cpp-flashcards/org/study_deck_02/dsa/math-geometry/2698-find-the-punishment-number-of-an-integer.org

#+ANKI_DECK: study_deck_02
* TODO 2698. Find the Punishment Number of an Integer :medium:
:PROPERTIES:
:NEETCODE: [[file:../../roadmap.org::*2698. Find the Punishment Number of an Integer][2698. Find the Punishment Number of an Integer]]
:END:

Given a positive integer ~n~, return /the *punishment number*/ of ~n~.

The *punishment number* of ~n~ is defined as the sum of the squares of all integers ~i~ such that:

 - ~1 <= i <= n~

 - The decimal representation of ~i * i~ can be partitioned into contiguous substrings such that the sum of the integer values of these substrings equals ~i~.

*Example 1:*


#+begin_src
Input: n = 10
Output: 182
Explanation: There are exactly 3 integers i in the range [1, 10] that satisfy the conditions in the statement:
- 1 since 1 * 1 = 1
- 9 since 9 * 9 = 81 and 81 can be partitioned into 8 and 1 with a sum equal to 8 + 1 == 9.
- 10 since 10 * 10 = 100 and 100 can be partitioned into 10 and 0 with a sum equal to 10 + 0 == 10.
Hence, the punishment number of 10 is 1 + 81 + 100 = 182
#+end_src


*Example 2:*


#+begin_src
Input: n = 37
Output: 1478
Explanation: There are exactly 4 integers i in the range [1, 37] that satisfy the conditions in the statement:
- 1 since 1 * 1 = 1. 
- 9 since 9 * 9 = 81 and 81 can be partitioned into 8 + 1. 
- 10 since 10 * 10 = 100 and 100 can be partitioned into 10 + 0. 
- 36 since 36 * 36 = 1296 and 1296 can be partitioned into 1 + 29 + 6.
Hence, the punishment number of 37 is 1 + 81 + 100 + 1296 = 1478
#+end_src


*Constraints:*

 - ~1 <= n <= 1000~

** TODO Approach
Write your approach here.

** TODO Python
#+begin_src python
class Solution:
    def punishmentNumber(self, n: int) -> int:
#+end_src

** TODO C++
#+begin_src cpp
class Solution {
public:
    int punishmentNumber(int n) {
        
    }
};
#+end_src