Find the Largest Cube by Deleting Minimum Digits from a Number in Python

Suppose we have a number N, we have to determine the largest perfect cube that can be generated by removing minimum digits (possibly 0) from the number. We can delete any digit from the given number to reach the target. As we know a number N is called a perfect cube if N = M^3 for some integer M.

So, if the input is like 806, then the output will be 8, as we can delete 0 and 6 from the number, then we will get 8, this is perfect cube of 2.

To solve this, we will follow these steps −

• Define a function preProcess() . This will take n
• temp_cubes := a new list
• for i in range 1 to ceiling of n^(1/3), do
  • cube = i^3
  • cubeString := cube as string
  • insert cubeString at the end of temp_cubes
  • return temp_cubes
• Define a function solve() . This will take num,temp_cubes
• reverse temp_cubes
• totalCubes := size of temp_cubes
• for i in range 0 to totalCubes, do
  • temp := temp_cubes[i]
  • digitsInCube := size of temp
  • index := 0
  • digitsInNumber := size of num
  • for j in range 0 to digitsInNumber, do
    • if num[j] is same as temp[index], then
      • index := index + 1
    • if digitsInCube is same as index, then
      • return temp
• return "Not Possible"
• From the method do the following −
• temp_cubes := preProcess(n)
• num := n as string
• ans := solve(num, temp_cubes)
• return ans

Example

Let us see the following implementation to get better understanding −

import math
def preProcess(n):
   temp_cubes = list()
   for i in range(1, math.ceil(n**(1. / 3.))):
      cube = i**3
      cubeString = str(cube)
      temp_cubes.append(cubeString)
   return temp_cubes
def solve(num,temp_cubes):
   temp_cubes = temp_cubes[::-1]
   totalCubes = len(temp_cubes)
   for i in range(totalCubes):
      temp = temp_cubes[i]
      digitsInCube = len(temp)
      index = 0
      digitsInNumber = len(num)
      for j in range(digitsInNumber):
      if (num[j] == temp[index]):
         index += 1
      if (digitsInCube == index):
         return temp
   return "Not Possible"
def getLargestCube(n):
   temp_cubes = preProcess(n)
   num = str(n)
   ans = solve(num, temp_cubes)
   return ans
n = 806
print(getLargestCube(n) )

Input

806

Output

8