## The challenge#

The maximum sum subarray problem consists in finding the maximum sum of a contiguous subsequence in an array or list of integers:

``````Max.sequence(new int[]{-2, 1, -3, 4, -1, 2, 1, -5, 4});
// should be 6: {4, -1, 2, 1}
``````

Easy case is when the list is made up of only positive numbers and the maximum sum is the sum of the whole array. If the list is made up of only negative numbers, return 0 instead.

An empty list is considered to have zero greatest sum. Note that the empty list or array is also a valid sublist/subarray.

## The solution in Java code#

Option 1:

``````public class Max {
public static int sequence(int[] arr) {
int m = 0, a = 0, s = 0;
for(int e : arr) {
s += e;
m = Math.min(s, m);
a = Math.max(a, s - m);
}
return a;
}
}
``````

Option 2:

``````public class Max {
public static int sequence(int[] arr) {
int inst = 0, max = 0;
for (int i : arr) {
inst = Math.max(0, inst + i);
max = Math.max(max, inst);
}
return max;
}
}
``````

Option 3:

``````import java.util.Arrays;

public class Max {
public static int sequence(int[] arr) {
final int[] max = {0};
return Arrays.stream(arr).map(i -> i = max[0] = i + max[0] > 0 ? max[0] + i : 0).max().orElse(0);  }
}
``````

## Test cases to validate our solution#

``````import org.junit.Test;
import static org.junit.Assert.assertEquals;

public class MaxSequenceTest {
@Test
public void testEmptyArray() throws Exception {
assertEquals("Empty arrays should have a max of 0", 0, Max.sequence(new int[]{}));
}
@Test
public void testExampleArray() throws Exception {
assertEquals("Example array should have a max of 6", 6, Max.sequence(new int[]{-2, 1, -3, 4, -1, 2, 1, -5, 4}));
}
@Test
public void testNegativeExampleArray() throws Exception {
assertEquals("Example array with all negative values should have a max of 0", 0, Max.sequence(new int[]{-2, -1, -3, -4, -1, -2, -1, -5, -4}));
}
@Test
public void testCompleteArray() throws Exception {
assertEquals("Should work on this too", 155, Max.sequence(new int[]{7, 4, 11, -11, 39, 36, 10, -6, 37, -10, -32, 44, -26, -34, 43, 43}));
}
@Test
public void testRandomArrays() throws Exception {
for(int i = 0; i < 50; i++) {
int[] rand = randArr((int)(Math.random() * 10 + 50));
assertEquals("Random array solution not as expected: ", solution(rand), Max.sequence(rand));
}
}
private int[] randArr(int size) {
int[] rand = new int[size];
for(int i = 0; i < size; i++) rand[i] = (int)(Math.random() * 60 - 30);
return rand;
}
private int solution(int[] arr) {
int m = 0, a = 0, s = 0;
for(int e : arr) {
s += e;
m = Math.min(s, m);
a = Math.max(a, s - m);
}
return a;
}
}
``````