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dsa-solutions/gfg-solutions/Hard/0101-0200/0111-Maximum-Number-of-coins.md

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+---
+id: maximum-number-of-coin
+title: Maximum Number of coins (Geeks for Geeks)
+sidebar_label: Maximum Number of coins Problem
+tags:
+  - Intermediate
+  - Geeks for Geeks
+  - CPP
+  - Python
+  - DSA
+description: "This is a solution to the Maximum Number of coins Problem  on Geeks for Geeks."
+---
+
+## Problem Description
+
+We have been given N balloons, each with a number of coins associated with it. On bursting a balloon i, the number of coins gained is equal to A[i-1]*A[i]*A[i+1].
+Also, balloons i-1 and i+1 now become adjacent. Find the maximum possible profit earned after bursting all the balloons. Assume an extra 1 at each boundary.
+
+## Examples
+
+**Example:**
+
+Consider the following graph:
+
+**Input:** ` N=2 , a[]={5, 10}`
+**Output:**  `60`
+**Explanation:** First Burst `5`, Coins = `1*5*10` , Then burst `10`, Coins+=` 1*10*1` , Total = `60`
+
+**Example:**
+
+**Input:** `N=4 , a[] = {3,1,5,8}`
+**Output:** 167
+**Explanation:**
+`nums = [3,1,5,8] --> [3,5,8] --> [3,8] --> [8] --> []`
+`coins =  3*1*5    +   3*5*8   +  1*3*8  + 1*8*1 = 167.`
+
+## Your Task
+
+You don't need to read input or print anything. Your task is to complete the function maxCoins() which takes the array arr[], its size N, and returns the maximum number of coins that can be collected.
+
+Expected Time Complexity: $O(N^3)$
+Expected Space Complexity: $O(N^2)$
+
+## Constraints
+- `1 <= N <= 400`
+- `0 <= a[i] <= 100`
+
+## Problem Explanation
+
+Here's the step-by-step breakdown of the Maximum Number of coins process:
+
+There are 3n piles of coins of varying size, you and your friends will take piles of coins as follows:
+
+**Step 1:** In each step, you will choose any 3 piles of coins (not necessarily consecutive).
+**Step 2 :**Of your choice, Alice will pick the pile with the maximum number of coins.
+**Step 3 :**You will pick the next pile with the maximum number of coins.
+**Step 4 :**Your friend Bob will pick the last pile.
+**Step 5 :**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.
+
+### Code Implementation
+
+<Tabs>
+  <TabItem value="Python" label="Python" default>
+  <SolutionAuthor name="@ngmuraqrdd"/> 
+  ```python
+
+class Solution:
+    def maxCoins(self, piles: List[int]) -> int:
+        piles.sort()
+        return sum(piles[-2:(len(piles)//3)-1:-2])
+
+  ```
+  </TabItem>
+  <TabItem value="C++" label="C++">
+  <SolutionAuthor name="@ngmuraqrdd"/>
+  ```cpp
+  class Solution {
+public:
+
+    int maxCoins(vector<int>& piles) {
+        // sort the piles in non-increasing order
+        sort(piles.begin(), piles.end(), greater<int>());
+
+        // greedy using two-pointers
+        int sum = 0;
+        for (int l = 0, r = piles.size() - 1; l < r; l += 2, r--) {
+            sum += piles[l + 1];
+        }
+        return sum;
+    }
+};
+  ```
+
+  </TabItem>
+</Tabs>
+
+## Solution Logic
+ - Sort the piles in non-increasing order
+ - Greedy using two-pointers
+
+
+## Time Complexity
+
+$$O(N^3)$$.
+
+## Space Complexity
+
+$$O(N^2)$$.
+
+## Resources
+
+- **GFG Problem:** [GFG Problem](https://www.geeksforgeeks.org/problems/maximum-number-of-coins--170647/1)
+- **LeetCode Problem:** [LeetCode Problem](https://leetcode.com/problems/maximum-number-of-coins-you-can-get/description/)
+- **Author's Geeks for Geeks Profile:**  | [DaminiChachane](https://leetcode.com/u/divcxl15/) |
+
+This format ensures that all necessary details about the problem and its solution are clearly presented and easy to follow.