Codility 25번 MaxSliceSum

MaxSliceSum

 

A non-empty 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).

Write an efficient algorithm for the following assumptions:

• 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].

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최대값으로 slice하는 문제는 dynamic programming의 하나인 Kadane’s Algorithm (카데인 알고리즘)으로 O(n)으로 해결할 수 있다.

https://sustainable-dev.tistory.com/23?category=809125

class Solution {
    public int solution(int[] A) {
         if(A.length == 1) return A[0];
    
        int localMaxSum = A[0];
        int globalMaxSum = A[0];
    
        for(int i = 1 ; i < A.length; i++) {
            localMaxSum = Math.max(A[i], localMaxSum + A[i]);
            globalMaxSum = Math.max(globalMaxSum, localMaxSum);
        }
    
        return globalMaxSum;
    }
}

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