Divisible Numbers - Amazon Top Interview Questions


Problem Statement :


You are given integers n, a, b, and c. Return the nth (0-indexed) term of the sorted sequence of integers divisible by a, b or c.

Note that by convention the first term of any sequence always starts with 1.

Example 1

Input

n = 8
a = 2
b = 5
c = 7

Output

12

Explanation

The first 9 terms of the sequence are [1, 2, 4, 5, 6, 7, 8, 10, 12]


Solution :



title-img 




                        Solution in C++ :

class Solution {
    public:
    int lcm(int x, int y) {
        return x * y / __gcd(x, y);
    }

    int a, b, c;

    int lesser(int n) {
        // how many elements less than it?
        return n / a + n / b + n / c - n / lcm(a, b) - n / lcm(b, c) - n / lcm(a, c) +
               n / lcm(a, lcm(b, c));
    }

    int solve(int n, int a, int b, int c) {
        this->a = a, this->b = b, this->c = c;

        int l = 1, r = INT_MAX;

        while (l < r) {
            int guess = l + (r - l) / 2;

            // i want the first value with >=n elements lesser than it!
            if (lesser(guess) >= n) {
                r = guess;
            } else {
                l = guess + 1;
                // guess is not the answer! +1 it
            }
        }

        return l;
    }
};

int solve(int n, int a, int b, int c) {
    return (new Solution())->solve(n, a, b, c);
}
                    


                        Solution in Java :

import java.util.*;

class Solution {
    public int solve(int n, int a, int b, int c) {
        int x = 1, y = 1, z = 1;
        int ans = 1;

        while (n-- > 0) {
            int xx = a * x;
            int yy = b * y;
            int zz = c * z;

            ans = Math.min(xx, Math.min(yy, zz));

            if (ans == xx) {
                x++;
            }

            if (ans == yy) {
                y++;
            }

            if (ans == zz) {
                z++;
            }
        }

        return ans;
    }
}
                    


                        Solution in Python : 
                            
class Solution:
    def find_points(self, goal, a, b, c, ab, ac, bc, abc):
        total = 0

        for item in (a, b, c, abc):
            total += goal // item

        for item in (ab, ac, bc):
            total -= goal // item

        return total

    def solve(self, n, a, b, c):

        if n == 0:
            return 1

        lcm_ab = a * b // gcd(a, b)
        lcm_ac = a * c // gcd(a, c)
        lcm_bc = b * c // gcd(b, c)
        lcm_abc = lcm_ab * c // gcd(lcm_ab, c)

        points = self.find_points(lcm_abc, a, b, c, lcm_ab, lcm_ac, lcm_bc, lcm_abc)
        total = n // points * lcm_abc

        if n % points == 0:
            return total

        goal = n % points

        approx = int(lcm_abc / points * goal)
        approx -= min(approx % a, approx % b, approx % c)
        calc = 0

        while calc != goal:
            calc = self.find_points(approx, a, b, c, lcm_ab, lcm_ac, lcm_bc, lcm_abc)

            if calc > goal:
                approx -= 1
                approx -= min(approx % a, approx % b, approx % c)
            if calc < goal:
                approx += min(a - approx % a, b - approx % b, c - approx % c)

        return total + approx


View More Similar Problems

Castle on the Grid

You are given a square grid with some cells open (.) and some blocked (X). Your playing piece can move along any row or column until it reaches the edge of the grid or a blocked cell. Given a grid, a start and a goal, determine the minmum number of moves to get to the goal. Function Description Complete the minimumMoves function in the editor. minimumMoves has the following parameter(s):

View Solution →

Down to Zero II

You are given Q queries. Each query consists of a single number N. You can perform any of the 2 operations N on in each move: 1: If we take 2 integers a and b where , N = a * b , then we can change N = max( a, b ) 2: Decrease the value of N by 1. Determine the minimum number of moves required to reduce the value of N to 0. Input Format The first line contains the integer Q.

View Solution →

Truck Tour

Suppose there is a circle. There are N petrol pumps on that circle. Petrol pumps are numbered 0 to (N-1) (both inclusive). You have two pieces of information corresponding to each of the petrol pump: (1) the amount of petrol that particular petrol pump will give, and (2) the distance from that petrol pump to the next petrol pump. Initially, you have a tank of infinite capacity carrying no petr

View Solution →

Queries with Fixed Length

Consider an -integer sequence, . We perform a query on by using an integer, , to calculate the result of the following expression: In other words, if we let , then you need to calculate . Given and queries, return a list of answers to each query. Example The first query uses all of the subarrays of length : . The maxima of the subarrays are . The minimum of these is . The secon

View Solution →

QHEAP1

This question is designed to help you get a better understanding of basic heap operations. You will be given queries of types: " 1 v " - Add an element to the heap. " 2 v " - Delete the element from the heap. "3" - Print the minimum of all the elements in the heap. NOTE: It is guaranteed that the element to be deleted will be there in the heap. Also, at any instant, only distinct element

View Solution →

Jesse and Cookies

Jesse loves cookies. He wants the sweetness of all his cookies to be greater than value K. To do this, Jesse repeatedly mixes two cookies with the least sweetness. He creates a special combined cookie with: sweetness Least sweet cookie 2nd least sweet cookie). He repeats this procedure until all the cookies in his collection have a sweetness > = K. You are given Jesse's cookies. Print t

View Solution →