#2698
Find the Punishment Number of an Integer
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Description
Given a positive integer n, the punishment number is the sum of i * i for every integer i in [1, n] whose square's decimal digits can be split into contiguous parts that sum back to i. Return this punishment number.
Example 1:
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
Example 2:
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
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