Find the Largest Cube formed by Deleting minimum Digits from a number

Given a number n, the task is to find the largest perfect cube that can be formed by deleting minimum digits(possibly 0) from the number.
X is called a perfect cube if X = Y³ for some Y.

Examples:

Input : 4125
Output : 125
Explanation
125 = 5³. We can form 125 by deleting digit 4 from 4125

Input : 876
Output :8
Explanation
8 = 2³. We can form 8 by deleting digits 7 and 6 from 876

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

We can generate cubes of all numbers till from 1 to N^1/3 (We don’t consider 0 as 0 is not considered as a perfect cube). We iterate the cubes from largest to the smallest.
Now if we look at the number n given to us, then we know that this number contains only log(n) + 1 digits, thus we can efficiently approach the problem if we treat this number n as a string hereafter.
While iterating on the perfect cubes, we check if the perfect cube is a subsequence of the number n when its represented as a string.If this is the case then the deletions required for changing the number n to the current perfect cube is:

No of deleted digits = No of digits in number n - 
                       Number of digits in current 
                                      perfect cube

Since we want the largest cube number we traverse the array of preprocessed cubes in reverse order.

C++

/* C++ code to implement maximum perfect cube  
   formed after deleting  minimum digits */
#include <bits/stdc++.h> 
using namespace std; 
  
// Returns vector of Pre Processed perfect cubes 
vector<string> preProcess(long long int n) 
{ 
    vector<string> preProcessedCubes; 
    for (int i = 1; i * i * i <= n; i++) { 
        long long int iThCube = i * i * i; 
  
        // convert the cube to string and push into 
        // preProcessedCubes vector 
        string cubeString = to_string(iThCube); 
        preProcessedCubes.push_back(cubeString); 
    } 
    return preProcessedCubes; 
} 
  
/* Utility function for findLargestCube().  
   Returns the Largest cube number that can be formed */
string findLargestCubeUtil(string num,  
                    vector<string> preProcessedCubes) 
{ 
    // reverse the preProcessed cubes so that we  
    // have the largest cube in the beginning 
    // of the vector 
    reverse(preProcessedCubes.begin(), preProcessedCubes.end()); 
  
    int totalCubes = preProcessedCubes.size(); 
  
    // iterate over all cubes 
    for (int i = 0; i < totalCubes; i++) { 
        string currCube = preProcessedCubes[i]; 
  
        int digitsInCube = currCube.length(); 
        int index = 0; 
        int digitsInNumber = num.length(); 
        for (int j = 0; j < digitsInNumber; j++) { 
  
            // check if the current digit of the cube 
            // matches with that of the number num 
            if (num[j] == currCube[index])  
                index++; 
              
            if (digitsInCube == index)                  
                return currCube;             
        } 
    } 
  
    // if control reaches here, the its  
    // not possible  to form a perfect cube 
    return "Not Possible"; 
} 
  
// wrapper for findLargestCubeUtil() 
void findLargestCube(long long int n) 
{ 
    // pre process perfect cubes 
    vector<string> preProcessedCubes = preProcess(n); 
  
    // convert number n to string 
    string num = to_string(n); 
  
    string ans = findLargestCubeUtil(num, preProcessedCubes); 
  
    cout << "Largest Cube that can be formed from "
         << n << " is " << ans << endl; 
} 
  
// Driver Code 
int main() 
{ 
    long long int n; 
    n = 4125; 
    findLargestCube(n); 
  
    n = 876; 
    findLargestCube(n); 
  
    return 0; 
} 

Java

/* Java code to implement maximum perfect cube  
formed after deleting minimum digits */
import java.util.*; 
class GFG  
{ 
  
    // Returns vector of Pre Processed perfect cubes 
    static Vector<String> preProcess(int n)  
    { 
        Vector<String> preProcessedCubes = new Vector<>(); 
        for (int i = 1; i * i * i <= n; i++) 
        { 
            int iThCube = i * i * i; 
  
            // convert the cube to String and push into 
            // preProcessedCubes vector 
            String cubeString = String.valueOf(iThCube); 
            preProcessedCubes.add(cubeString); 
        } 
        return preProcessedCubes; 
    } 
  
