# Maximum amount of money that can be collected by a player in a game of coins

Given a 2D array **Arr[][]** consisting of **N** rows and two persons **A** and **B** playing a game of alternate turns based on the following rules:

- A row is chosen at random, where
**A**can only take the leftmost remaining coin while**B**can only take the rightmost remaining coin in the chosen row. - The game ends when there are no coins left.

The task is to determine the maximum amount of money obtained by **A**.

**Examples:**

Input:N = 2, Arr[][] = {{ 5, 2, 3, 4 }, { 1, 6 }}Output:8Explanation:

Row 1: 5, 2, 3, 4

Row 2: 1, 6

Operations:

- A takes the coin with value 5
- B takes the coin with value 4
- A takes the coin with value 2
- B takes the coin with value 3
- A takes the coin with value 1
- B takes the coin with value 6
Optimally, money collected by A = 5 + 2 + 1 = 8

Money collected by B = 3 + 4 + 6 = 13

Input:N = 1, Arr[] = {{ 1, 2, 3 }}Output: 3

** ****Approach:** Follow the steps below to solve the problem

- In a game played with optimal strategy
- Initialize a variable, say
**amount**, to store the money obtained by**A**. - If
**N**is even,**A**will collect the first half of the coins - Otherwise, first,
**(N / 2)**coins would be collected by**A**and last**(N / 2)**would be collected by**B** - If N is odd, the coin at the middle can be collected by
**A**or**B**, depending upon the sequence of moves. - Store the coin at the middle of all odd sized rows in a variable, say
**mid_odd[].** - Sort the array
**mid_odd[]**in descending order. - Optimally,
**A**would collect all coins at**even indices**of**min_odd[]** - Finally, print the score of
**A**.

Below is the implementation of the above approach:

## C++

`// CPP Program to implement` `// the above approach` `#include<bits/stdc++.h>` `using` `namespace` `std;` `// Function to calculate the` `// maximum amount collected by A` `void` `find(` `int` `N, vector<vector<` `int` `>>Arr)` `{` ` ` ` ` `// Stores the money` ` ` `// obtained by A` ` ` `int` `amount = 0;` ` ` `// Stores mid elements` ` ` `// of odd sized rows` ` ` `vector<` `int` `> mid_odd;` ` ` `for` `(` `int` `i = 0; i < N; i++)` ` ` `{` ` ` `// Size of current row` ` ` `int` `siz = Arr[i].size();` ` ` `// Increase money collected by A` ` ` `for` `(` `int` `j = 0; j < siz / 2; j++)` ` ` `amount = amount + Arr[i][j];` ` ` `if` `(siz % 2 == 1)` ` ` `mid_odd.push_back(Arr[i][siz/2]);` ` ` `}` ` ` `// Add coins at even indices` ` ` `// to the amount collected by A` ` ` `sort(mid_odd.begin(),mid_odd.end());` ` ` `for` `(` `int` `i = 0; i < mid_odd.size(); i++)` ` ` `if` `(i % 2 == 0)` ` ` `amount = amount + mid_odd[i];` ` ` `// Print the amount` ` ` `cout<<amount<<endl;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `N = 2;` ` ` `vector<vector<` `int` `>>Arr{{5, 2, 3, 4}, {1, 6}};` ` ` `// Function call to calculate the` ` ` `// amount of coins collected by A` ` ` `find(N, Arr);` `}` `// This code is contributed by ipg2016107.` |

## Java

`// Java program to implement` `// the above approach` `import` `java.util.*;` `class` `GFG` `{` ` ` `// Function to calculate the` `// maximum amount collected by A` `static` `void` `find(` `int` `N, ` `int` `[][] Arr)` `{` ` ` ` ` `// Stores the money` ` ` `// obtained by A` ` ` `int` `amount = ` `0` `;` ` ` `// Stores mid elements` ` ` `// of odd sized rows` ` ` `ArrayList<Integer> mid_odd` ` ` `= ` `new` `ArrayList<Integer>();` ` ` `for` `(` `int` `i = ` `0` `; i < N; i++)` ` ` `{` ` ` `// Size of current row` ` ` `int` `siz = Arr[i].length;` ` ` `// Increase money collected by A` ` ` `for` `(` `int` `j = ` `0` `; j < siz / ` `2` `; j++)` ` ` `amount = amount + Arr[i][j];` ` ` `if` `(siz % ` `2` `== ` `1` `)` ` ` `mid_odd.add(Arr[i][siz/` `2` `]);` ` ` `}` ` ` `// Add coins at even indices` ` ` `// to the amount collected by A` ` ` `Collections.sort(mid_odd);` ` ` ` ` `for` `(` `int` `i = ` `0` `; i < mid_odd.size(); i++){` ` ` `if` `(i % ` `2` `== ` `0` `)` ` ` `amount = amount + mid_odd.get(i);` ` ` `}` ` ` `// Print the amount` ` ` `System.out.println(amount);` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `N = ` `2` `;` ` ` `int` `[][] Arr = {{` `5` `, ` `2` `, ` `3` `, ` `4` `}, {` `1` `, ` `6` `}};` ` ` `// Function call to calculate the` ` ` `// amount of coins collected by A` ` ` `find(N, Arr);` `}` `}` ` ` `// This code is contributed by splevel62.` |

