Leetcode 53. Maximum Subarray

Find the contiguous subarray within an array (containing at least one number) which has the largest sum.

For example, given the array

[−2,1,−3,4,−1,2,1,−5,4]

,

the contiguous subarray

[4,−1,2,1]

has the largest sum =

6

.

click to show more practice.

More practice:
If you have figured out the O(n) solution, try coding another solution using the divide and conquer approach, which is more subtle.

[Solution]
dynamic programming:
let local_suffix[0...i....n] represet max subarray contains the ith number in A[],

if (local_suffix[i - 1] <= 0)
　　local_suffix[i] = A[i - 1];
else
　　local_suffix[i] = local_suffix[i - 1] + A[i - 1];

int maxSubArray(int A[], int n)
{
if (n <= 0)
return -1;
int global_suffix = INT_MIN, *local_suffix = new int[n + 1];

local_suffix[0] = 0;
for (int i = 1; i <= n; i++)
{
if (local_suffix[i - 1] <= 0)
local_suffix[i] = A[i - 1];
else
local_suffix[i] = local_suffix[i - 1] + A[i - 1];

if (global_suffix < local_suffix[i])
global_suffix = local_suffix[i];
}

delete[] local_suffix;
return global_suffix;
}

However, this uses O(n) memory. We can use just local_suffix instead.

int maxSubArray(int A[], int n)
{
if (n <= 0)
return -1;
int global_suffix = INT_MIN, local_suffix;

for (int i = 0; i < n; i++)
{
if (local_suffix <= 0)
local_suffix = A[i];
else
local_suffix = local_suffix + A[i];

if (global_suffix < local_suffix)
global_suffix = local_suffix;
}

return global_suffix;
}