Count Contained Intervals - Amazon Top Interview Questions


Problem Statement :


You are given a two-dimensional list of integers intervals. Each value is unique and contains an inclusive interval [start, end]. Return the number of intervals are contained by another interval. An interval that's contained by multiple other intervals should only be counted once.

An interval [s0, e0] contains another interval [s1, e1] if s0 ≤ s1 and e0 ≥ e1.

Constraints

0 ≤ n ≤ 100,000 where n is the length of intervals

Example 1

Input

intervals = [
    [1, 5],
    [2, 3],
    [3, 6],
    [4, 4]
]

Output

2

Explanation


[2, 3] and [4, 4] are contained by [1, 5]. [4, 4] is also contained by [3, 6] but we don't count it again.


Example 2

Input

intervals = [
    [1, 2],
    [2, 3],
    [1, 5]
]

Output

2

Explanation

Both [1, 2] and [2, 3] are contained by [1, 5]


Solution :



title-img 




                        Solution in C++ :

int solve(vector<vector<int>>& nums) {
    sort(nums.begin(), nums.end(), [](vector<int>& a, vector<int>& b) {
        if (a[0] == b[0]) return a[1] > b[1];
        return a[0] < b[0];
    });
    int count = 0, pe = INT_MIN;
    for (auto& n : nums) {
        if (n[1] <= pe) {
            count += 1;
        } else {
            pe = n[1];
        }
    }
    return count;
}
                    




                        Solution in Python : 
                            
class Solution:
    def solve(self, intervals):
        events = []
        OPEN, CLOSE = 0, 1

        for i, (start, end) in enumerate(intervals):
            events.append((start, OPEN, end, i))
            events.append((end, CLOSE, end, i))

        events.sort(key=lambda x: (x[0], -x[2]))

        ans = 0
        balance = 0
        max_end = float("-inf")

        for time, event_type, end, idx in events:
            if event_type == OPEN and end <= max_end:
                ans += 1

            if event_type == OPEN:
                max_end = max(max_end, end)

        return ans


View More Similar Problems

Pair Sums

Given an array, we define its value to be the value obtained by following these instructions: Write down all pairs of numbers from this array. Compute the product of each pair. Find the sum of all the products. For example, for a given array, for a given array [7,2 ,-1 ,2 ] Note that ( 7 , 2 ) is listed twice, one for each occurrence of 2. Given an array of integers, find the largest v

View Solution →

Lazy White Falcon

White Falcon just solved the data structure problem below using heavy-light decomposition. Can you help her find a new solution that doesn't require implementing any fancy techniques? There are 2 types of query operations that can be performed on a tree: 1 u x: Assign x as the value of node u. 2 u v: Print the sum of the node values in the unique path from node u to node v. Given a tree wi

View Solution →

Ticket to Ride

Simon received the board game Ticket to Ride as a birthday present. After playing it with his friends, he decides to come up with a strategy for the game. There are n cities on the map and n - 1 road plans. Each road plan consists of the following: Two cities which can be directly connected by a road. The length of the proposed road. The entire road plan is designed in such a way that if o

View Solution →

Heavy Light White Falcon

Our lazy white falcon finally decided to learn heavy-light decomposition. Her teacher gave an assignment for her to practice this new technique. Please help her by solving this problem. You are given a tree with N nodes and each node's value is initially 0. The problem asks you to operate the following two types of queries: "1 u x" assign x to the value of the node . "2 u v" print the maxim

View Solution →

Number Game on a Tree

Andy and Lily love playing games with numbers and trees. Today they have a tree consisting of n nodes and n -1 edges. Each edge i has an integer weight, wi. Before the game starts, Andy chooses an unordered pair of distinct nodes, ( u , v ), and uses all the edge weights present on the unique path from node u to node v to construct a list of numbers. For example, in the diagram below, Andy

View Solution →

Heavy Light 2 White Falcon

White Falcon was amazed by what she can do with heavy-light decomposition on trees. As a resut, she wants to improve her expertise on heavy-light decomposition. Her teacher gave her an another assignment which requires path updates. As always, White Falcon needs your help with the assignment. You are given a tree with N nodes and each node's value Vi is initially 0. Let's denote the path fr

View Solution →