## Python3

`# Python Program to implement` `# the above approach` `# Function to calculate the` `# maximum amount collected by A` `def` `find(N, Arr):` ` ` `# Stores the money` ` ` `# obtained by A` ` ` `amount ` `=` `0` ` ` `# Stores mid elements` ` ` `# of odd sized rows` ` ` `mid_odd ` `=` `[]` ` ` `for` `i ` `in` `range` `(N):` ` ` `# Size of current row` ` ` `siz ` `=` `len` `(Arr[i])` ` ` `# Increase money collected by A` ` ` `for` `j ` `in` `range` `(` `0` `, siz ` `/` `/` `2` `):` ` ` `amount ` `=` `amount ` `+` `Arr[i][j]` ` ` `if` `(siz ` `%` `2` `=` `=` `1` `):` ` ` `mid_odd.append(Arr[i][siz ` `/` `/` `2` `])` ` ` `# Add coins at even indices` ` ` `# to the amount collected by A` ` ` `mid_odd.sort(reverse` `=` `True` `)` ` ` `for` `i ` `in` `range` `(` `len` `(mid_odd)):` ` ` `if` `i ` `%` `2` `=` `=` `0` `:` ` ` `amount ` `=` `amount ` `+` `mid_odd[i]` ` ` `# Print the amount` ` ` `print` `(amount)` `# Driver Code` `N ` `=` `2` `Arr ` `=` `[[` `5` `, ` `2` `, ` `3` `, ` `4` `], [` `1` `, ` `6` `]]` `# Function call to calculate the` `# amount of coins collected by A` `find(N, Arr)` |

## C#

`// C# Program to implement` `// the above approach` `using` `System;` `using` `System.Collections.Generic;` `class` `GFG {` ` ` `// Function to calculate the` ` ` `// maximum amount collected by A` ` ` `static` `void` `find(` `int` `N, List<List<` `int` `>> Arr)` ` ` `{` ` ` `// Stores the money` ` ` `// obtained by A` ` ` `int` `amount = 0;` ` ` `// Stores mid elements` ` ` `// of odd sized rows` ` ` `List<` `int` `> mid_odd = ` `new` `List<` `int` `>();` ` ` `for` `(` `int` `i = 0; i < N; i++)` ` ` `{` ` ` `// Size of current row` ` ` `int` `siz = Arr[i].Count;` ` ` `// Increase money collected by A` ` ` `for` `(` `int` `j = 0; j < siz / 2; j++)` ` ` `amount = amount + Arr[i][j];` ` ` `if` `(siz % 2 == 1)` ` ` `mid_odd.Add(Arr[i][siz/2]);` ` ` `}` ` ` `// Add coins at even indices` ` ` `// to the amount collected by A` ` ` `mid_odd.Sort();` ` ` `for` `(` `int` `i = 0; i < mid_odd.Count; i++)` ` ` `if` `(i % 2 == 0)` ` ` `amount = amount + mid_odd[i];` ` ` `// Print the amount` ` ` `Console.WriteLine(amount);` ` ` `}` ` ` `// Driver code` ` ` `static` `void` `Main()` ` ` `{` ` ` `int` `N = 2;` ` ` `List<List<` `int` `>> Arr = ` `new` `List<List<` `int` `>>();` ` ` `Arr.Add(` `new` `List<` `int` `>());` ` ` `Arr[0].Add(5);` ` ` `Arr[0].Add(2);` ` ` `Arr[0].Add(3);` ` ` `Arr[0].Add(4);` ` ` `Arr.Add(` `new` `List<` `int` `>());` ` ` `Arr[1].Add(1);` ` ` `Arr[1].Add(6);` ` ` `// Function call to calculate the` ` ` `// amount of coins collected by A` ` ` `find(N, Arr);` ` ` `}` `}` `// This code is contributed by divyesh072019.` |

## Javascript

`<script>` `// Javascript Program to implement` `// the above approach` `// Function to calculate the` `// maximum amount collected by A` `function` `find(N, Arr)` `{` ` ` ` ` `// Stores the money` ` ` `// obtained by A` ` ` `var` `amount = 0;` ` ` `// Stores mid elements` ` ` `// of odd sized rows` ` ` `var` `mid_odd = [];` ` ` `for` `(` `var` `i = 0; i < N; i++)` ` ` `{` ` ` `// Size of current row` ` ` `var` `siz = Arr[i].length;` ` ` `// Increase money collected by A` ` ` `for` `(` `var` `j = 0; j < siz / 2; j++)` ` ` `amount = amount + Arr[i][j];` ` ` `if` `(siz % 2 == 1)` ` ` `mid_odd.push(Arr[i][siz/2]);` ` ` `}` ` ` `// Add coins at even indices` ` ` `// to the amount collected by A` ` ` `mid_odd.sort((a,b)=>a-b)` ` ` `for` `(` `var` `i = 0; i < mid_odd.length; i++)` ` ` `if` `(i % 2 == 0)` ` ` `amount = amount + mid_odd[i];` ` ` `// Print the amount` ` ` `document.write( amount + ` `"<br>"` `);` `}` `// Driver Code` `var` `N = 2;` `var` `Arr = [[5, 2, 3, 4], [1, 6]];` `// Function call to calculate the` `// amount of coins collected by A` `find(N, Arr);` `// This code is contributed by importantly.` `</script>` |

**Output:**

8

**Time Complexity : **O(N)**Auxiliary Space : **O(1)