
Problem Statement
In this scenario, we're given an array arr
composed of distinct integers and a number k
. The task involves a sequential game conducted between the first two elements of the array: arr[0]
and arr[1]
. In each game round, the two elements are compared, and the larger one wins the round, maintaining its position at the start of the array, while the loser shifts to the array's end. This game persists until an integer secures k
consecutive wins. The objective is to determine which integer will reach the mark of k
consecutive wins first. Considering the array's elements are unique and the range of values within, there is an assurance of a definitive winner by the game's conclusion.
Examples
Example 1
Input:
arr = [2,1,3,5,4,6,7], k = 2
Output:
5
Explanation:
Let's see the rounds of the game: Round | arr | winner | win_count 1 | [2,1,3,5,4,6,7] | 2 | 1 2 | [2,3,5,4,6,7,1] | 3 | 1 3 | [3,5,4,6,7,1,2] | 5 | 1 4 | [5,4,6,7,1,2,3] | 5 | 2 So we can see that 4 rounds will be played and 5 is the winner because it wins 2 consecutive games.
Example 2
Input:
arr = [3,2,1], k = 10
Output:
3
Explanation:
3 will win the first 10 rounds consecutively.
Constraints
2 <= arr.length <= 105
1 <= arr[i] <= 106
arr
contains distinct integers.1 <= k <= 109
Approach and Intuition
The handling of the problem can be visualized as a process where iteratively the leading pair in the array contest and post their comparison, restructured based on the winner:
- Initialize two counters: one for the current winner and another for the count of consecutive wins (
current_winner
andwin_count
). - As the larger of the first two elements becomes
current_winner
, compare it with the next in line. Ifcurrent_winner
prevails, incrementwin_count
; otherwise, resetwin_count
to 1. - The key observation is the potential domination by a particularly large number, reducing the need for many comparisons once it has its first win, simplifying the process:
- If
k
is exceedingly large but there exists one very large element in the array, after it moves to the front due to an initial victory, it will continue winning against all subsequent smaller numbers. - This cycle might only need to revisit comparisons when the element
current_winner
is minuscule relative tok
. Still, since it shifts outer competitors (lower values) successively to the array's end, rare is the occasion for extended series of evaluations.
- If
- Therefore, an optimal approach utilizes direct pairwise comparisons without explicit full array rotations, and the algorithm significantly abbreviates when
current_winner
consecutively defeats k-1 challengers.
In essence, the approach utilizes a queue-like behavior without actual queue operations by manipulating array indices and element monitoring, ensuring efficiency even as input constraints extend to larger sizes and values.
Solutions
- C++
- Java
- Python
class Solution {
public:
int determineWinner(vector<int>& nums, int k) {
int highest = nums[0];
for (int i = 1; i < nums.size(); i++) {
highest = max(highest, nums[i]);
}
int current = nums[0];
int consecutiveWins = 0;
for (int i = 1; i < nums.size(); i++) {
int nextCompetitor = nums[i];
if (current > nextCompetitor) {
consecutiveWins++;
} else {
current = nextCompetitor;
consecutiveWins = 1;
}
if (consecutiveWins == k || current == highest) {
return current;
}
}
return -1;
}
};
The problem "Find the Winner of an Array Game" is solved in C++ using a straightforward approach that hinges on iterating through the number list and maintaining track of the maximum number. Here's a breakdown of the solution:
- Start by determining the highest number in the array, as this number has the potential to end the competition early if it reaches the required consecutive wins.
- Initialize the game with the first number in the array and set its initial consecutive wins to zero.
- Loop through each element in the array starting from the second element, treating it as the next competitor.
- Compare the current number with the next competitor:
- If the current number is greater, increment the count of its consecutive wins.
- If the next competitor is greater, switch the current number to this competitor and reset consecutive wins to one.
- Check after each comparison:
- If a number's consecutive wins equal the specified threshold
k
, or if the current number equals the highest number in the array, return this number as it has won the game.
