TCS Codevita | Holes And Balls

Given two arrays of H[] and B[] consisting of N and M integers respectively, denoting the diameter of holes and balls respectively. M number of balls are made to roll from A to B on a sloping surface with N holes, each having different depth as shown in the figure below:

The task is to find the eventual position of each ball in the order of the ball released considering the following:

• A ball will fall into a hole if its diameter is less than or equal to the diameter of the hole.
• A hole H_i will become full if i numbers of balls fall into it.
• If a hole is full, then no more balls fall into it.
• A ball will reach B from A, if and only if it is not falling into any one of the holes.
• If a ball is in hole P_i, then its position is i. If a ball reached the bottom point B, then take its position as 0.

Examples:

Input: H[] = {21, 3, 6}, B[] = {20, 15, 5, 7, 10, 4, 2, 1, 3, 6, 8}
Output: 1 0 3 0 0 3 3 2 2 0 0
Explanation:
Ball of diameter 20 will fall into the hole H₁ and the hole H₁ will become full.
Balls with diameter 15, 7 and 10 will reach bottom, since the hole H₁ is full and diameters of holes H₂ and H₃ are less than the diameters of the balls.
Balls with diameters 5, 4 and 2 will fall into the hole H₃.
Ball with diameter 1 will fall into the hole H₂ since the hole H₃ is already full.
Ball with diameter 3 will fall into hole H₂.
Balls with diameters 6, and 8 will reach the bottom point B.
The position of ball 20 is 1 because it is in hole H₁.
Positions of ball 15, 7, 10, 3, 6, and 8 are 0 because they reached the bottom point B.
Therefore, the balls with diameter 5, 4 and 2 are in the 3rd hole H₃, the ball with diameter 1 and 3 are in the 2nd hole H₂.

Input: H[] = {20, 15, 10, 5, 25}, B[] = {5, 10, 15, 20, 25, 30, 4, 9, 14, 19}
Output: 5 5 5 5 5 0 4 3 2 1

Approach: Follow the steps below to solve the problem:

• Initialize an array position[] of size N to store the final position of each ball and an array depth[] of size N to store the capacity of each hole.
• Iterate over the range [1,  N] using the variable i and set the initial depth[i] of the hole[i] to i+1.
• Traverse the array ball[] using the variable i and do the following:
  • Initialize flag to False.
  • Iterate over the array hole[] using variable j in reverse order.
    • Check if the diameter of the hole is greater than or equal to that of the ball, i.e., hole[j] ? ball[i], and if that hole is not full, i.e., depth[j] ? j then, place the ball in that hole by appending j + 1 in the position[] array and incrementing the depth of the hole by 1 and flag equal to True 
    • break out of the loop.
  • If the ball doesn’t fit in any hole (has reached at end of the slope) the flag will be False, then append 0 in the position[] array.
• After the above steps, print the value stored in the array position[] as the result.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include<bits/stdc++.h>
using namespace std;

// Function to find and print the final
// position of balls
vector<int> ballPositionFinder(vector<int>holes,vector<int>balls){

        // Array of zero equal to length of holes array
    // to store the no. of balls in the hole
    vector<int>depth(holes.size(),0);

    // Stores the positions of balls
    vector<int>positions;

    // Iterate through balls array
    // and holes array in reverse order.
    for(int i : balls){
        // Initialize flag equal to false
        bool flag = false;

        vector<int>array;
        for(int i=0;i<holes.size();i++){
            array.push_back(i);
        }
        reverse(array.begin(),array.end());

        for(auto j : array)
        {
        // Check if the diameter of ball is less than the
        // diameter of hole and depth is less than the index.
            if(i <= holes[j] && depth[j] <= j)
            {

                // If the condition is true push the position
                // for ball in position array and increment depth of hole by 1.
                positions.push_back(j + 1);
                depth[j] += 1;

            // Here the ball will fall into the hole
            // so make the flag True and break the loop.
                flag = true;
                break;
            }
        }

        // Check if the ball has reached the bottom
        // if the ball reaches bottom flag will remain false
        // so then push 0 to the position array.
        if(flag == false)
            positions.push_back(0);
    }
    return positions;
}

// Driver Code
int main()
{
    vector<int>holes = {21, 3, 6};

    vector<int>balls = {20, 15, 5, 7, 10, 4, 2, 1, 3, 6, 8};

    // Function Call
    vector<int> output = ballPositionFinder(holes, balls);
    for(auto i : output)
        cout<<i<<" ";
}

// This code is contributed by shinjanpatra

Python3

# Python program for the above approach

# Function to find and print the final
# position of balls


def ballPositionFinder(holes, balls):

        # Array of zero equal to length of holes array
    # to store the no. of balls in the hole
    depth = [0 for i in range(len(holes))]

    # Stores the positions of balls
    positions = []

    # Iterate through balls array
    # and holes array in reverse order.
    for i in balls:
        # Initialize flag equal to false
        flag = False

        for j in reversed(range(len(holes))):
          # Check if the diameter of ball is less than the
          # diameter of hole and depth is less than the index.
            if i <= holes[j] and depth[j] <= j:
                # If the condition is true append the position
                # for ball in position array and increment depth of hole by 1.
                positions.append(j+1)
                depth[j] += 1
            # Here the ball will fall into the hole
            # so make the flag True and break the loop.
                flag = True
                break

