You are given an arr[] of distinct positive integers along with an integer X (X ? 1). arr[] contains only 1 and all possible powers of prime number such that every element of arr[] is at most X. Two players A and B are playing a game on integer X alternatively. In each turn, one can choose a number arr[i] from arr[] such that arr[i]? X and update X to X – arr[i]. The game goes on until X becomes 0. The task is to find the winner if A starts first and both play optimally.
Examples:
Input: arr[] = {1, 2, 3, 4, 5, 7}, X = 7
Output: A
Explanation: Player A choose arr[5] = 7 from the arr[] and update X to 7 – 7 = 0.
Therefore, A wins the game because B can’t make any move on 0.Input: arr[] = {1}, X = 1
Output: A
Explanation: Player A choose arr[0] = 1 from the arr[] and update X to 1 – 1 = 0.
Therefore, A wins the game because B can’t make any move on 0.
Approach: Implement the idea below to solve the problem
if X % 6 = 0. Then, player B wins else player A wins.
Proof of the approach:
Let’s see the cases for X = [1, 2, 3, . . . ., 7]
For X = 1: arr[] will be: {1}
- Player A can subtract 1 from X .So, that X becomes 0 and player B can’t make any move on X further.Therefore, player A wins.
For X = 2: arr[] will be: {1, 2}
- Player A can subtract 2 from X .So, that X becomes 0 and player B can’t make any move on X further.Therefore, player A wins.
For X = 3: arr[] will be: {1, 2, 3}
- Player A can subtract 3 from X .So, that X becomes 0 and player B can’t make any move on X further.Therefore, player A wins.
For X = 4: arr[] will be: {1, 2, 3, 4}
- Player A can subtract 4 from X .So, that X becomes 0 and player B can’t make any move on X further.Therefore, player A wins.
For X = 5: arr[] will be: {1, 2, 3, 4, 5}
- Player A can subtract 5 from X .So, that X becomes 0 and player B can’t make any move on X further.Therefore, player A wins.
For X = 6: arr[] will be: {1, 2, 3, 4, 5}
- Player A loses here.
All possible cases:
- (i) Player A makes X as = (6-1) = 5, Player B can directly subtract 5.Hence B wins.
- (ii) Player A makes X as = (6-2) = 4, Player B can directly subtract 4.Hence B wins.
- (iii) Player A makes X as = (6-3) = 3, Player B can directly subtract 3.Hence B wins.
- (iv) Player A makes X as = (6-4) = 2, Player B can directly subtract 2.Hence B wins.
- (v) Player A makes X as = (6-5) = 1, Player B can directly subtract 1.Hence B wins.
In all above cases it can be verified that there is no such move possible so that A can be winner of the game.
For X = 7: arr[] will be: {1, 2, 3, 4, 5, 7}
- Player A can subtract 7 from X .So, that X becomes 0 and player B can’t make any move on X further.Therefore, player A wins.
- Till, Now We observe a pattern that if X is a multiple of 6, Then B wins else A wins.
Below is the implementation of the above approach.
#include <bits/stdc++.h> using namespace std;
// Function which is called in main() string Find_Winner( int X)
{ // Checking if X is a multiple of 6
if (X % 6 == 0) {
return "B" ;
}
// If X is not a multiple of 6
else {
return "A" ;
}
} int main()
{ int X = 7;
int arr[] = { 1, 2, 3, 4, 5, 7 };
// Function call
cout << Find_Winner(X);
return 0;
} // This code is contributed by akashish__ |
// Java code to implement the approach: import java.io.*;
class GFG {
// Driver Function
public static void main(String[] args)
{
int X = 7 ;
int [] arr = { 1 , 2 , 3 , 4 , 5 , 7 };
// Function call
System.out.println(Find_Winner(X));
}
// Function which is called in main()
static String Find_Winner( int X)
{
// Checking if X is a multiple of 6
if (X % 6 == 0 ) {
return "B" ;
}
// If X is not a multiple of 6
else {
return "A" ;
}
}
} |
# python3 code to implement the approach: # Function which is called in main() def Find_Winner(X):
# Checking if X is a multiple of 6
if (X % 6 = = 0 ):
return "B"
# If X is not a multiple of 6
else :
return "A"
# Driver Function if __name__ = = "__main__" :
X = 7
arr = [ 1 , 2 , 3 , 4 , 5 , 7 ]
# Function call
print (Find_Winner(X))
# This code is contributed by rakeshsahni
|
// C# code to implement the above approach: using System;
public class GFG {
// Driver Function
public static void Main( string [] args)
{
int X = 7;
int [] arr = { 1, 2, 3, 4, 5, 7 };
// Function call
Console.WriteLine(Find_Winner(X));
}
// Function which is called in main()
static string Find_Winner( int X)
{
// Checking if X is a multiple of 6
if (X % 6 == 0) {
return "B" ;
}
// If X is not a multiple of 6
else {
return "A" ;
}
}
} // This code is contributed by AnkThon |
// Javascript code to implement the approach: // Driver Function let X = 7; let arr = [1, 2, 3, 4, 5, 7] // Function call console.log(Find_Winner(X)); // Function which is called in main() function Find_Winner(X) {
// Checking if X is a multiple of 6
if (X % 6 == 0) {
return "B" ;
}
// If X is not a multiple of 6
else {
return "A" ;
}
} // This code is contributed saurabh_jaiswal. |
A
Time Complexity: O(1)
Auxiliary Space: O(1)