Dividing Sticks Problem

Given a list of integer each representing the length of each stick and an integer which tells how many times we can break a stick into half parts, we have to find maximum desired length sticks can be obtained from the group of sticks. 
Note 1: When we break a stick it gets converted into two half parts for example for a stick of length 10 two sticks can be obtained of both 5 in length and for a stick of length 5 two sticks will be obtained of length 2 and 3 respectively.
Note 2: Discarded part can’t be used again for making sticks such that if a stick of length 11 is given we can break it into 5 and 6 of length pieces then we have to discard one of the pieces which can’t be used further.
Examples:

Input: 
list = [2, 3, 4, 11] 
n = 2 
desired_length = 3 
Output : 
Maximum sticks of desired length that can be obtained are : 3
Explanation : 
We already have one stick of length 3 and two more sticks can be obtained 
by breaking stick of length 11 into [5, 3, 3] pieces therefore total sticks will be 3.

Input: 
list = [2, 1, 4, 5] 
n = 2 
desired_length = 4 
Output : 
Maximum sticks of desired length that can be obtained are : 1
Explanation : 
We already have one stick of length 4 and no more sticks can be obtained 
by breaking any stick therefore total sticks will be 1

Approach:
To solve the problem mentioned above we will first do a linear search operation to find all the sticks which have exact same length as of the desired stick length and count them. We will then store the count in the variable. Obviously we have to discard all the sticks which have a length less than the desired length as with them we can’t make any desired length stick. Then pass the value of sticks that have length more than the desired length to a function which calculate how many sticks can be obtained by breaking them. With the help of recursion find number of ways in which sticks can be obtained.

Below is the implementation of the above approach:

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

#include<bits/stdc++.h>
using namespace std;
  
// Method to find number of sticks by breaking them 
int sticks_break(int stick_length,int n, 
                 int desired_length)
{
  
    // If stick cant be break any more 
    if (n < 1)
        return 0;
      
    // Check if stick length became 
    // smaller than the desired length 
    if (stick_length < desired_length)
        return 0;
          
    // Check if stick length is even number 
    if (stick_length % 2 == 0)
          
        // Check if half of stick 
        // length is equal to desired length 
        if (stick_length / 2 == desired_length) 
            return 2;
              
        // Check if half of stick length 
        // is greater than the desired length 
        else if (stick_length / 2 > desired_length)
            return (sticks_break(stick_length / 2,
                        n - 1, desired_length));
              
    // Check if stick length is odd number 
    if (stick_length % 2 != 0)
      
        // For odd number two halves will be 
        // generated checking if first half 
        // is equal to desired length 
        if (stick_length / 2 == desired_length) 
            return 1;
              
        // Checking if second half 
        // is equal to desired length 
        if (stick_length / 2 + 1 == desired_length)
            return 1;
          
        // Check if half of stick length 
        // is greater than the desired length 
        if (stick_length/2 > desired_length)
            return (max (sticks_break(
                         stick_length / 2, n - 1,
                         desired_length),
                         sticks_break(
                         stick_length / 2 + 1,
                         n - 1, desired_length))); 
          
    return 0;
  
// Method to find number of sticks     
int numberOfSticks(vector<int>list_length,
                   int n, int desired_length)
{
    int count = 0;
      
    for(auto stick_lenght : list_length)
    {
          
        // Check if desired length is found 
        if (desired_length == stick_lenght)
          
            // Incrementing the count 
            count = count + 1;
              
        // Check if stick length is 
        // greater than desired length 
        else if (stick_lenght> desired_length) 
          
            // Incrementing count 
            // after break the sticks 
            count = count + sticks_break(
                            stick_lenght, n,
                            desired_length);
    
      
    // Return count 
    return count;
}
      
// Driver code
int main()
{
      
    // List of integers 
    vector<int>list_length = { 1, 2, 3, 21 };
      
    // Number of ways stick can be break 
    int n = 3;
      
    // Desired length
    int desired_length = 3;
      
    int count = numberOfSticks(list_length, n, 
                            desired_length);
                              
    // Print result
    cout << count << endl;
}
  
// This code is contributed by Stream_Cipher

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

import java.util.*; 
  
class GFG{
      
// Method to find number of sticks by breaking them 
static int sticks_break(int stick_length,
                        int n, int desired_length)
{
  
    // If stick cant be break any more 
    if (n < 1)
        return 0;
      
    // Check if stick length became 
    // smaller than the desired length 
    if (stick_length < desired_length)
        return 0;
          
    // Check if stick length is even number 
    if (stick_length % 2 == 0)
          
        // Check if half of stick 
        // length is equal to desired length 
        if (stick_length / 2 == desired_length) 
            return 2;
              
        // Check if half of stick length 
        // is greater than the desired length 
        else if (stick_length / 2 > desired_length)
            return (sticks_break(stick_length / 2,
                        n - 1, desired_length));
              
    // Check if stick length is odd number 
    if (stick_length % 2 != 0)
      
        // For odd number two halves will be 
        // generated checking if first half
        // is equal to desired length 
        if (stick_length / 2 == desired_length) 
            return 1;
              
        // Checking if second half 
        // is equal to desired length 
        if (stick_length / 2 + 1 == desired_length)
            return 1;
          
        // Check if half of stick length 
        // is greater than the desired length 
        if (stick_length/2 > desired_length)
            return (Math.max (sticks_break(
                               stick_length / 2,
                               n - 1, desired_length),
                               sticks_break(
                               stick_length / 2 + 1
                               n - 1, desired_length))); 
          
    return 0;
  
