Given an array of an integer of size, N. Array contains N ropes of length Ropes[i]. You have to perform a cut operation on ropes such that all of them are reduced by the length of the smallest rope. Display the number of ropes left after every cut. Perform operations till the length of each rope becomes zero.
Note: IF no ropes left after a single operation, in this case, we print 0.
Examples:
Input : Ropes[] = { 5, 1, 1, 2, 3, 5 }
Output : 4 3 2
Explanation : In first operation the minimum ropes is 1 so we reduce length 1 from all of them after reducing we left with 4 ropes and we do same for rest.Input : Ropes[] = { 5, 1, 6, 9, 8, 11, 2, 2, 6, 5 }
Output : 9 7 5 3 2 1
Simple solution is to we traverse a loop from [0…n-1], In each iterations first we find min length rope. After that, we reduce all ropes length by it and then count how many ropes are left whose length is greater than zero. this process is done until all ropes length is greater than zero. This solution work in O(n2) time.
Efficient solution works in O(nlog(n)). First we have to sort all Ropes in increasing order of their length. after that we have follow the step.
//initial cutting length "min rope" CuttingLength = Ropes[0] Now Traverse a loop from left to right [1...n] .During traverse we check that is current ropes length is greater than zero or not IF ( Ropes[i] - CuttingLength > 0 ) .... IF Yes then all ropes to it's right side also greater than 0 .... Print number of ropes remains (n - i) ....update Cutting Length by current rope length ...... CuttingLength = Ropes[i] Do the same process for the rest.
Below is the implementation of above idea.
C++
// C++ program to print how many // Ropes are Left After Every Cut #include <bits/stdc++.h> using namespace std; // Function print how many Ropes are // Left AfterEvery Cutting operation void cuttingRopes(int Ropes[], int n) { // sort all Ropes in increase // of their length sort(Ropes, Ropes + n); int singleOperation = 0; // min length rope int cuttingLength = Ropes[0]; // now traverse through the given // Ropes in increase order of length for (int i = 1; i < n; i++) { // After cutting if current rope length // is greater than '0' that mean all // ropes to it's right side are also // greater than 0 if (Ropes[i] - cuttingLength > 0) { // print number of ropes remains cout << (n - i) << " "; // now current rope become // min length rope cuttingLength = Ropes[i]; singleOperation++; } } if (singleOperation == 0) cout << "0 "; } int main() { int Ropes[] = { 5, 1, 1, 2, 3, 5 }; int n = sizeof(Ropes) / sizeof(Ropes[0]); cuttingRopes(Ropes, n); return 0; } |
Java
// Java program to print how many// Ropes are Left After Every Cutimport java.util.*;import java.lang.*;import java.io.*;class GFG { // function print how many Ropes are Left After // Every Cutting operation public static void cuttingRopes(int Ropes[], int n) { // sort all Ropes in increasing // order of their length Arrays.sort(Ropes); int singleOperation = 0; // min length rope int cuttingLength = Ropes[0]; // now traverse through the given Ropes in // increase order of length for (int i = 1; i < n; i++) { // After cutting if current rope length // is greater than '0' that mean all // ropes to it's right side are also // greater than 0 if (Ropes[i] - cuttingLength > 0) { System.out.print(n - i + " "); // now current rope become // min length rope cuttingLength = Ropes[i]; singleOperation++; } } // after first operation all ropes // length become zero if (singleOperation == 0) System.out.print("0"); } public static void main(String[] arg) { int[] Ropes = { 5, 1, 1, 2, 3, 5 }; int n = Ropes.length; cuttingRopes(Ropes, n); }} |
Python3
# Python program to print how many# Ropes are Left After Every Cut# Function print how many Ropes are# Left After Every Cutting operationdef cuttingRopes(Ropes, n): # Sort all Ropes in increasing # order of their length Ropes.sort() singleOperation = 0 # min length rope cuttingLength = Ropes[0] # Now traverse through the given # Ropes in increase order of length for i in range(1,n): # After cutting if current rope length # is greater than '0' that mean all # ropes to it's right side are also # greater than 0 if (Ropes[i] - cuttingLength > 0): print(n - i,end = " ") # Now current rope become # min length rope cuttingLength = Ropes[i] singleOperation += 1 # After first operation all ropes # length become zero if (singleOperation == 0): print("0")# Driver CodeRopes = [ 5, 1, 1, 2, 3, 5 ]n = len(Ropes)cuttingRopes(Ropes, n)# This code is contributed by shinjanpatra |
C#
// C# program to print how many// Ropes are Left After Every Cutusing System;class GFG { // function print how many Ropes are Left After // Every Cutting operation public static void cuttingRopes(int []Ropes, int n) { // sort all Ropes in increasing // order of their length Array.Sort(Ropes); int singleOperation = 0; // min length rope int cuttingLength = Ropes[0]; // now traverse through the given Ropes in // increase order of length for (int i = 1; i < n; i++) { // After cutting if current rope length // is greater than '0' that mean all // ropes to it's right side are also // greater than 0 if (Ropes[i] - cuttingLength > 0) { Console.Write(n - i + " "); // now current rope become // min length rope cuttingLength = Ropes[i]; singleOperation++; } } // after first operation all ropes // length become zero if (singleOperation == 0) Console.Write("0"); } // Driver code public static void Main() { int[] Ropes = { 5, 1, 1, 2, 3, 5 }; int n = Ropes.Length; cuttingRopes(Ropes, n); }}// This code is contributed by vt_m. |
PHP
<?php// PHP program to print how many// Ropes are Left After Every Cut// Function print how many Ropes are // Left AfterEvery Cutting operationfunction cuttingRopes($Ropes, $n){ // sort all Ropes in increase // of their length sort($Ropes); $singleOperation = 0; // min length rope $cuttingLength = $Ropes[0]; // now traverse through the given // Ropes in increase order of length for ($i = 1; $i < $n; $i++) { // After cutting if current rope length // is greater than '0' that mean all // ropes to it's right side are also // greater than 0 if ($Ropes[$i] - $cuttingLength > 0) { // print number of ropes remains echo ($n - $i). " "; // now current rope become // min length rope $cuttingLength = $Ropes[$i]; $singleOperation++; } } if ($singleOperation == 0) echo "0 ";} // Driver Code $Ropes = array(5, 1, 1, 2, 3, 5); $n = count($Ropes); cuttingRopes($Ropes, $n);// This code is contributed by Sam007?> |
Javascript
<script>// JavaScript program to print how many// Ropes are Left After Every Cut// Function print how many Ropes are// Left After Every Cutting operationfunction cuttingRopes(Ropes, n){ // Sort all Ropes in increasing // order of their length Ropes.sort(); let singleOperation = 0; // min length rope let cuttingLength = Ropes[0]; // Now traverse through the given // Ropes in increase order of length for(let i = 1; i < n; i++) { // After cutting if current rope length // is greater than '0' that mean all // ropes to it's right side are also // greater than 0 if (Ropes[i] - cuttingLength > 0) { document.write(n - i + " "); // Now current rope become // min length rope cuttingLength = Ropes[i]; singleOperation++; } } // After first operation all ropes // length become zero if (singleOperation == 0) document.write("0");}// Driver Codelet Ropes = [ 5, 1, 1, 2, 3, 5 ];let n = Ropes.length;cuttingRopes(Ropes, n);// This code is contributed by avijitmondal1998</script> |
Output
4 3 2
Time Complexity : O(n log (n))
Space complexity : O(1)
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