Maximum length possible by cutting N given woods into at least K pieces

Given an array wood[] of size N, representing the length of N pieces of wood and an integer K, at least K pieces of the same length need to be cut from the given wooden pieces. The task is to find the maximum possible length of these K wooden pieces that can be obtained.

Examples:

Input: wood[] = {5, 9, 7}, K = 3 
Output:
Explanation: 
Cut arr[0] = 5 = 5 
Cut arr[1] = 9 = 5 + 4 
Cut arr[2] = 5 = 5 + 2 
Therefore, the maximum length that can be obtained by cutting the woods into 3 pieces is 5.

Input: wood[] = {5, 9, 7}, K = 4 
Output:
Explanation: 
Cut arr[0] = 5 = 4 + 1 
Cut arr[1] = 9 = 2 * 4 + 1 
Cut arr[2] = 7 = 4 + 3 
Therefore, the maximum length that can be obtained by cutting the woods into 4 pieces is 4.

Approach: The problem can be solved using a Binary search. Follow the steps below to solve the problem:



  • Find the maximum element from the array wood[] and store it in a variable, say Max.
  • The value of L must lie in the raneg [1, Max]. Therefore, apply binary search over the range [1, Max].
  • Initialize two variables say, left = 1 and right = Max to store the range in which the value of L lies.
  • Check if it is possible to cut the woods into K pieces with length of each piece equal to (left + right) / 2 or not. If found to be true, then update left = (left + right) / 2.
  • Otherwise, update right = (left + right) / 2 .

Below is the implementation of the above approach:

C++

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// C++ program to implement
// the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to check if it is possible to cut
// woods into K pieces of length len
bool isValid(int wood[], int N, int len, int K)
{
 
    // Stores count of pieces
    // having length equal to K
    int count = 0;
 
    // Traverse wood[] array
    for (int i = 0; i < N; i++) {
 
        // Update count
        count += wood[i] / len;
    }
    return count >= K;
}
 
// Function to find the maximum value of L
int findMaxLen(int wood[], int N, int K)
{
 
    // Stores minimum possible of L
    int left = 1;
 
    // Stores maximum possible value of L
    int right = *max_element(wood,
                             wood + N);
 
    // Apply binary search over
    // the range [left, right]
    while (left <= right) {
 
        // Stores mid value of
        // left and right
        int mid = left + (right - left) / 2;
 
        // If it is possible to cut woods
        // into K pieces having length
        // of each piece equal to mid
        if (isValid(wood, N, mid,
                    K)) {
 
            // Update left
            left = mid + 1;
        }
        else {
 
            // Update right
            right = mid - 1;
        }
    }
    return right;
}
 
// Driver Code
int main()
{
    int wood[] = { 5, 9, 7 };
    int N = sizeof(wood) / sizeof(wood[0]);
    int K = 4;
    cout << findMaxLen(wood, N, K);
}

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Java

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// Java program to implement
// the above approach
import java.util.*;
 
class GFG{
 
// Function to check if it is possible
// to cut woods into K pieces of
// length len
static boolean isValid(int wood[], int N,
                       int len, int K)
{
     
    // Stores count of pieces
    // having length equal to K
    int count = 0;
 
    // Traverse wood[] array
    for(int i = 0; i < N; i++)
    {
         
        // Update count
        count += wood[i] / len;
    }
    return count >= K;
}
 
// Function to find the maximum value of L
static int findMaxLen(int wood[], int N,
                      int K)
{
     
    // Stores minimum possible of L
    int left = 1;
 
    // Stores maximum possible value of L
    int right = Arrays.stream(wood).max().getAsInt();
 
    // Apply binary search over
    // the range [left, right]
    while (left <= right)
    {
         
        // Stores mid value of
        // left and right
        int mid = left + (right - left) / 2;
 
        // If it is possible to cut woods
        // into K pieces having length
        // of each piece equal to mid
        if (isValid(wood, N, mid, K))
        {
             
            // Update left
            left = mid + 1;
        }
        else
        {
             
            // Update right
            right = mid - 1;
        }
    }
    return right;
}
 
// Driver Code
public static void main(String[] args)
{
    int wood[] = { 5, 9, 7 };
    int N = wood.length;
    int K = 4;
     
    System.out.print(findMaxLen(wood, N, K));
}
}
 
// This code is contributed by Princi Singh

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Python3

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# Python3 program to implement
# the above approach
 
# Function to check if it is possible to
# cut woods into K pieces of length len
def isValid(wood, N, len, K):
 
    # Stores count of pieces
    # having length equal to K
    count = 0
 
    # Traverse wood[] array
    for i in range(N):
 
        # Update count
        count += wood[i] // len
         
    return (count >= K)
 
# Function to find the maximum value of L
def findMaxLen(wood, N, K):
 
    # Stores minimum possible of L
    left = 1
 
    # Stores maximum possible value of L
    right = max(wood)
 
    # Apply binary search over
    # the range [left, right]
    while (left <= right):
         
        # Stores mid value of
        # left and right
        mid = left + (right - left) // 2
 
        # If it is possible to cut woods
        # into K pieces having length
        # of each piece equal to mid
        if (isValid(wood, N, mid, K)):
 
            # Update left
            left = mid + 1
        else:
             
            # Update right
            right = mid - 1
             
    return right
 
# Driver Code
if __name__ == '__main__':
 
    wood = [ 5, 9, 7 ]
    N = len(wood)
    K = 4
     
    print(findMaxLen(wood, N, K))
 
# This code is contributed by mohit kumar 29

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C#

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// C# program to implement
// the above approach
using System;
using System.Linq;
class GFG{
 
// Function to check if it is possible
// to cut woods into K pieces of
// length len
static bool isValid(int []wood, int N,
                    int len, int K)
{   
  // Stores count of pieces
  // having length equal to K
  int count = 0;
 
  // Traverse wood[] array
  for(int i = 0; i < N; i++)
  {
    // Update count
    count += wood[i] / len;
  }
  return count >= K;
}
 
// Function to find the maximum
// value of L
static int findMaxLen(int []wood,
                      int N, int K)
{   
  // Stores minimum possible
  // of L
  int left = 1;
 
  // Stores maximum possible
  // value of L
  int right = wood.Max();
 
  // Apply binary search over
  // the range [left, right]
  while (left <= right)
  {
    // Stores mid value of
    // left and right
    int mid = left +
              (right - left) / 2;
 
    // If it is possible to cut woods
    // into K pieces having length
    // of each piece equal to mid
    if (isValid(wood, N,
                mid, K))
    {
      // Update left
      left = mid + 1;
    }
    else
    {
      // Update right
      right = mid - 1;
    }
  }
  return right;
}
 
// Driver Code
public static void Main(String[] args)
{
  int []wood = {5, 9, 7};
  int N = wood.Length;
  int K = 4;
  Console.Write(findMaxLen(wood,
                           N, K));
}
}
 
// This code is contributed by shikhasingrajput

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Output: 

4












 

Time Complexity: O(N * Log2M), where M is the maximum element of the given array
Auxiliary Space: O(1)

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