- If a number's consecutive wins equal the specified threshold
- If the loop terminates without finding a winner that meets the criteria, return -1.
This implements a strategy that models the game's rules effectively, ensuring that it efficiently determines the winner by exploiting the given constraints and conditions with proper handling of potential early termination scenarios. By utilizing standard C++ vector operations and control structures, the given implementation offers a clear and direct method to resolve the problem.
class Solution {
public int determineWinner(int[] nums, int k) {
int highestValue = nums[0];
for (int i = 1; i < nums.length; i++) {
highestValue = Math.max(highestValue, nums[i]);
}
int currentWinner = nums[0];
int consecutiveWins = 0;
for (int i = 1; i < nums.length; i++) {
int challenger = nums[i];
if (currentWinner > challenger) {
consecutiveWins++;
} else {
currentWinner = challenger;
consecutiveWins = 1;
}
if (consecutiveWins == k || currentWinner == highestValue) {
return currentWinner;
}
}
return -1;
}
}
In the provided Java program, the task is to determine the winner of an array game. The winner is decided based on the number of consecutive wins required (k
) or if any player becomes the dominant player by winning against the highest value in the array.
Here's how the provided code achieves this:
Initialize Variables:
highestValue
starts as the first element of the arraynums
, and iteratively updates to maintain the maximum value found in the array.currentWinner
starts as the first element, representing the current winner in the game loop.consecutiveWins
, initialized to 0, tracks the number of consecutive wins thecurrentWinner
has.
Determine the Maximum Value:
- Loop through each element in the array
nums
to find the maximum valuehighestValue
. This step is crucial to identify a short-circuit condition where the current winner has already won against the highest possible value.
- Loop through each element in the array
Game Logic to Determine the Winner:
- Iterate through the array, starting from the second element, and compare each element (challenger) to the
currentWinner
. - If
currentWinner
is greater than the challenger, incrementconsecutiveWins
. If not, updatecurrentWinner
to the challenger and resetconsecutiveWins
to 1. - The loop exits in two scenarios:
- If
consecutiveWins
reachesk
, indicating thecurrentWinner
has won consecutivelyk
times. - If
currentWinner
becomes equal tohighestValue
, indicating that the player has won against the highest value in the array.
- If
- Iterate through the array, starting from the second element, and compare each element (challenger) to the
Return Statement:
- If neither of the above conditions is satisfied by the end of the loop, the function returns -1, indicating no winner based on the given conditions.
- Otherwise, the function returns the
currentWinner
when one of the exit conditions is met during the loop.
The solution efficiently utilizes conditional checks and updates within loops to determine the game's winner based on the described rules, providing an optimal solution to the array game challenge.
class Solution:
def determine_winner(self, arr: List[int], k: int) -> int:
highest_value = max(arr)
current_leader = arr[0]
consecutive_wins = 0
for index in range(1, len(arr)):
rival = arr[index]
if current_leader > rival:
consecutive_wins += 1
else:
current_leader = rival
consecutive_wins = 1
if consecutive_wins == k or current_leader == highest_value:
return current_leader
This solution for the problem "Find the Winner of an Array Game" is implemented in Python and focuses on identifying the winner based on the rules provided. The function determine_winner
takes an array arr
and an integer k
, and determines the winner using the following steps:
- Identify the
highest_value
in the array using Python'smax()
function. - Initialize a
current_leader
to the first element of the array and setconsecutive_wins
to 0. - Iterate through the array starting from the second element. For each element:
- Compare it with the
current_leader
. Ifcurrent_leader
is higher, incrementconsecutive_wins
. - If the rival (current element) is greater, update
current_leader
to this new value and resetconsecutive_wins
to 1.
- Compare it with the
- If at any point
consecutive_wins
equalsk
or thecurrent_leader
matches thehighest_value
, return thecurrent_leader
as the winner.
This algorithm primarily revolves around tracking wins in sequence and checking if any player dominates as per the 'k' threshold or is already the highest value in the array. With these conditions met, the winner is immediately decided and returned.
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