        # Check if the ball has reached the bottom
        # if the ball reaches bottom flag will remain false
        # so then append 0 to the position array.
        if flag == False:
            positions.append(0)

    return positions


# Driver Code
if __name__ == "__main__":

    holes = [21, 3, 6]

    balls = [20, 15, 5, 7, 10, 4,
             2, 1, 3, 6, 8]

    # Function Call
    output = ballPositionFinder(holes, balls)
    for i in output:
        print(i, end=" ")

Java

/*package whatever //do not write package name here */

import java.io.*;
import java.util.*;

class GFG {
    // Java program for the above approach


// Function to find and print the final
// position of balls
static ArrayList<Integer> ballPositionFinder(int[] holes,int[] balls){

        // Array of zero equal to length of holes array
    // to store the no. of balls in the hole
    int[] depth = new int[holes.length];
    Arrays.fill(depth, 0);

    // Stores the positions of balls
    ArrayList<Integer> positions = new ArrayList<>();

    // Iterate through balls array
    // and holes array in reverse order.
    for(int i : balls){
        // Initialize flag equal to false
        boolean flag = false;

        ArrayList<Integer> array = new ArrayList<>();
        for(int j=0;j<holes.length;j++){
            array.add(j);
        }
        Collections.reverse(array);

        for(int j : array)
        {
        // Check if the diameter of ball is less than the
        // diameter of hole and depth is less than the index.
            if(i <= holes[j] && depth[j] <= j)
            {

                // If the condition is true push the position
                // for ball in position array and increment depth of hole by 1.
                positions.add(j + 1);
                depth[j] += 1;

            // Here the ball will fall into the hole
            // so make the flag True and break the loop.
                flag = true;
                break;
            }
        }

        // Check if the ball has reached the bottom
        // if the ball reaches bottom flag will remain false
        // so then push 0 to the position array.
        if(flag == false)
            positions.add(0);
    }
    return positions;
}


// Driver Code
public static void main(String args[])
{
    int[] holes = {21, 3, 6};

    int[] balls = {20, 15, 5, 7, 10, 4, 2, 1, 3, 6, 8};

    // Function Call
    ArrayList<Integer> output = ballPositionFinder(holes, balls);
    for(int i : output)
        System.out.print(i + " ");
}
}

// code is contributed by shinjanpatra

C#

using System;
using System.Collections.Generic;

class GFG
{
    // Function to find and print the final
    // position of balls
    static List<int> BallPositionFinder(int[] holes, int[] balls)
    {
        // Array of zero equal to length of holes array
        // to store the no. of balls in the hole
        int[] depth = new int[holes.Length];
        Array.Fill(depth, 0);

        // Stores the positions of balls
        List<int> positions = new List<int>();

        // Iterate through balls array
        // and holes array in reverse order.
        foreach (int i in balls)
        {
            // Initialize flag equal to false
            bool flag = false;

            List<int> array = new List<int>();
            for (int j = 0; j < holes.Length; j++)
            {
                array.Add(j);
            }
            array.Reverse();

            foreach (int j in array)
            {
                // Check if the diameter of ball is less than the
                // diameter of hole and depth is less than the index.
                if (i <= holes[j] && depth[j] <= j)
                {
                    // If the condition is true push the position
                    // for ball in position array and increment depth of hole by 1.
                    positions.Add(j + 1);
                    depth[j] += 1;

                    // Here the ball will fall into the hole
                    // so make the flag True and break the loop.
                    flag = true;
                    break;
                }
            }

            // Check if the ball has reached the bottom
            // if the ball reaches bottom flag will remain false
            // so then push 0 to the position array.
            if (flag == false)
                positions.Add(0);
        }
        return positions;
    }

    // Driver Code
    static void Main()
    {
        int[] holes = { 21, 3, 6 };

        int[] balls = { 20, 15, 5, 7, 10, 4, 2, 1, 3, 6, 8 };

        // Function Call
        List<int> output = BallPositionFinder(holes, balls);
        foreach (int i in output)
            Console.Write(i + " ");
    }
}

Javascript

<script>

// JavaScript program for the above approach

// Function to find and print the final
// position of balls
function ballPositionFinder(holes, balls){

        // Array of zero equal to length of holes array
    // to store the no. of balls in the hole
    let depth = new Array(holes.length).fill(0)

    // Stores the positions of balls
    let positions = []

    // Iterate through balls array
    // and holes array in reverse order.
    for(let i of balls){
        // Initialize flag equal to false
        let flag = false

        let array = []
        for(let i=0;i<holes.length;i++){
            array.push(i)
        }
        array.reverse()

        for(let j of array)
        {
          // Check if the diameter of ball is less than the
          // diameter of hole and depth is less than the index.
            if(i <= holes[j] && depth[j] <= j)
            {

                // If the condition is true push the position
                // for ball in position array and increment depth of hole by 1.
                positions.push(j + 1)
                depth[j] += 1

            // Here the ball will fall into the hole
            // so make the flag True and break the loop.
                flag = true
                break
            }
        }

        // Check if the ball has reached the bottom
        // if the ball reaches bottom flag will remain false
        // so then push 0 to the position array.
        if(flag == false)
            positions.push(0)
    }
    return positions
}

// Driver Code
let holes = [21, 3, 6]

let balls = [20, 15, 5, 7, 10, 4,
             2, 1, 3, 6, 8]

// Function Call
let output = ballPositionFinder(holes, balls)
for(let i of output)
    document.write(i," ")

// This code is contributed by shinjanpatra

</script>

Output

1 0 3 0 0 3 3 2 2 0 0 

Time Complexity: O(N*M)
Auxiliary Space: O(N)