# Minimum cost for acquiring all coins with k extra coins allowed with every coin

You are given a list of N coins of different denominations. you can pay an amount equivalent to any 1 coin and can acquire that coin. In addition, once you have paid for a coin, we can choose at most K more coins and can acquire those for free. The task is to find the minimum amount required to acquire all the N coins for a given value of K.

Examples :

```Input : coin[] = {100, 20, 50, 10, 2, 5},
k = 3
Output : 7

Input : coin[] = {1, 2, 5, 10, 20, 50},
k = 3
Output : 3
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

As per question, we can see that at a cost of 1 coin, we can acquire at most K+1 coins. Therefore, in order to acquire all the n coins, we will be choosing ceil(n/(k+1)) coins and the cost of choosing coins will be minimum if we choose smallest ceil(n/(k+1)) ( Greedy approach). Smallest ceil(n/(k+1)) coins can be found by simply sorting all the N values in increasing order.
If we should check for time complexity (n log n) is for sorting element and (k) is for adding the total amount. So, finally Time Complexity : O(n log n).

## C++

 `// C++ program to acquire all n coins  ` `#include ` `using` `namespace` `std; ` ` `  `// function to calculate min cost ` `int` `minCost(``int` `coin[], ``int` `n, ``int` `k)  ` `{ ` `    ``// sort the coins value ` `    ``sort(coin, coin + n); ` ` `  `    ``// calculate no. of ` `    ``// coins needed ` `    ``int` `coins_needed = ``ceil``(1.0 * n /  ` `                            ``(k + 1)); ` ` `  `    ``// calculate sum of  ` `    ``// all selected coins ` `    ``int` `ans = 0; ` `    ``for` `(``int` `i = 0; i <= coins_needed - 1;  ` `                                      ``i++)  ` `        ``ans += coin[i]; ` `     `  `    ``return` `ans; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `coin[] = {8, 5, 3, 10, ` `                  ``2, 1, 15, 25}; ` `    ``int` `n = ``sizeof``(coin) / ``sizeof``(coin[0]); ` `    ``int` `k = 3; ` `    ``cout << minCost(coin, n, k); ` `    ``return` `0; ` `}  `

## Java

 `// Java program to acquire ` `// all n coins ` `import` `java.util.Arrays; ` ` `  `class` `GFG  ` `{ ` `     `  `    ``// function to calculate min cost ` `    ``static` `int` `minCost(``int` `coin[],  ` `                       ``int` `n, ``int` `k) ` `    ``{ ` `         `  `        ``// sort the coins value ` `        ``Arrays.sort(coin); ` ` `  `        ``// calculate no. of  ` `        ``// coins needed ` `        ``int` `coins_needed = (``int``)Math.ceil(``1.0` `* ` `                                  ``n / (k + ``1``)); ` ` `  `        ``// calculate sum of  ` `        ``// all selected coins ` `        ``int` `ans = ``0``; ` `         `  `        ``for` `(``int` `i = ``0``; i <= coins_needed - ``1``;  ` `                                          ``i++) ` `            ``ans += coin[i]; ` ` `  `        ``return` `ans; ` `    ``} ` `     `  `    ``// Driver code ` `    ``public` `static` `void` `main(String arg[]) ` `    ``{ ` `        ``int` `coin[] = { ``8``, ``5``, ``3``, ``10``,  ` `                       ``2``, ``1``, ``15``, ``25` `}; ` `        ``int` `n = coin.length; ` `        ``int` `k = ``3``; ` `         `  `        ``System.out.print(minCost(coin, n, k)); ` `    ``} ` `} ` ` `  `// This code is contributed ` `// by Anant Agarwal. `

## Python3

 `# Python program to ` `# acquire all n coins  ` ` `  `import` `math ` ` `  `# function to calculate min cost ` `def` `minCost(coin, n, k):  ` ` `  `    ``# sort the coins value ` `    ``coin.sort() ` ` `  `    ``# calculate no. of ` `    ``# coins needed ` `    ``coins_needed ``=` `math.ceil(``1.0` `*` `n ``/``/` `                            ``(k ``+` `1``)); ` ` `  `    ``# calculate sum of all ` `    ``# selected coins ` `    ``ans ``=` `0` `    ``for` `i ``in` `range``(coins_needed ``-` `1` `+` `1``):  ` `        ``ans ``+``=` `coin[i] ` `     `  `    ``return` `ans ` ` `  `# Driver code ` `coin ``=` `[``8``, ``5``, ``3``, ``10``,  ` `        ``2``, ``1``, ``15``, ``25``] ` `n ``=` `len``(coin) ` `k ``=` `3` ` `  `print``(minCost(coin, n, k)) ` ` `  `# This code is contributed ` `# by Anant Agarwal. `

