714273. Max Coins
Medium
Max Coins
Slug: max-coins--170647 Difficulty: Medium Id: 714273 Topic Tags: Dynamic Programming, Greedy, Sorting, Algorithms Company Tags: None
Summary
The Max Coins problem involves finding the maximum number of coins that can be collected given a set of coin values and their corresponding frequencies. This problem is a classic example of a dynamic programming problem, requiring the use of greedy algorithms to solve efficiently.
Detailed Explanation
The problem can be broken down into the following steps:
- Initialize an array
dpof sizen, wherenis the number of coin values. - Sort the coin values in descending order and initialize a variable
max_coinsto 0. - Iterate through the sorted coin values, for each value:
- Calculate the maximum coins that can be collected with this coin using the formula:
min(frequency, dp[previous_coin_value]), wherefrequencyis the frequency of the current coin anddp[previous_coin_value]is the maximum coins collected so far. - Update
max_coinsto the maximum value calculated in step 3.1.
- Calculate the maximum coins that can be collected with this coin using the formula:
- Return
max_coins.
Time complexity: O(n log n) due to sorting, where n is the number of coin values.
Space complexity: O(n), where n is the number of coin values.
Optimized Solutions
Java
public int maxCoins(int[] coins) {
Arrays.sort(coins);
int max_coins = 0;
for (int i = coins.length - 1; i >= 0; i--) {
int freq = coins[i];
if (freq > dp[coins[i-1]]) {
dp[coins[i-1]] = freq;
max_coins += freq;
}
}
return max_coins;
}