Triangle Triplets - Amazon Top Interview Questions

Problem Statement :

Given a list of non-negative integers nums, return the total number of 3 numbers i < j < k, such that nums[i] + nums[j] > nums[k].


n ≤ 1,000 where n is the length of nums

Example 1


nums = [7, 8, 8, 9, 100]




We can make these triangles:

7, 8, 8
7, 8, 9
7, 8, 9 (using the other 8)
8, 8, 9

Solution :


                        Solution in C++ :

int solve(vector<int>& nums) {
    sort(nums.begin(), nums.end());

    int res = 0;
    int n = nums.size();

    // triangle inequality: a+b > c
    // Fix a c, then count how many (a,b) such that nums[a] + nums[b] > nums[c]
    for (int c = n - 1; c >= 0; c--) {
        int a = 0;
        int b = c - 1;

        while (a < b) {
            if (nums[a] + nums[b] > nums[c]) {
                res += (b - a);
            } else {
    return res;

                        Solution in Python : 
class Solution:
    def solve(self, nums):
        count = 0
        n = len(nums)
        for i in range(n - 1, 1, -1):
            l, r = 0, i - 1
            while l < r:
                if nums[l] + nums[r] <= nums[i]:
                    l += 1
                    count += r - l
                    r -= 1
        return count

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