## C#

 `// C# program to acquire all n coins ` `using` `System; ` ` `  `class` `GFG  ` `{ ` `     `  `    ``// function to calculate min cost ` `    ``static` `int` `minCost(``int` `[]coin,  ` `                       ``int` `n, ``int` `k) ` `    ``{ ` `        ``// sort the coins value ` `        ``Array.Sort(coin); ` ` `  `        ``// calculate no. of coins needed ` `        ``int` `coins_needed = (``int``)Math.Ceiling(1.0 * ` `                                     ``n / (k + 1)); ` ` `  `        ``// calculate sum of  ` `        ``// all selected coins ` `        ``int` `ans = 0; ` `         `  `        ``for` `(``int` `i = 0; i <= coins_needed - 1; i++) ` `            ``ans += coin[i]; ` ` `  `        ``return` `ans; ` `    ``} ` `     `  `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `[]coin = {8, 5, 3, 10,  ` `                      ``2, 1, 15, 25}; ` `        ``int` `n = coin.Length; ` `        ``int` `k = 3; ` `         `  `        ``// Function calling ` `        ``Console.Write(minCost(coin, n, k)); ` `    ``} ` `} ` ` `  `// This code is contributed ` `// by nitin mittal. `

/div>

## PHP

 ` `

Output :

```3
```

Note that there are more efficient approaches to find given number of smallest values. For example, method 6 of m largest(or smallest) elements in an array can find m’th smallest element in (n-m) Log m + m Log m).

How to handle multiple queries for a single predefined array?
In the case, if you are asked to find the above answer for many different values of K, you have to compute it fast and our time complexity got increased as per number of queries for k. For the purpose to serve, we can maintain a prefix sum array after sorting all the N values and can answer queries easily and quickly.
Suppose

## C++

 `// C++ program to acquire all  ` `// n coins at minimum cost ` `// with multiple values of k. ` `#include ` `using` `namespace` `std; ` ` `  `// Converts coin[] to prefix sum array ` `void` `preprocess(``int` `coin[], ``int` `n) ` `{ ` `    ``// sort the coins value ` `    ``sort(coin, coin + n); ` ` `  `    ``// Maintain prefix sum array ` `    ``for` `(``int` `i = 1; i <= n - 1; i++) ` `        ``coin[i] += coin[i - 1]; ` `} ` ` `  `// Function to calculate min  ` `// cost when we can get k extra ` `// coins after paying cost of one. ` `int` `minCost(``int` `coin[], ``int` `n, ``int` `k) ` `{ ` `    ``// calculate no. of coins needed ` `    ``int` `coins_needed = ``ceil``(1.0 * n / (k + 1)); ` ` `  `    ``// return sum of from prefix array ` `    ``return` `coin[coins_needed - 1]; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `coin[] = {8, 5, 3, 10,  ` `                  ``2, 1, 15, 25}; ` `    ``int` `n = ``sizeof``(coin) / ``sizeof``(coin[0]); ` `    ``preprocess(coin, n); ` `    ``int` `k = 3; ` `    ``cout << minCost(coin, n, k) << endl; ` `    ``k = 7; ` `    ``cout << minCost(coin, n, k) << endl; ` `    ``return` `0; ` `} `

