Given an array arr[] of N integers and two players A and B are playing a game where the players pick the element with the maximum digit sum in their turns. In the end, the player with the maximum sum of the picked elements wins the game. Assuming that the player A always starts the game first and both the players play optimally, the task is to find the winner of the game.
Examples:
Input: arr[] = {12, 43, 25, 23, 30}
Output: B
A choses 43
B chooses 25
A chooses 23
B chooses 30
A chooses 12
A’s score = 43 + 23 + 12 = 78
B’s score = 25 + 30 = 55Input: arr[] = {2, 1, 1, 2}
Output: Draw
Approach: Sort the array based on the digit sum values of the integers, if the digit sum of two integers is same then they will be compared based on their values, this is because the value will maximize the sum in the end. After the array has been sorted based on the custom comparator, player A will try to pick the elements starting from the greatest (greedily).
Below is the implementation of the above approach:
C++
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std; // Function that returns the// sum of the digits of nint digit_sum(int n){ int s = 0; while (n > 0) { s += n % 10; n /= 10; } return s;} // Compares two integers according// to their digit sumbool comparator(int a, int b){ // Sum of digits of a int s1 = digit_sum(a); // Sum of digits of b int s2 = digit_sum(b); // If the digit sum of a is equal // to the digit sum of b if (s1 == s2) return (a < b); return (s1 < s2);} // Function to return the winner of the gamestring findTheWinner(int arr[], int n){ // Sort the elements based on // the digit sum values sort(arr, arr + n, comparator); // Find player A's score int scoreA = 0; for (int i = n - 1; i >= 0; i -= 2) scoreA += arr[i]; // Find player A's score int scoreB = 0; for (int i = n - 2; i >= 0; i -= 2) scoreB += arr[i]; // Find the winner if (scoreA == scoreB) return "Draw"; else if (scoreA > scoreB) return "A"; return "B";} // Driver codeint main(){ int arr[] = { 12, 43, 25, 23, 30 }; int n = sizeof(arr) / sizeof(int); cout << findTheWinner(arr, n); return 0;} |
Python3
# Python3 implementation of the above approach # Function that returns the # sum of the digits of n def digit_sum(n): s = 0; while n > 0: s += n % 10 n /= 10 return s # Function to return the winner # of the game def findTheWinner(arr, n): # Sort the elements based on # the digit sum values arr.sort(key = digit_sum) # Find player A's score scoreA = 0 i = n - 1 while i >= 0: scoreA += arr[i] i -= 2 # Find player A's score scoreB = 0 i = n - 2 while i >= 0: scoreA += arr[i] i -= 2 # Find the winner if scoreA == scoreB: return "Draw" elif (scoreA > scoreB): return "A" return "B" # Driver code if __name__=="__main__": arr = [ 12, 43, 25, 23, 30 ] n = len(arr); print(findTheWinner(arr, n)) # This code is contributed by Yash_R |
A
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