    /* Utility function for findLargestCube().  
    Returns the Largest cube number that can be formed */
    static String findLargestCubeUtil(String num, 
            Vector<String> preProcessedCubes)  
    { 
        // reverse the preProcessed cubes so that we  
        // have the largest cube in the beginning 
        // of the vector 
        Collections.reverse(preProcessedCubes); 
  
        int totalCubes = preProcessedCubes.size(); 
  
        // iterate over all cubes 
        for (int i = 0; i < totalCubes; i++) 
        { 
            String currCube = preProcessedCubes.get(i); 
  
            int digitsInCube = currCube.length(); 
            int index = 0; 
            int digitsInNumber = num.length(); 
            for (int j = 0; j < digitsInNumber; j++) 
            { 
  
                // check if the current digit of the cube 
                // matches with that of the number num 
                if (num.charAt(j) == currCube.charAt(index))  
                { 
                    index++; 
                } 
  
                if (digitsInCube == index)  
                { 
                    return currCube; 
                } 
            } 
        } 
  
        // if control reaches here, the its  
        // not possible to form a perfect cube 
        return "Not Possible"; 
    } 
  
    // wrapper for findLargestCubeUtil() 
    static void findLargestCube(int n)  
    { 
        // pre process perfect cubes 
        Vector<String> preProcessedCubes = preProcess(n); 
  
        // convert number n to String 
        String num = String.valueOf(n); 
  
        String ans = findLargestCubeUtil(num, preProcessedCubes); 
  
        System.out.println("Largest Cube that can be formed from "
                + n + " is " + ans); 
    } 
  
    // Driver Code 
    public static void main(String[] args)  
    { 
        int n; 
        n = 4125; 
        findLargestCube(n); 
  
        n = 876; 
        findLargestCube(n); 
    } 
} 
  
// This code has been contributed by 29AjayKumar 

Python3

# Python3 code to implement maximum perfect 
# cube formed after deleting minimum digits  
import math as mt 
  
# Returns vector of Pre Processed 
# perfect cubes 
def preProcess(n): 
  
    preProcessedCubes = list() 
    for i in range(1, mt.ceil(n**(1. / 3.))): 
        iThCube = i**3
          
        # convert the cube to string and  
        # push into preProcessedCubes vector 
        cubeString = str(iThCube) 
        preProcessedCubes.append(cubeString) 
          
    return preProcessedCubes 
  
# Utility function for findLargestCube().  
# Returns the Largest cube number that 
# can be formed  
def findLargestCubeUtil(num,preProcessedCubes): 
      
    # reverse the preProcessed cubes so  
    # that we have the largest cube in  
    # the beginning of the vector 
    preProcessedCubes = preProcessedCubes[::-1] 
  
    totalCubes = len(preProcessedCubes) 
  
    # iterate over all cubes 
    for i in range(totalCubes): 
        currCube = preProcessedCubes[i] 
  
        digitsInCube = len(currCube) 
        index = 0
        digitsInNumber = len(num) 
        for j in range(digitsInNumber): 
              
            # check if the current digit of the cube 
            # matches with that of the number num 
            if (num[j] == currCube[index]):  
                index += 1
              
            if (digitsInCube == index):              
                return currCube          
      
    # if control reaches here, the its  
    # not possible to form a perfect cube 
    return "Not Possible"
  
# wrapper for findLargestCubeUtil() 
def findLargestCube(n): 
  
    # pre process perfect cubes 
    preProcessedCubes = preProcess(n) 
  
    num = str(n) 
  
    ans = findLargestCubeUtil(num, preProcessedCubes) 
  
    print("Largest Cube that can be formed from",  
                                    n, "is", ans) 
  
# Driver Code 
n = 4125
findLargestCube(n) 
  
n = 876
findLargestCube(n) 
      
# This code is contributed  
# by mohit kumar 29 

C#

/* C# code to implement maximum perfect cube  
formed after deleting minimum digits */
using System; 
using System.Collections.Generic; 
  
class GFG  
{  
  
    // Returns vector of Pre Processed perfect cubes  
    static List<String> preProcess(int n)  
    {  
        List<String> preProcessedCubes = new List<String>();  
        for (int i = 1; i * i * i <= n; i++)  
        {  
            int iThCube = i * i * i;  
  
            // convert the cube to String and push into  
            // preProcessedCubes vector  
            String cubeString = String.Join("",iThCube);  
            preProcessedCubes.Add(cubeString);  
        }  
        return preProcessedCubes;  
    }  
  
