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Problem of the day

You are given an array “arr'' of integers. Your task is to find the contiguous subarray within the array which has the largest product of its elements. You have to report this maximum product.

```
An array c is a subarray of array d if c can be obtained from d by deletion of several elements from the beginning and several elements from the end.
For e.g.- The non-empty subarrays of an array [1,2,3] will be- [1],[2],[3],[1,2],[2,3],[1,2,3].
```

```
If arr = {-3,4,5}.
All the possible non-empty contiguous subarrays of “arr” are {-3}, {4}, {5}, {-3,4}, {4,5} and {-3,4,5}.
The product of these subarrays are -3, 4, 5, -12, 20 and -60 respectively.
The maximum product is 20. Hence, the answer is 20.
```

```
Can you solve this in linear time and constant space complexity?
```

Detailed explanation

```
1 <= T <= 100
1 <= N <= 5000
-100 <= arr[i] <= 100
where N is the size of the array “arr”.
Time limit: 1 second
```

```
2
4
3 5 -2 -4
5
2 4 3 5 6
```

```
120
720
```

```
For the first test case, all the possible non-empty contiguous subarrays of “arr” are {3}, {5}, {-2}, {-4}, {3,5}, {5,-2}, {-2,-4}, {3,5,-2}, {5,-2,-4} and {3,5,-2,-4}.
The product of these subarrays are 3, 5, -2, -4, 15, -10, 8, -30, 40 and 120 respectively.
So, the maximum product is 120.
For the second test case, since all the elements in the array “arr” are positive, we get the maximum product subarray by multiplying all the elements in the array. So, the maximum product is 720.
```

```
2
4
6 0 2 -4
3
-1 -3 -4
```

```
6
12
```