Package g3301_3400.s3320_count_the_number_of_winning_sequences

Class Solution

  • All Implemented Interfaces:
    
public final class Solution

    3320 - Count The Number of Winning Sequences.

    Hard

    Alice and Bob are playing a fantasy battle game consisting of n rounds where they summon one of three magical creatures each round: a Fire Dragon, a Water Serpent, or an Earth Golem. In each round, players simultaneously summon their creature and are awarded points as follows:

    • If one player summons a Fire Dragon and the other summons an Earth Golem, the player who summoned the Fire Dragon is awarded a point.

    • If one player summons a Water Serpent and the other summons a Fire Dragon, the player who summoned the Water Serpent is awarded a point.

    • If one player summons an Earth Golem and the other summons a Water Serpent, the player who summoned the Earth Golem is awarded a point.

    • If both players summon the same creature, no player is awarded a point.

    You are given a string s consisting of n characters 'F', 'W', and 'E', representing the sequence of creatures Alice will summon in each round:

    • If s[i] == 'F', Alice summons a Fire Dragon.

    • If s[i] == 'W', Alice summons a Water Serpent.

    • If s[i] == 'E', Alice summons an Earth Golem.

    Bob’s sequence of moves is unknown, but it is guaranteed that Bob will never summon the same creature in two consecutive rounds. Bob beats Alice if the total number of points awarded to Bob after n rounds is strictly greater than the points awarded to Alice.

    Return the number of distinct sequences Bob can use to beat Alice.

    Since the answer may be very large, return it modulo <code>10<sup>9</sup> + 7</code>.

    Example 1:

    Input: s = "FFF"

    Output: 3

    Explanation:

    Bob can beat Alice by making one of the following sequences of moves: "WFW", "FWF", or "WEW". Note that other winning sequences like "WWE" or "EWW" are invalid since Bob cannot make the same move twice in a row.

    Example 2:

    Input: s = "FWEFW"

    Output: 18

    Explanation:

    Bob can beat Alice by making one of the following sequences of moves: "FWFWF", "FWFWE", "FWEFE", "FWEWE", "FEFWF", "FEFWE", "FEFEW", "FEWFE", "WFEFE", "WFEWE", "WEFWF", "WEFWE", "WEFEF", "WEFEW", "WEWFW", "WEWFE", "EWFWE", or "EWEWE".

    Constraints:

    • 1 &lt;= s.length &lt;= 1000

    • s[i] is one of 'F', 'W', or 'E'.

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Field Summary

      Fields 
      Modifier and Type Field Description

    • Constructor Summary

      Constructors 
      Constructor Description
      Solution()

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      final Integer countWinningSequences(String s)

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait