Maximum Contiguous Sum in Java

The challenge

Given an unsorted array of integer values, find the maximum positive sum of any contiguous range within the array.

An array containing only negative values can return 0. Your solution should be efficient enough to not throw a timeout exception.

Example:

// returns 24
maxContiguousSum([3, -4, 8, 7, -10, 19, -3]);

// returns 5
maxContiguousSum([-8, -10, -12, -2, -3, 5]);

Visual example:

[3, -4, 8, 7, -10, 19, -3]
       |_____________|
             ||
             \/
             24

The solution in Java code

Option 1:

public class Solution {
    public static int maxContiguousSum(final int[] arr) {
        int max = 0, sum = 0;
        for (int num : arr) {
            sum = Math.max(sum + num, 0);
            max = Math.max(sum, max);
        }
        return max;    
    }
}

Option 2:

import java.util.Arrays;

public class Solution {
    public static int maxContiguousSum(final 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); 
    }
}

Option 3:

public class Solution {
    public static int maxContiguousSum(final int[] arr) {
        int max = 0;
        int prev = 0;
        for (int i = 0; i < arr.length; ++i) {
            int prevExt = prev + arr[i];
            if (prevExt > arr[i]) {
                prev = prevExt;
            } else {
                prev = arr[i];
            }
            if (prev > max) {
                max = prev;
            }
        }
        return max; 
    }
}

Test cases to validate our solution

import org.junit.Test;
import static org.junit.Assert.assertEquals;
import org.junit.runners.JUnit4;
import java.util.*;
public class SolutionTest {
    private static int randint(int a, int b) {return a + new Random().nextInt(b - a + 1);}
    @Test
    public void fixedTests() {
        doTest(new int[]{3, -4, 8, 7, -10, 19, -3}, 24);
        doTest(new int[]{2, -3, -3, 9, -29, 8, -9}, 9);
        doTest(new int[]{1, 2, 3, -8, 3, 3, 4, -2, 7, -2}, 15);        
        doTest(new int[]{-8, 1, 7, -2, -3, 4, -2, 5}, 10);
        doTest(new int[]{7, -7, 8, -2, 3, -2, 1, -1}, 9);
        doTest(new int[]{-2, -1, 4, -2, 2, 3, -2}, 7);
        doTest(new int[]{32, -11, -56, 78, -8, 1, -2}, 78);
        doTest(new int[]{-10, 8, 3, -100, 23, 12, 56}, 91);
        doTest(new int[]{58, 10, -32, -22, 3, -4, 34}, 68);
        doTest(new int[]{7, -7, 8, -2, 3, -2, 1, -11 -2}, 9);
        doTest(new int[]{3, 4, -3, 2, -9, -9, -4, -2, 32}, 32);
        doTest(new int[]{-1, -2, -3}, 0);
    }
    @Test
    public void randomTests() {
        for (int trial = 0; trial < 100; trial++) {
            int[] v = new int[randint(1,30)];
            for (int i = 0; i < v.length; i++)
                v[i] = randint(-10,10);
            doTest(v, solution(v));
        }
    }
    @Test
    public void moreRandomTests() {
        for (int trial = 0; trial < 1000; trial++) {
            int[] v = new int[10000];
            for (int i = 0; i < 10000; i++)
                v[i] = randint(-5000,5000);
            doTest(v, solution(v));
        }
    }
    private int solution(final int[] arr) {
        int max_so_far = arr[0]; 
        int curr_max = arr[0]; 
        int cnt = (arr[0] < 0)? 1 : 0;
        for (int i = 1; i < arr.length; i++) { 
            if(arr[i] < 0) cnt++;
            curr_max = Math.max(arr[i], curr_max+arr[i]); 
            max_so_far = Math.max(max_so_far, curr_max); 
        } 
        return cnt == arr.length? 0: max_so_far; 
    }
    private void doTest(final int[] numbers, final int expected) {
        assertEquals(expected, Solution.maxContiguousSum(numbers));
    }
}