// Method to find number of sticks 
static int numberOfSticks(int list_length[],
                          int n, int desired_length)
{
    int count = 0;
      
    for(int i = 0; i < list_length.length; i++)
    {
          
        // Check if desired length is found 
        if (desired_length == list_length[i])
          
            // Incrementing the count 
            count = count + 1;
              
        // Check if stick length is 
        // greater than desired length 
        else if (list_length[i]> desired_length)
          
            // Incrementing count 
            // after break the sticks 
            count = count + sticks_break(list_length[i],
                                   n, desired_length);
    
      
    // Return count 
    return count;
}
  
// Driver code
public static void main(String args[]) 
      
    // List of integers 
    int[] list_length = new int[]{ 1, 2, 3, 21 }; 
      
    // Number of ways stick can be break 
    int n = 3;
      
    // Desired length
    int desired_length = 3;
      
    int count = numberOfSticks(list_length, n,
                            desired_length);
                              
    // Print result
    System.out.println(count);
}
}
  
// This code is contributed by Stream_Cipher

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# method to find number of sticks by breaking them 
def sticks_break(stick_length, n, desired_length): 
      
    # if stick cant be break any more 
    if n < 1
          
        return 0
      
    # check if stick length became 
    # smaller than the desired length 
    if stick_length < desired_length: 
          
        return 0
          
    # check if stick length is even number 
    if stick_length % 2 == 0
          
        # check if half of stick 
        # length is equal to desired length 
        if stick_length / 2 == desired_length: 
              
            return 2
              
        # check if half of stick length 
        # is greater than the desired length 
        elif stick_length / 2 > desired_length: 
              
            return sticks_break(stick_length / 2, n-1, desired_length) 
              
    # check if stick length is odd number 
    if stick_length % 2 != 0
          
        # for odd number two halves will be generated 
        # checking if first half is equal to desired length 
        if stick_length // 2 == desired_length: 
              
            return 1
          
        # checking if second half 
        # is equal to desired length 
        if stick_length // 2 + 1 == desired_length: 
              
            return 1
          
        # check if half of stick length 
        # is greater than the desired length 
        if stick_length//2 > desired_length: 
              
            return max (sticks_break(stick_length//2, n-1, desired_length), sticks_break(stick_length//2 + 1, n-1, desired_length)) 
          
      
    return 0
  
  
# method to find number of sticks 
def numberOfSticks(list_length, n, desired_length): 
      
    count = 0
      
    for stick_length in list_length: 
          
        # check if desired length is found 
        if desired_length == stick_length: 
              
            # incrementing the count 
            count = count + 1
          
        # check if stick length is 
        # greater than desired length 
        elif stick_length > desired_length: 
              
            # incrementing count 
            # after break the sticks 
            count = count + sticks_break(stick_length, n, desired_length) 
      
    # return count     
    return count 
  
# driver code 
if __name__ == "__main__"
      
    # list of integers 
    list_length =[1, 2, 3, 21
      
    # number of ways stick can be break 
    n = 3
      
    # desired length 
    desired_length = 3
  
    count = numberOfSticks(list_length, n, desired_length) 
      
    # print result 
    print(str(count)) 

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

using System; 
class GFG{
      
// Method to find number of sticks by breaking them 
static int sticks_break(int stick_length,
                        int n, int desired_length)
{
  
    // If stick cant be break any more 
    if (n < 1 )
        return 0;
      
    // Check if stick length became 
    // smaller than the desired length 
    if (stick_length < desired_length)
        return 0;
          
    // Check if stick length is even number 
    if (stick_length % 2 == 0)
          
        // Check if half of stick 
        // length is equal to desired length 
        if (stick_length / 2 == desired_length) 
            return 2;
              
        // Check if half of stick length 
        // is greater than the desired length 
        else if (stick_length / 2 > desired_length)
            return (sticks_break(stick_length / 2,
                        n - 1, desired_length));
              
    // Check if stick length is odd number 
    if (stick_length % 2 != 0)
      
        // For odd number two halves will be
        // generated checking if first half 
        // is equal to desired length 
        if (stick_length / 2 == desired_length) 
            return 1;
              
        // Checking if second half 
        // is equal to desired length 
        if (stick_length / 2 + 1 == desired_length)
            return 1;
          
        // Check if half of stick length 
        // is greater than the desired length 
        if (stick_length/2 > desired_length)
            return (Math.Max(sticks_break(
                             stick_length / 2,
                             n - 1, desired_length),
                             sticks_break(
                             stick_length / 2 + 1, 
                             n - 1, desired_length))); 
          
    return 0;
  
// Method to find number of sticks 
static int numberOfSticks(int []list_length,
                          int n, int desired_length)
{
    int count = 0;
    for(int i = 0; i < list_length.Length; i++)
    {
          
        // Check if desired length is found 
        if (desired_length == list_length[i])
          
            // Incrementing the count 
            count = count + 1;
              
        // Check if stick length is 
        // greater than desired length 
        else if (list_length[i]> desired_length) 
          
            // Incrementing count 
            // after break the sticks 
            count = count + sticks_break(list_length[i],
                                   n, desired_length);
    
      
    // Return count 
    return count;
}
  
// Driver code
public static void Main() 
      
    // list of integers 
    int []list_length = { 1, 2, 3, 21 };
      
    // Number of ways stick can be break 
    int n = 3;
      
    // Desired length
    int desired_length = 3;
    int count = numberOfSticks(list_length,
                         n, desired_length);
                           
    // Print result
    Console.WriteLine(count); 
}
}
  
// This code is contributed by Stream_Cipher

chevron_right


Output: 

3

competitive-programming-img




My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Improved By : Stream_Cipher