1561

1561. Maximum Number of Coins You Can Get (Medium)

There are 3n piles of coins of varying size, you and your friends will take piles of coins as follows:

• In each step, you will choose any 3 piles of coins (not necessarily consecutive).
• Of your choice, Alice will pick the pile with the maximum number of coins.
• You will pick the next pile with the maximum number of coins.
• Your friend Bob will pick the last pile.
• Repeat until there are no more piles of coins.

Given an array of integers piles where piles[i] is the number of coins in the ith pile.

Return the maximum number of coins that you can have.

 

Example 1:

Input: piles = [2,4,1,2,7,8]
Output: 9
Explanation: Choose the triplet (2, 7, 8), Alice Pick the pile with 8 coins, you the pile with 7 coins and Bob the last one.
Choose the triplet (1, 2, 4), Alice Pick the pile with 4 coins, you the pile with 2 coins and Bob the last one.
The maximum number of coins which you can have are: 7 + 2 = 9.
On the other hand if we choose this arrangement (1, 2, 8), (2, 4, 7) you only get 2 + 4 = 6 coins which is not optimal.

Example 2:

Input: piles = [2,4,5]
Output: 4

Example 3:

Input: piles = [9,8,7,6,5,1,2,3,4]
Output: 18

 

Constraints:

• 3 <= piles.length <= 105
• piles.length % 3 == 0
• 1 <= piles[i] <= 104

Companies: Cleartrip, Flipkart, Dunzo

Related Topics:
Array, Math, Greedy, Sorting, Game Theory

Hints:

• Which pile of coins will you never be able to pick up?
• Bob is forced to take the last pile of coins, no matter what it is. Which pile should you give to him?

Solution 1.

// OJ: https://leetcode.com/problems/maximum-number-of-coins-you-can-get/
// Author: github.com/lzl124631x
// Time: O(NlogN)
// Space: O(1)
class Solution {
public:
    int maxCoins(vector<int>& A) {
        sort(begin(A), end(A));
        int ans = 0;
        for (int i = 0, j = A.size() - 1; i < j; ++i, j -= 2) ans += A[j - 1];
        return ans;
    }
};

Solution 2.

// OJ: https://leetcode.com/problems/maximum-number-of-coins-you-can-get/
// Author: github.com/lzl124631x
// Time: O(NlogN)
// Space: O(1)
class Solution {
public:
    int maxCoins(vector<int>& A) {
        sort(begin(A), end(A));
        int N = A.size(), ans = 0;
        for (int i = N / 3; i < N; i += 2) ans += A[i];
        return ans;
    }
};