Given an array of varying heights above sea level for adjacent plots, and the array of water levels on consecutive days, find the number of islands. An island is a slice of array such that plots adjacent to the boundary of the island are under water.

class Solution { 

public int[] solution(int[] A, int[] B) {

    return Arrays

    .stream(B)

    .map(water -> IntStream

         .range(0, N)

         .filter(j -> (A[j] > water) && (j == N - 1 || A[j + 1] <= water))

         .map(i -> 1)

         .sum()) .toArray();

}

}

For example, given the following arrays A and B:

    A[0] = 2    B[0] = 0

    A[1] = 1    B[1] = 1

    A[2] = 3    B[2] = 2

    A[3] = 2    B[3] = 3

    A[4] = 3    B[4] = 1

Solution: 

result[0] = 1

result[1] = 2

result[2] = 2

result[3] = 0

result[4] = 2

For a water level, the number of islands is just the sum of changes in the number of islands as the water level is decreasing.

Optimized solution:

class Solution { 

public int[] solution(int[] A, int[] B) {

     int limit = Math.max(maxLevel(A), maxLevel(B));

     int[] island = new int[limit + 2];

     IntStream.range(0, A.length - 1)

                       .filter( j -> A[j]  > A[j+1])

                      .forEach(j ->  {

                                       island[A[j]] += 1;

                                       island[A[j + 1]] -= 1;

                       });

     island[A[A.length-1]] += 1;

     IntStream.range(-limit, 0)

                      .forEach(i -> island[-i] += island[-i+1]);

     return Arrays.stream(B).map(water -> island[water + 1]).toArray();

}

public int maxLevel(int[] A) {

       return Arrays.stream(A).max().getAsInt();

}

}

// before cumulation

island[0] = 0

island[1] = -1

island[2] = 0

island[3] = 2

island[4] = 0

// after cumulation

island[0] = 1

island[1] = 1

island[2] = 2

island[3] = 2

island[4] = 0

result[0] = 1

result[1] = 2

result[2] = 2

result[3] = 0

result[4] = 2