给定一个二进制字符串S ,任务是根据以下条件,当两个玩家交替使用给定的字符串最佳游戏时,确定游戏的获胜者:
- 玩家 1总是先开始。
- 在每一轮中,玩家从给定的字符串删除一个非空的子字符串。
- 在给定的字符串清空后,最小计数为0的玩家将赢得比赛。如果两个玩家的0秒数相等,则打印“ Tie ”。
例子:
Input: S = “00011”
Output: Player 1
Explanation: Substrings can be chosen as follows:
Turn 1: Player 1 removes the substring S[4…5]. Therefore, Player 1 contains “11”.
Turn 2: Player 2 removes the substring S[0…0]. Therefore, Player 2 contains “0”.
Turn 3: Player 1 removes the substring S[0…0]. Therefore, Player 1 contains “110”.
Turn 4: Player 2 removes the substring S[0…0]. Therefore, Player 2 contains “00”.
Therefore, Player 1 wins the game.
Input: S = “0110011”
Output: Player 2
方法:该问题可以基于以下观察来解决:
- 如果字符串中0的计数是偶数,则玩家 1 和玩家 2 在每一轮中都选择子字符串“0” ,并且没有玩家会赢得这场比赛。
- 否则,将连续1的计数存储在一个数组中,并在该数组上应用 nim 规则的游戏。
- Nim-Sum:在游戏的任何时刻,每堆/堆中硬币/石头数量(此处为连续 1)的累积异或值称为该点的 Nim-Sum。
请按照以下步骤解决问题:
- 初始化一个变量,比如cntZero ,以在字符串存储0的计数。
- 初始化一个变量,比如cntConOne ,以存储字符串中连续1的计数。
- 初始化一个变量,比如nimSum ,以存储给定字符串的连续1的 Nim-Sum 。
- 遍历数组并计算0 s 和nimSum的计数。
- 最后,检查cntZero的值是否为偶数。如果发现是真的,则打印Tie 。
- 否则,检查nimSum的值是否大于0 。如果发现为真,则打印Player 1 。
- 否则,打印player 2 。
下面是上述方法的实现:
C++
// C++ program to implement
// the above approach
#include
using namespace std;
// Function to find the player
// who wins the game
void FindwinnerOfGame(string& S)
{
// Stores total count
// of 0s in the string
int cntZero = 0;
// Stores count of
// consecutive 1s
int cntConOne = 0;
// Stores Nim-Sum on count
// of consecutive 1s
int nimSum = 0;
// Stores length
// of the string
int N = S.length();
// Traverse the string
for (int i = 0; i < N; i++) {
// If the current
// character is 1
if (S[i] == '1') {
// Update cntConOne
cntConOne += 1;
}
else {
// Update nimSum
nimSum ^= cntConOne;
// Update cntConOne
cntConOne = 0;
// Update cntZero
cntZero++;
}
}
// Update nimSum
nimSum ^= cntConOne;
// If countZero is
// an even number
if (cntZero % 2 == 0) {
cout << "Tie";
}
// nimSum is not 0
else if (nimSum) {
cout << "player 1";
}
// If nimSum is zero
else {
cout << "player 2";
}
}
// Driver Code
int main()
{
string S = "0110011";
FindwinnerOfGame(S);
}
Java
// Java program to implement
// the above approach
// Function to find the player
// who wins the game
class GFG {
public static void FindwinnerOfGame(String S)
{
// Stores total count
// of 0s in the string
int cntZero = 0;
// Stores count of
// consecutive 1s
int cntConOne = 0;
// Stores Nim-Sum on count
// of consecutive 1s
int nimSum = 0;
// Stores length
// of the string
int N = S.length();
// Traverse the string
for (int i = 0; i < N; i++) {
// If the current
// character is 1
if (S.charAt(i) == '1') {
// Update cntConOne
cntConOne += 1;
}
else {
// Update nimSum
nimSum ^= cntConOne;
// Update cntConOne
cntConOne = 0;
// Update cntZero
cntZero++;
}
}
// Update nimSum
nimSum ^= cntConOne;
// If countZero is
// an even number
if (cntZero % 2 == 0) {
System.out.print("Tie");
}
// nimSum is not 0
else if (nimSum != 0) {
System.out.print("player 1");
}
// If nimSum is zero
else {
System.out.print("player 2");
}
}
// Driver Code
public static void main(String[] args)
{
String S = "0110011";
FindwinnerOfGame(S);
}
}
// This code is contributed by grand_master.
Python3
# Python 3 program to implement
# the above approach
# Function to find the player
# who wins the game
def FindwinnerOfGame(S):
# Stores total count
# of 0s in the string
cntZero = 0
# Stores count of
# consecutive 1s
cntConOne = 0
# Stores Nim-Sum on count
# of consecutive 1s
nimSum = 0
# Stores length
# of the string
N = len(S)
# Traverse the string
for i in range(N):
# If the current
# character is 1
if (S[i] == '1'):
# Update cntConOne
cntConOne += 1
else:
# Update nimSum
nimSum ^= cntConOne
# Update cntConOne
cntConOne = 0
# Update cntZero
cntZero += 1
# Update nimSum
nimSum ^= cntConOne
# If countZero is
# an even number
if (cntZero % 2 == 0):
print("Tie")
# nimSum is not 0
elif(nimSum):
print("player 1")
# If nimSum is zero
else:
print("player 2")
# Driver Code
if __name__ == '__main__':
S = "0110011"
FindwinnerOfGame(S)
# this code is contributed by SURENDRA_GANGWAR.
C#
// C# program to implement
// the above approach
using System;
// Function to find the player
// who wins the game
class GFG {
public static void FindwinnerOfGame(string S)
{
// Stores total count
// of 0s in the string
int cntZero = 0;
// Stores count of
// consecutive 1s
int cntConOne = 0;
// Stores Nim-Sum on count
// of consecutive 1s
int nimSum = 0;
// Stores length
// of the string
int N = S.Length;
// Traverse the string
for (int i = 0; i < N; i++) {
// If the current
// character is 1
if (S[i] == '1') {
// Update cntConOne
cntConOne += 1;
}
else {
// Update nimSum
nimSum ^= cntConOne;
// Update cntConOne
cntConOne = 0;
// Update cntZero
cntZero++;
}
}
// Update nimSum
nimSum ^= cntConOne;
// If countZero is
// an even number
if (cntZero % 2 == 0) {
Console.Write("Tie");
}
// nimSum is not 0
else if (nimSum != 0) {
Console.Write("player 1");
}
// If nimSum is zero
else {
Console.Write("player 2");
}
}
// Driver Code
public static void Main(string[] args)
{
string S = "0110011";
FindwinnerOfGame(S);
}
}
// This code is contributed by ukasp.
Javascript
player 2
时间复杂度: O(N),其中 N 是字符串的长度
辅助空间: O(1)
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