A non-empty zero-indexed array A consisting of N integers is given. A pair of integers (P, Q), such that 0 ≤ P ≤ Q < N, is called a slice of array A. The sum of a slice (P, Q) is the total of A[P] + A[P+1] + ... + A[Q].
Write a function:
class Solution { public int solution(int[] A); }
that, given an array A consisting of N integers, returns the maximum sum of any slice of A.
For example, given array A such that:
A[0] = 3 A[1] = 2 A[2] = -6 A[3] = 4 A[4] = 0
the function should return 5 because:
- (3, 4) is a slice of A that has sum 4,
- (2, 2) is a slice of A that has sum −6,
- (0, 1) is a slice of A that has sum 5,
- no other slice of A has sum greater than (0, 1).
Assume that:
- N is an integer within the range [1..1,000,000];
- each element of array A is an integer within the range [−1,000,000..1,000,000];
- the result will be an integer within the range [−2,147,483,648..2,147,483,647].
Complexity:
- expected worst-case time complexity is O(N);
- expected worst-case space complexity is O(N), beyond input storage (not counting the storage required for input arguments).
Elements of input arrays can be modified.
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SOLUTION (100%, time complexity O9N))
class Solution {
public int solution(int[] A) {
// write your code in C# 6.0 with .NET 4.5 (Mono)
long max_end=-1000000;
long max_slice=-1000000;
int l= A.Length;
if (l ==1) return A[0];
for (int i=0; i<l; i++)
{
max_end=Math.Max(A[i], max_end+A[i]);
max_slice=Math.Max(max_slice, max_end);
}
return (int) max_slice;
}
}
The method is actually quite well explained here:
