# Largest Sum Contiguous Subarray

Python Programming - Largest Sum Contiguous Subarray - Dynamic Programming Write program to find the sum of contiguous subarray within one-dimensional array

Largest Sum Contiguous Subarray

Write an efficient Python program to find the sum of contiguous subarray within a one-dimensional array of numbers which has the largest sum.

```Initialize:
max_so_far = 0
max_ending_here = 0

Loop for each element of the array
(a) max_ending_here = max_ending_here + a[i]
(b) if(max_ending_here < 0)
max_ending_here = 0
(c) if(max_so_far < max_ending_here)
max_so_far = max_ending_here
return max_so_far
```

### Explanation:

Simple idea of the Kadane’s algorithm is to look for all positive contiguous segments of the array (max_ending_here is used for this). And keep track of maximum sum contiguous segment among all positive segments (max_so_far is used for this). Each time we get a positive sum compare it with max_so_far and update max_so_far if it is greater than max_so_far

```    Lets take the example:
{-2, -3, 4, -1, -2, 1, 5, -3}

max_so_far = max_ending_here = 0

for i=0,  a[0] =  -2
max_ending_here = max_ending_here + (-2)
Set max_ending_here = 0 because max_ending_here < 0

for i=1,  a[1] =  -3
max_ending_here = max_ending_here + (-3)
Set max_ending_here = 0 because max_ending_here < 0

for i=2,  a[2] =  4
max_ending_here = max_ending_here + (4)
max_ending_here = 4
max_so_far is updated to 4 because max_ending_here greater
than max_so_far which was 0 till now

for i=3,  a[3] =  -1
max_ending_here = max_ending_here + (-1)
max_ending_here = 3

for i=4,  a[4] =  -2
max_ending_here = max_ending_here + (-2)
max_ending_here = 1

for i=5,  a[5] =  1
max_ending_here = max_ending_here + (1)
max_ending_here = 2

for i=6,  a[6] =  5
max_ending_here = max_ending_here + (5)
max_ending_here = 7
max_so_far is updated to 7 because max_ending_here is
greater than max_so_far

for i=7,  a[7] =  -3
max_ending_here = max_ending_here + (-3)
max_ending_here = 4
```

### Program for Largest Sum Contiguous Subarray

Python
``````
# Python program to find maximum contiguous subarray

# Function to find the maximum contiguous subarray
from sys import maxint
def maxSubArraySum(a,size):

max_so_far = -maxint - 1
max_ending_here = 0

for i in range(0, size):
max_ending_here = max_ending_here + a[i]
if (max_so_far < max_ending_here):
max_so_far = max_ending_here

if max_ending_here < 0:
max_ending_here = 0
return max_so_far

# Driver function to check the above function
a = [-13, -3, -25, -20, -3, -16, -23, -12, -5, -22, -15, -4, -7]
print "Maximum contiguous sum is", maxSubArraySum(a,len(a)) ``````

### Output :

`Maximum contiguous sum is -3`

Above program can be optimized further, if we compare max_so_far with max_ending_here only if max_ending_here is greater than 0.

READ  Find if there is a path between two vertices in a directed graph

### Program

Python
``````
def maxSubArraySum(a,size):

max_so_far = 0
max_ending_here = 0

for i in range(0, size):
max_ending_here = max_ending_here + a[i]
if max_ending_here < 0:
max_ending_here = 0

# Do not compare for all elements. Compare only
# when  max_ending_here > 0
elif (max_so_far < max_ending_here):
max_so_far = max_ending_here

return max_so_far ``````

Time Complexity: O(n)

The implementation handles the case when all numbers in array are negative.

### Program

Python
``````
# Python program to find maximum contiguous subarray

def maxSubArraySum(a,size):

max_so_far =a[0]
curr_max = a[0]

for i in range(1,size):
curr_max = max(a[i], curr_max + a[i])
max_so_far = max(max_so_far,curr_max)

return max_so_far

# Driver function to check the above function
a = [-2, -3, 4, -1, -2, 1, 5, -3]
print"Maximum contiguous sum is" , maxSubArraySum(a,len(a)) ``````

### Output :

`Maximum contiguous sum is 7`

To print the subarray with the maximum sum, we maintain indices whenever we get the maximum sum.

### Program

Python
``````# Python program to print largest contiguous array sum

from sys import maxsize

# Function to find the maximum contiguous subarray
# and print its starting and end index
def maxSubArraySum(a,size):

max_so_far = -maxsize - 1
max_ending_here = 0
start = 0
end = 0
s = 0

for i in range(0,size):

max_ending_here += a[i]

if max_so_far < max_ending_here:
max_so_far = max_ending_here
start = s
end = i

if max_ending_here < 0:
max_ending_here = 0
s = i+1

print ("Maximum contiguous sum is %d"%(max_so_far))
print ("Starting Index %d"%(start))
print ("Ending Index %d"%(end))

# Driver program to test maxSubArraySum
a = [-2, -3, 4, -1, -2, 1, 5, -3]
maxSubArraySum(a,len(a)) ``````

### Output :

```Maximum contiguous sum is 7
Starting index 2
Ending index 6```