Dividing Sticks Problem

18 Aug, 2021
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 : 3Explanation : 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 : 1Explanation : 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 a length more than the desired length to a function that calculates how many sticks can be obtained by breaking them. With the help of recursion find a number of ways in which sticks can be obtained.Below is the implementation of the above approach:
C++
Java
Python3
C#
Javascript
#include<bits/stdc++.h>using namespace std; // Method to find number of sticks by breaking themint 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 codeint 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
import java.util.*; class GFG{     // Method to find number of sticks by breaking themstatic 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 sticksstatic 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 codepublic 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
# method to find number of sticks by breaking themdef 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 sticksdef 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 codeif __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))
using System;class GFG{     // Method to find number of sticks by breaking themstatic 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 sticksstatic 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 codepublic 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
<script>    // Method to find number of sticks by breaking them    function 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 (parseInt(stick_length / 2, 10) == desired_length)                return 2;             // Check if half of stick length            // is greater than the desired length            else if (parseInt(stick_length / 2, 10) > desired_length)                return (sticks_break(parseInt(stick_length / 2, 10),                            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 (parseInt(stick_length / 2, 10) == desired_length)                return 1;             // Checking if second half            // is equal to desired length            if (parseInt(stick_length / 2, 10) + 1 == desired_length)                return 1;             // Check if half of stick length            // is greater than the desired length            if (parseInt(stick_length/2, 10) > desired_length)                return (Math.max(sticks_break(                                   parseInt(stick_length / 2, 10),                                   n - 1, desired_length),                                   sticks_break(                                   parseInt(stick_length / 2, 10) + 1,                                   n - 1, desired_length)));         return 0;    }     // Method to find number of sticks    function numberOfSticks(list_length, n, desired_length)    {        let count = 0;         for(let 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;    }         // List of integers    let list_length = [ 1, 2, 3, 21 ];           // Number of ways stick can be break    let n = 3;           // Desired length    let desired_length = 3;           let count = numberOfSticks(list_length, n,                            desired_length);                                   // Print result    document.write(count);     </script>
3
Time Complexity: O(N^2)Auxiliary Space: O(N)
Stream_Cipher
decode2207
pankajsharmagfg
Algorithms
Competitive Programming
Python
Recursion
Recursion
Algorithms
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