Least number to be added to or subtracted from N to make it a Perfect Cube
Given a number N, Find the minimum number that needs to be added to or subtracted from N, to make it a perfect cube. If the number is to be added, print it with a + sign, else if the number is to be subtracted, print it with a – sign.
Examples:
Input: N = 25
Output: 2
Nearest perfect cube before 25 = 8
Nearest perfect cube after 25 = 27
Therefore 2 needs to be added to 25 to get the closest perfect cubeInput: N = 40
Output: -13
Nearest perfect cube before 40 = 25
Nearest perfect cube after 40 = 64
Therefore 13 needs to be subtracted from 40 to get the closest perfect cube
Approach:
- Get the number.
- Find the cube root of the number and convert the result as an integer.
- After converting the double value to integer, this will contain the root of the perfect cube before N, i.e. floor(cube root(N)).
- Then find the cube of this number, which will be the perfect cube before N.
- Find the root of the perfect cube after N, i.e. the ceil(cube root(N)).
- Then find the cube of this number, which will be the perfect cube after N.
- Check whether the cube of floor value is nearest to N or the ceil value.
- If the cube of floor value is nearest to N, print the difference with a -sign. Else print the difference between the cube of the ceil value and N with a + sign.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach #include <bits/stdc++.h>using namespace std; // Function to return the Least numberint nearest(int n){ // Get the perfect cube // before and after N int prevCube = cbrt(n); int nextCube = prevCube + 1; prevCube = prevCube * prevCube * prevCube; nextCube = nextCube * nextCube * nextCube; // Check which is nearest to N int ans = (n - prevCube) < (nextCube - n) ? (prevCube - n) : (nextCube - n); // return the result return ans;} // Driver codeint main(){ int n = 25; cout << nearest(n) << endl; n = 27; cout << nearest(n) << endl; n = 40; cout << nearest(n) << endl; return 0;} |
Java
// Java implementation of the approach class GFG { // Function to return the Least number static int nearest(int n) { // Get the perfect cube // before and after N int prevCube = (int)Math.cbrt(n); int nextCube = prevCube + 1; prevCube = prevCube * prevCube * prevCube; nextCube = nextCube * nextCube * nextCube; // Check which is nearest to N int ans = (n - prevCube) < (nextCube - n) ? (prevCube - n) : (nextCube - n); // return the result return ans; } // Driver code public static void main (String[] args) { int n = 25; System.out.println(nearest(n)); n = 27; System.out.println(nearest(n)) ; n = 40; System.out.println(nearest(n)) ; } } // This code is contributed by Yash_R |
2 0 -13
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