## Question

Given an integer array `nums`

, find a subarray that has the largest product, and return *the product*.

The test cases are generated so that the answer will fit in a **32-bit** integer.

**Example 1:**

```
Input: nums = [2,3,-2,4]
Output: 6
Explanation: [2,3] has the largest product 6.
```

**Example 2:**

```
Input: nums = [-2,0,-1]
Output: 0
Explanation: The result cannot be 2, because [-2,-1] is not a subarray.
```

**Constraints:**

`1 <= nums.length <= 2 * 104`

`-10 <= nums[i] <= 10`

- The product of any prefix or suffix of
`nums`

is**guaranteed**to fit in a**32-bit**integer.

## Algorithm

- The Constrains is a little misleading, making me think it may leverage prefix products;
- A tricky way in my view, leverage dynamic programming.
- Maintain the max so far and min so far, each number next can be
- the largest, or
- multiply max
- be the max
- or min,

- Miltiply min
- Be the max
- Or min

- By loop all the elements in one pass we get the max.

## Code

class Solution { public int maxProduct(int[] nums) { int max = nums[0], min = nums[0], res = nums[0]; for (int i = 1; i < nums.length; i++) { int temp = max; max = Math.max(nums[i], Math.max(nums[i] * max, nums[i] * min)); min = Math.min(nums[i], Math.min(nums[i] * temp, nums[i] * min)); res = Math.max(res, max); } return res; } }