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Competition Arena > CharmingTickets
SRM 382 · 2007-12-11 · by dkorduban · Dynamic Programming, Math
Class Name: CharmingTickets
Return Type: int
Method Name: count
Arg Types: (int, string)
Problem Statement

Problem Statement

A ticket number that contains exactly 2*K digits is called charming if and only if at least one of the following conditions is satisfied:

  • The sum of the first K digits is equal to the sum of the last K digits.
  • The sum of all the digits at positions with odd indices is equal to the sum of all the digits at positions with even indices.

Also, you think that some digits are better than others, so a charming number must contain only digits that you consider to be good. These digits are given in the String good. Determine the number of different charming numbers containing exactly 2*K digits. Return this number modulo 999983. Remember that ticket numbers may contain leading zeroes.

Constraints

  • K will be between 1 and 1000, inclusive.
  • good will contain between 1 and 10 characters, inclusive.
  • good will contain only digits ('0' - '9').
  • All characters in good will be distinct.
Examples
0)
1
"0123456789"
Returns: 10

Only "XX" numbers are charming.

1)
2
"21"
Returns: 8

Only 1111, 1122, 1212, 1221, 2112, 2121, 2211, 2222 are charming numbers.

2)
2
"0987654321"
Returns: 1240
3)
137
"0123456789"
Returns: 630063
4)
1000
"0123456789"
Returns: 495241

max test

5)
1000
"8"
Returns: 1

border case: single digit

6)
1
"2"
Returns: 1

border case: single digit

7)
123
"8123"
Returns: 894140

digits aren't sorted

8)
971
"82109467"
Returns: 166953

digits aren't sorted

Submissions are judged against all 93 archived test cases, of which 9 are shown here. Case numbers match the judge’s.

Coding Area

Language: C++17 · define a public class CharmingTickets with a public method int count(int K, string good) · 93 test cases · 2 s / 256 MB per case

Submitting as anonymous