Given an array of numbers, calculate the largest sum of all possible blocks of consecutive elements within the array. The numbers will be a mix of positive and negative values. If all numbers of the sequence are nonnegative, the answer will be the sum of the entire array. If all numbers in the array are negative, your algorithm should return zero. Similarly, an empty array should result in a zero return from your algorithm.

```
largestSum([-1,-2,-3]) == 0
largestSum([]) == 0
largestSum([1,2,3]) == 6
```

Easy, right? This becomes a lot more interesting with a mix of positive and negative numbers:

```
largestSum([31,-41,59,26,-53,58,97,-93,-23,84]) == 187
```

The largest sum comes from elements in positions 3 through 7:
```59+26+(-53)+58+97 == 187```

Once your algorithm works with these, the test-cases will try your submission with increasingly larger random problem sizes.

Source: codewars | Difficulty: EASY
Tags: Fundamentals

Mathematics

Starter code: def largest_sum(arr):
	

Solutions:
def largest_sum(arr):
	sum = max_sum = 0
	for n in arr:
		sum = max(sum + n, 0)
		max_sum = max(sum, max_sum)
	return max_sum


def largest_sum(arr):
	(a, b, ar) = (0, 0, arr[:])
	for i in ar:
		b += i
		if b < 0:
			b = 0
		if b > a:
			a = b
	return a


def largest_sum(a):
	m = c = 0
	for i in a:
		c = max(0, c + i)
		m = max(m, c)
	return m


def largest_sum(arr):
	current = so_far = 0
	for n in arr:
		current += n
		if current > so_far:
			so_far = current
		if current <= 0:
			current = 0
	return so_far


def largest_sum(arr):
	(c, m) = (0, 0)
	for n in arr:
		c = max(0, c + n)
		m = max(m, c)
	return m


def largest_sum(arr):
	largest = 0
	temp = 0
	for num in arr:
		temp += num
		if temp < 0:
			temp = 0
		elif temp > largest:
			largest = temp
	return largest


def largest_sum(arr):
	if len(arr) == 0:
		return 0
	cache = [arr[0]]
	for i in range(1, len(arr)):
		cache.append(max(arr[i], cache[-1] + arr[i]))
	return 0 if max(cache) < 0 else max(cache)


def largest_sum(arr):
	best_sum = 0
	current_sum = 0
	for item in arr:
		current_sum += item
		if current_sum < 0:
			current_sum = 0
		elif current_sum > best_sum:
			best_sum = current_sum
	return best_sum


def largest_sum(a):
	best_sum = 0
	current_sum = 0
	for x in a:
		current_sum = max(0, current_sum + x)
		best_sum = max(best_sum, current_sum)
	return best_sum


def largest_sum(arr):
	(ans, sum) = (0, 0)
	for i in range(len(arr)):
		sum = max(arr[i], arr[i] + sum)
		ans = max(ans, sum)
	return ans