You are organizing a series of game rounds for a tournament, with each round represented by a team number by English alphabetical letter. However, there's a constraint: according to the game rules, rounds for the same team must be separated by at least n intervals to ensure fair gameplay which is under game rules. Your task is to determine the minimum number of intervals required to complete all the game rounds, considering the constraint on the separation of rounds for the same team. Example 1: Input: ["A","A","A","B","B","B"] 2 Output: 8 Explanation: A possible sequence is: A -> B -> idle -> A -> B -> idle -> A -> B. After participate team A, you must wait two cycles before participating A again. The same applies to team B. In the 3rd interval, neither A nor B can be done, so you idle. By the 4th cycle, you can do A again as 2 intervals have passed. Example 2: Input: ["A","C","A","B","D","B"] 1 Output: 6 Explanation: A possible sequence is: A -> B -> C -> D -> A -> B. With a interval of 1, you can participate a team after just one other round. Example 3: Input: ["A","A","A", "B","B","B"] 3 Output: 10 Explanation: A possible sequence is: A -> B -> idle -> idle -> A -> B -> idle -> idle -> A -> B. There are only two types of teams, A and B, which need to be separated by 3 intervals. This leads to idling twice between repetitions of these team rounds. Input Format First-line contains an array of teams The second line contains n as the interval Constraints 1 <= rounds.length <= 104 teams[i] is an uppercase English letter. 0 <= n <= 100 Output Format n Sample Input 0 ["A","A","A","B","B","B"] 2 Sample Output 0 8 Sample Input 1 ["A","C","A","B","D","B"] 1 Sample Output 1 6 Sample Input 2 ['Y', 'K', 'F', 'H', 'K', 'W', 'W', 'C', 'H', 'N', 'A', 'B', 'P', 'B', 'B', 'G', 'X', 'Z', 'O', 'X', 'C', 'C', 'P', 'X', 'N', 'O', 'Y', 'R', 'G', 'U', 'O', 'P', 'U', 'S', 'T', 'K', 'E', 'F', 'G', 'N', 'T', 'O', 'W', 'B', 'A', 'B', 'W', 'S', 'Y', 'M', 'P', 'I', 'M', 'O', 'K', 'Z', 'G', 'H', 'U', 'I', 'I', 'M', 'X', 'Y', 'D', 'B', 'K', 'T', 'H', 'J', 'L', 'I', 'M'] 96 Sample Output 2 486
Question
You are organizing a series of game rounds for a tournament, with each round represented by a team number by English alphabetical letter. However, there's a constraint: according to the game rules, rounds for the same team must be separated by at least n intervals to ensure fair gameplay which is under game rules. Your task is to determine the minimum number of intervals required to complete all the game rounds, considering the constraint on the separation of rounds for the same team.
Example 1:
Input:
["A","A","A","B","B","B"] 2 Output:
8 Explanation: A possible sequence is: A -> B -> idle -> A -> B -> idle -> A -> B.
After participate team A, you must wait two cycles before participating A again. The same applies to team B. In the 3rd interval, neither A nor B can be done, so you idle. By the 4th cycle, you can do A again as 2 intervals have passed.
Example 2:
Input:
["A","C","A","B","D","B"] 1 Output:
6 Explanation: A possible sequence is: A -> B -> C -> D -> A -> B.
With a interval of 1, you can participate a team after just one other round.
Example 3:
Input:
["A","A","A", "B","B","B"] 3 Output:
10 Explanation: A possible sequence is: A -> B -> idle -> idle -> A -> B -> idle -> idle -> A -> B.
There are only two types of teams, A and B, which need to be separated by 3 intervals. This leads to idling twice between repetitions of these team rounds.
Input Format
First-line contains an array of teams The second line contains n as the interval
Constraints
1 <= rounds.length <= 104
teams[i] is an uppercase English letter.
0 <= n <= 100
Output Format
n
Sample Input 0
["A","A","A","B","B","B"] 2 Sample Output 0
8 Sample Input 1
["A","C","A","B","D","B"] 1 Sample Output 1
6 Sample Input 2
['Y', 'K', 'F', 'H', 'K', 'W', 'W', 'C', 'H', 'N', 'A', 'B', 'P', 'B', 'B', 'G', 'X', 'Z', 'O', 'X', 'C', 'C', 'P', 'X', 'N', 'O', 'Y', 'R', 'G', 'U', 'O', 'P', 'U', 'S', 'T', 'K', 'E', 'F', 'G', 'N', 'T', 'O', 'W', 'B', 'A', 'B', 'W', 'S', 'Y', 'M', 'P', 'I', 'M', 'O', 'K', 'Z', 'G', 'H', 'U', 'I', 'I', 'M', 'X', 'Y', 'D', 'B', 'K', 'T', 'H', 'J', 'L', 'I', 'M'] 96 Sample Output 2
486
Solution
This problem is about scheduling game rounds for a tournament. The rounds are represented by team numbers, which are given as English alphabetical letters. The constraint is that rounds for the same team must be separated by at least n intervals to ensure fair gameplay. The task is to determine the minimum number of intervals required to complete all the game rounds, considering this constraint.
The problem can be solved using a priority queue to keep track of the next available time for each team. The priority queue is sorted by the next available time in ascending order.
Here are the steps to solve the problem:
- Count the frequency of each team in the input array and store it in a map.
- Create a priority queue and add all teams from the map to the queue. The priority queue is sorted by the next available time in ascending order. If two teams have the same next available time, the team with the higher frequency is given higher priority.
- Initialize a variable, currentTime, to 0. This variable keeps track of the current time.
- While the queue is not empty, remove the team with the highest priority from the queue. If the next available time of the team is greater than currentTime, then increment currentTime to the next available time of the team. Then, decrement the frequency of the team by 1. If the frequency of the team is not 0, then add the team back to the queue with the next available time being currentTime + n + 1.
- The minimum number of intervals required to complete all the game rounds is the final value of currentTime.
This algorithm ensures that each team's rounds are separated by at least n intervals and all rounds are completed in the minimum number of intervals.
Similar Questions
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