# Maximum Product of Three Numbers

Given an integer array, find three numbers whose product is maximum and output the maximum product.

## Example

**Example 1:**

```
Input:
 [1,2,3]

Output:
 6
```

**Example 2:**

```
Input:
 [1,2,3,4]

Output:
 24
```

## Note

找最小的两个数（对应负数情况）

同时找最大的三个数

```
Math.max(min1 * min2 * max1, max1 * max2 * max3);
```

## Code

```java
class Solution {
    public int maximumProduct(int[] nums) {
        int min1 = Integer.MAX_VALUE, min2 = Integer.MAX_VALUE;
        int max1 = Integer.MIN_VALUE, max2 = Integer.MIN_VALUE, max3 = Integer.MIN_VALUE;
        for (int n: nums) {
            if (n <= min1) {
                min2 = min1;
                min1 = n;
            } else if (n <= min2) {     // n lies between min1 and min2
                min2 = n;
            }
            if (n >= max1) {            // n is greater than max1, max2 and max3
                max3 = max2;
                max2 = max1;
                max1 = n;
            } else if (n >= max2) {     // n lies betweeen max1 and max2
                max3 = max2;
                max2 = n;
            } else if (n >= max3) {     // n lies betwen max2 and max3
                max3 = n;
            }
        }
        return Math.max(min1 * min2 * max1, max1 * max2 * max3);
    }
}
```


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