elements.
First line: N
Second line: N elements.
Output
One element. the minimal difference that can be achieved.
Sample 1 Input
5
3 1 2 4 3
Sample 1 Output
1