    /* Utility function for findLargestCube().  
    Returns the Largest cube number that can be formed */
    static String findLargestCubeUtil(String num,  
            List<String> preProcessedCubes)  
    {  
        // reverse the preProcessed cubes so that we  
        // have the largest cube in the beginning  
        // of the vector  
        preProcessedCubes.Reverse();  
  
        int totalCubes = preProcessedCubes.Count;  
  
        // iterate over all cubes  
        for (int i = 0; i < totalCubes; i++)  
        {  
            String currCube = preProcessedCubes[i];  
  
            int digitsInCube = currCube.Length;  
            int index = 0;  
            int digitsInNumber = num.Length;  
            for (int j = 0; j < digitsInNumber; j++)  
            {  
  
                // check if the current digit of the cube  
                // matches with that of the number num  
                if (num[j] == currCube[index])  
                {  
                    index++;  
                }  
  
                if (digitsInCube == index)  
                {  
                    return currCube;  
                }  
            }  
        }  
  
        // if control reaches here, the its  
        // not possible to form a perfect cube  
        return "Not Possible";  
    }  
  
    // wrapper for findLargestCubeUtil()  
    static void findLargestCube(int n)  
    {  
        // pre process perfect cubes  
        List<String> preProcessedCubes = preProcess(n);  
  
        // convert number n to String  
        String num = String.Join("",n);  
  
        String ans = findLargestCubeUtil(num, preProcessedCubes);  
  
        Console.WriteLine("Largest Cube that can be formed from "
                + n + " is " + ans);  
    }  
  
    // Driver Code  
    public static void Main(String[] args)  
    {  
        int n;  
        n = 4125;  
        findLargestCube(n);  
  
        n = 876;  
        findLargestCube(n);  
    }  
}  
  
// This code contributed by Rajput-Ji 

PHP

<?php 
// PHP code to implement maximum perfect 
// cube formed after deleting minimum digits  
  
// Returns vector of Pre Processed 
// perfect cubes 
function preProcess($n) 
{ 
  
    $preProcessedCubes = array(); 
    for ($i = 1; $i * $i * $i < $n; $i++) 
    { 
        $iThCube = $i * $i * $i; 
          
        // convert the cube to string and  
        // push into preProcessedCubes vector 
        $cubeString = strval($iThCube); 
        array_push($preProcessedCubes,$cubeString); 
    } 
    return $preProcessedCubes; 
} 
  
// Utility function for findLargestCube().  
// Returns the Largest cube number that 
// can be formed  
function findLargestCubeUtil($num,$preProcessedCubes) 
{  
    // reverse the preProcessed cubes so  
    // that we have the largest cube in  
    // the beginning of the vector 
    $preProcessedCubes = array_reverse($preProcessedCubes); 
  
    $totalCubes = count($preProcessedCubes); 
  
    // iterate over all cubes 
    for($i = 0; $i < $totalCubes; $i++) 
    { 
        $currCube = $preProcessedCubes[$i]; 
  
        $digitsInCube = strlen($currCube); 
        $index = 0; 
        $digitsInNumber = strlen($num); 
        for ($j = 0; $j < $digitsInNumber; $j++) 
        { 
              
            // check if the current digit of the cube 
            // matches with that of the number num 
            if ($num[$j] == $currCube[$index])  
                $index += 1; 
              
            if ($digitsInCube == $index)              
                return $currCube;      
        } 
    } 
    // if control reaches here, the its  
    // not possible to form a perfect cube 
    return "Not Possible"; 
} 
  
// wrapper for findLargestCubeUtil() 
function findLargestCube($n) 
{ 
  
    // pre process perfect cubes 
    $preProcessedCubes = preProcess($n); 
  
    $num = strval($n); 
  
    $ans = findLargestCubeUtil($num, $preProcessedCubes); 
  
    print("Largest Cube that can be formed from ".$n." is ".$ans."\n"); 
} 
  
// Driver Code 
$n = 4125; 
findLargestCube($n); 
  
$n = 876; 
findLargestCube($n) 
      
// This code is contributed by mits 
?> 

Output:

Largest Cube that can be formed from 4125 is 125
Largest Cube that can be formed from 876 is 8

Time Complexity of the above algorithm is O(N^1/3log(N) log(N) is due to the fact that the number of digits in N are Log(N) + 1.

My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

PHP

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