
Problem Statement
In the context of a tournament-style competition, such as the NBA playoffs, an interesting strategy involves pairing teams so that the strongest plays against the weakest, the second strongest against the second weakest, and so on. This approach aims to make the matches more engaging and balanced. We're tasked with a challenge where given n
teams, each labeled from 1
(strongest) to n
(weakest), we must arrange them in such pairing patterns and depict this as a single string representation.
Each match or pairing is represented using parentheses '('
and ')'
and separated by commas ','
. The process of generating this string involves multiple rounds of pairing, where each consecutive round takes the winners of the previous round until a final matchup is formed. The ultimate goal is to return a string that represents the entire sequence of matches from the start to the final.
Examples
Example 1
Input:
n = 4
Output:
"((1,4),(2,3))"
Explanation:
In the first round, we pair the team 1 and 4, the teams 2 and 3 together, as we need to make the strong team and weak team together. And we got (1, 4),(2, 3). In the second round, the winners of (1, 4) and (2, 3) need to play again to generate the final winner, so you need to add the paratheses outside them. And we got the final answer ((1,4),(2,3)).
Example 2
Input:
n = 8
Output:
"(((1,8),(4,5)),((2,7),(3,6)))"
Explanation:
First round: (1, 8),(2, 7),(3, 6),(4, 5) Second round: ((1, 8),(4, 5)),((2, 7),(3, 6)) Third round: (((1, 8),(4, 5)),((2, 7),(3, 6))) Since the third round will generate the final winner, you need to output the answer (((1,8),(4,5)),((2,7),(3,6))).
Constraints
n == 2x
wherex
in in the range[1, 12]
.
Approach and Intuition
Given the problem's constraints and requirements, the solution involves several key steps, each building upon the previous to generate the final output.
Initialization: Start by representing each team as a string number of its rank. This provides a base for the first round of pairing.
Pairing Process:
- In each round, pair the first team in the current list with the last, the second with the second last, and so forth until you reach the midpoint of the list.
- Combine these teams into pairs using the designated string format - for instance, "1" and "n" become "(1,n)".
- After each round of pairing, the results become the input list for the next round.
Building up the Rounds:
- After forming the initial pairs, each subsequent round takes the results of the previous round and pairs them similarly until only one pair remains.
- During this process, enclose each new pair from the previous results within additional parentheses - representing the progression in tournament rounds.
Completion:
- The process repeats until the list of results contains only a single string, which represents the final layout of matches from the initial to the last round.
- This final string is returned as the solution.
The idea is to use a structured approach to iteratively reduce the number of teams/participants by half each round, simulating the tournament's progression until the champion emerges. The process visually and structurally organizes the participants in a manner illustrating each match in each round, providing a clear view of the entire tournament's progression. Each operation's time complexity effectively involves string manipulations and list management, optimized by the constraints given (the maximum n
is considerably manageable).
Solutions
- Java
class MatchFinder {
int[] players;
int index;
StringBuilder result;
public String generateMatch(int size) {
players = new int[size];
index = 0;
result = new StringBuilder();
generate(size, Integer.numberOfTrailingZeros(size));
return result.toString();
}
public void generate(int size, int level) {
if (level == 0) {
int x = Integer.lowestOneBit(index);
players[index] = x > 0 ? size / x + 1 - players[index - x] : 1;
result.append("" + players[index++]);
} else {
result.append("(");
generate(size, level - 1);
result.append(",");
generate(size, level - 1);
result.append(")");
}
}
}
The Java program written titled "Output Contest Matches" is designed to generate the pairing of players in a tournament bracket. The program employs a recursive strategy to pair players until all possible matches are represented in a structural format. Here's a breakdown of how this solution works:
- The
MatchFinder
class maintains an arrayplayers
, an indexindex
, and aStringBuilder
result
to construct the output string. - The
generateMatch
method initializes theplayers
array,index
, andresult
for a given tournament size, and calls thegenerate
method. - The recursive method
generate
determines how to pair players based on the current "level" of recursion:- At the base case (
level == 0
), it assigns players to matches where theplayers
values depend on their binary index position. The results of these pairings are then appended toresult
. - If not at the base case, the method appends an opening parenthesis
(
, makes a recursive call to generate the next level of pairings, inserts a comma,
, makes another recursive call for the next set of pairings, and then appends a closing parenthesis)
.
- At the base case (
Utilize the following approach to execute:
- Instantiate the
MatchFinder
class. - Call the
generateMatch
method with a specified size representing the total number of players or positions in the initial round of the tournament. - Retrieve and utilize the resulting string that illustrates the hierarchical matches. This structure helps visually understand the pairing order required for a knockout or elimination-style tournament.
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