# Triangle Count

Given an array of integers, how many three numbers can be found in the array, so that we can build an triangle whose three edges length is the three numbers that we find?

## Example

Given array S =`[3,4,6,7]`, return`3`. They are:

```
[3,4,6]
[3,6,7]
[4,6,7]
```

Given array S =`[4,4,4,4]`, return`4`. They are:

```
[4(1),4(2),4(3)]
[4(1),4(2),4(4)]
[4(1),4(3),4(4)]
[4(2),4(3),4(4)]
```

## Note

其实有点三指针的味道，本质还是3-Sum，注意外层循环是最大的那个元素（和3sum反过来了），两边和大于第三边（更大的那个）保证了三角形的存在，排序是肯定要排序的

计数的时候利用排序的大小关系和双指针进行剪枝

## Code

```java
public class Solution {
    /**
     * @param nums: A list of integers
     * @return: An integer
     */
    public int triangleCount(int[] nums) {
        // write your code here
        if (nums == null || nums.length < 3) {
            return 0;
        }
        Arrays.sort(nums);
        int res = 0;
        // 3 4 6 7 8
        //         i
        // l     r
        for (int i = 2; i < nums.length; i++) {
            int left = 0;
            int right = i - 1;
            while (left < right) {
                if (nums[left] + nums[right] > nums[i]) {
                    res += right - left;
                    right--;
                } else {
                    left++;
                }
            }
        }
        return res;
    }
}
```


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