611. Valid Triangle Number

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Given an array consists of non-negative integers, your task is to count the number of triplets chosen from the array that can make triangles if we take them as side lengths of a triangle.

Example 1:

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Input: [2,2,3,4]
Output: 3
Explanation:
Valid combinations are:
2,3,4 (using the first 2)
2,3,4 (using the second 2)
2,2,3

Note:

The length of the given array won't exceed 1000.
The integers in the given array are in the range of [0, 1000].

解法1：O(N^2)

这题的思路和3SUM smaller很像，也可以用O(N^2)解决。
首先要确定，满足一个三角形的条件是任意两条边之和要大于第三条边。那么如果先对数组排序。
如果AC, 另外两个条件一定也满足。
用3sum smaller的算法是先固定一个点。这题里面我们固定住最大的边比较好想
从后往前扫描，用双指针指向最小的两条边。如果left + right > 第三边,那么从left 到right的所有边都可以满足[right, last]这个组合。

C++

1

Java

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public class Solution {
    public int triangleNumber(int[] nums) {
        if (nums.length == 0) {
            return 0;
        }
        Arrays.sort(nums);
        int res = 0;
        if (nums.length < 3) {
            return res;
        }
        int n = nums.length;
        for (int i = n - 1; i >= 2; i--) {
            int left = 0, right = i - 1;
            while (left < right) {
                if (nums[left] + nums[right] > nums[i]) {
                    res += right - left;
                    right--;
                } else {
                    left++;
                }
            }
        }
        return res;
    }
}