## Java

 `// C# program to acquire all n coins at  ` `// minimum cost with multiple values of k. ` `import` `java .io.*; ` `import` `java.util.Arrays; ` ` `  `public` `class` `GFG { ` `     `  `    ``// Converts coin[] to prefix sum array ` `    ``static` `void` `preprocess(``int` `[]coin, ``int` `n) ` `    ``{ ` `         `  `        ``// sort the coins value ` `        ``Arrays.sort(coin); ` `     `  `        ``// Maintain prefix sum array ` `        ``for` `(``int` `i = ``1``; i <= n - ``1``; i++) ` `            ``coin[i] += coin[i - ``1``]; ` `    ``} ` `     `  `    ``// Function to calculate min cost when we ` `    ``// can get k extra coins after paying  ` `    ``// cost of one. ` `    ``static` `int` `minCost(``int` `[]coin, ``int` `n, ``int` `k) ` `    ``{ ` `         `  `        ``// calculate no. of coins needed ` `        ``int` `coins_needed =(``int``) Math.ceil(``1.0`  `                                ``* n / (k + ``1``)); ` `     `  `        ``// return sum of from prefix array ` `        ``return` `coin[coins_needed - ``1``]; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``static` `public` `void` `main (String[] args) ` `    ``{ ` `        ``int` `[]coin = {``8``, ``5``, ``3``, ``10``, ``2``, ``1``, ``15``, ``25``}; ` `        ``int` `n = coin.length; ` `         `  `        ``preprocess(coin, n); ` `         `  `        ``int` `k = ``3``; ` `        ``System.out.println(minCost(coin, n, k)); ` `         `  `        ``k = ``7``; ` `        ``System.out.println( minCost(coin, n, k)); ` `    ``} ` `} ` ` `  `// This code is contributed by anuj_67. `

## Python3

 `# Python3 program to acquire all n coins at  ` `# minimum cost with multiple values of k. ` `import` `math as mt ` ` `  `# Converts coin[] to prefix sum array ` `def` `preprocess(coin, n): ` ` `  `    ``# sort the coins values ` `    ``coin.sort() ` `     `  `    ``# maintain prefix sum array ` `    ``for` `i ``in` `range``(``1``, n): ` `        ``coin[i] ``+``=` `coin[i ``-` `1``] ` `     `  `# Function to calculate min cost when we can   ` `# get k extra coins after paying cost of one. ` `def` `minCost(coin, n, k): ` `     `  `    ``# calculate no. of coins needed ` `    ``coins_needed ``=` `mt.ceil(``1.0` `*` `n ``/` `(k ``+` `1``)) ` `     `  `    ``# return sum of from prefix array ` `    ``return` `coin[coins_needed ``-` `1``] ` `     `  `# Driver code ` `coin ``=` `[``8``, ``5``, ``3``, ``10``, ``2``, ``1``, ``15``, ``25``] ` ` `  `n ``=` `len``(coin) ` ` `  `preprocess(coin, n) ` `k ``=` `3` ` `  `print``(minCost(coin, n, k)) ` ` `  `k ``=` `7` ` `  `print``(minCost(coin, n, k)) ` ` `  `# This code is contributed  ` `# by Mohit kumar 29  `

## C#

 `// C# program to acquire all n coins at  ` `// minimum cost with multiple values of k. ` `using` `System; ` ` `  `public` `class` `GFG { ` `     `  `    ``// Converts coin[] to prefix sum array ` `    ``static` `void` `preprocess(``int` `[]coin, ``int` `n) ` `    ``{ ` `         `  `        ``// sort the coins value ` `        ``Array.Sort(coin); ` `     `  `        ``// Maintain prefix sum array ` `        ``for` `(``int` `i = 1; i <= n - 1; i++) ` `            ``coin[i] += coin[i - 1]; ` `    ``} ` `     `  `    ``// Function to calculate min cost when we ` `    ``// can get k extra coins after paying  ` `    ``// cost of one. ` `    ``static` `int` `minCost(``int` `[]coin, ``int` `n, ``int` `k) ` `    ``{ ` `         `  `        ``// calculate no. of coins needed ` `        ``int` `coins_needed =(``int``) Math.Ceiling(1.0  ` `                                 ``* n / (k + 1)); ` `     `  `        ``// return sum of from prefix array ` `        ``return` `coin[coins_needed - 1]; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``static` `public` `void` `Main () ` `    ``{ ` `        ``int` `[]coin = {8, 5, 3, 10, 2, 1, 15, 25}; ` `        ``int` `n = coin.Length; ` `         `  `        ``preprocess(coin, n); ` `         `  `        ``int` `k = 3; ` `        ``Console.WriteLine(minCost(coin, n, k)); ` `         `  `        ``k = 7; ` `        ``Console.WriteLine( minCost(coin, n, k)); ` `    ``} ` `} ` ` `  `// This code is contributed by anuj_67. `

## PHP

 ` `

Output :

```3
1
```

After preprocessing, every query for a k takes O(1) time.

## tags:

Greedy prefix-sum prefix-sum Greedy

code