# Minimize coins required to obtain all possible values up to N

Given an integer **N**, the task is to find the minimum count of **{1, 2, 5}**-valued coins such that changes of all possible values in the range **[1, N]** can be formed and it is not possible to obtain values **N**.

**Examples:**

Input:N = 8Output:

Count of 5 values coins: 0

Count of 2 rupees coins: 3

Count of 1 rupees coins: 2Explanation:

Coins required for 1 cent = 1

Coins required for 2 cent = 1

Coins required for 3 cent = 2

Coins required for 4 cent = 2

Coins required for 5 cent = 3

Coins required for 6 cent = 3

Coins required for 7 cent = 4

Coins required for 8 cent = 5

Input:N = 17Output:

Count of 5 rupees coins: 2

Count of 2 rupees coins: 3

Count of 1 rupees coins: 1

**Approach: **The problem can be solved using the greedy technique. The idea is based on the following observations:

Any number, X from the range [1, N] can be represented as

X = 5 * (Integer) + Y * (Integer)

Y is one of the values from the range [0, 4]

Follow the steps below to solve the problem:

- Initialize three variables, say
**F, T**, and**O**, to store the count of**5**,**2**and**1**-valued coins. - Calculate count of
**5**-valued coins using**F = (N – 4)/5.** - If (N – 5 * F) is even, then count of one valued coins can be calculated as
**O = 1**. - Otherwise, count of one valued coins can be calculated as
**O = 2**. - Calculate count of two valued coins can be calculated as
**T = (N – 5 * F – O) / 2.** - Finally, print values of
**F, T**, and**O.**

Below is the implementation of the above approach:,

## C++

`#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find minimum count of {1, 2, 5}` `// valued coins required to make a change of` `// all values in the range [1, N]` `void` `find(` `int` `N)` `{ ` ` ` `int` `T, F, O;` ` ` `// Number of 5 valueds coins required` ` ` `F = ` `int` `((N - 4) / 5);` ` ` `// Number of 1 valued coins required` ` ` `if` `(((N - 5 * F) % 2) == 0)` ` ` `{` ` ` `O = 2;` ` ` `}` ` ` `else` ` ` `{` ` ` `O = 1 ;` ` ` `}` ` ` `// Number of 2 valued coins required` ` ` `T = ` `floor` `((N - 5 * F - O)/2);` ` ` `cout<< ` `"Count of 5 valueds coins: "` `<< F << endl;` ` ` `cout<< ` `"Count of 2 valueds coins: "` `<< T<< endl;` ` ` `cout<< ` `"Count of 1 valueds coins: "` `<< O << endl;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `N = 8;` ` ` `find(N);` ` ` `return` `0;` `}` `// This code is contributed by Jana_sayantan.` |

## Java

`// Java program to implement ` `// the above approach ` `import` `java.util.*;` `class` `GFG{` `// Function to find minimum count of {1, 2, 5}` `// valued coins required to make a change of` `// all values in the range [1, N]` `static` `void` `find(` `int` `N)` `{ ` ` ` `int` `T, F, O;` ` ` `// Number of 5 valueds coins required` ` ` `F = (` `int` `)((N - ` `4` `) / ` `5` `);` ` ` `// Number of 1 valued coins required` ` ` `if` `(((N - ` `5` `* F) % ` `2` `) == ` `0` `)` ` ` `{` ` ` `O = ` `2` `;` ` ` `}` ` ` `else` ` ` `{` ` ` `O = ` `1` `;` ` ` `}` ` ` `// Number of 2 valued coins required` ` ` `T = (` `int` `)Math.floor((N - ` `5` `* F - O)/` `2` `);` ` ` `System.out.println(` `"Count of 5 valueds coins: "` `+ F);` ` ` `System.out.println(` `"Count of 2 valueds coins: "` `+ T);` ` ` `System.out.println(` `"Count of 1 valueds coins: "` `+ O);` `}` `// Driver Code` `public` `static` `void` `main(String args[])` `{` ` ` `int` `N = ` `8` `;` ` ` `find(N);` `}` `}` `// This code is contributed by splevel62.` |

## Python3

`# Python Program for the above approach` `# Function to find minimum count of {1, 2, 5}` `# valued coins required to make a change of` `# all values in the range [1, N]` `def` `find(N):` ` ` ` ` `# Number of 5 valueds coins required` ` ` `F ` `=` `int` `((N ` `-` `4` `) ` `/` `5` `)` ` ` `# Number of 1 valued coins required` ` ` `if` `((N ` `-` `5` `*` `F) ` `%` `2` `) ` `=` `=` `0` `:` ` ` `O ` `=` `2` ` ` `else` `:` ` ` `O ` `=` `1` ` ` `# Number of 2 valued coins required` ` ` `T ` `=` `(N ` `-` `5` `*` `F ` `-` `O)` `/` `/` `2` ` ` `print` `(` `"Count of 5 valueds coins: "` `, F)` ` ` `print` `(` `"Count of 2 valueds coins: "` `, T)` ` ` `print` `(` `"Count of 1 valueds coins: "` `, O)` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` ` ` `N ` `=` `8` ` ` `find(N)` |

## C#

`// C# program to implement ` `// the above approach ` `using` `System;` `public` `class` `GFG` `{` `// Function to find minimum count of {1, 2, 5}` `// valued coins required to make a change of` `// all values in the range [1, N]` `static` `void` `find(` `int` `N)` `{ ` ` ` `int` `T, F, O;` ` ` `// Number of 5 valueds coins required` ` ` `F = (` `int` `)((N - 4) / 5);` ` ` `// Number of 1 valued coins required` ` ` `if` `(((N - 5 * F) % 2) == 0)` ` ` `{` ` ` `O = 2;` ` ` `}` ` ` `else` ` ` `{` ` ` `O = 1 ;` ` ` `}` ` ` `// Number of 2 valued coins required` ` ` `T = (` `int` `)Math.Floor((` `double` `)(N - 5 * F - O)/2);` ` ` `Console.WriteLine(` `"Count of 5 valueds coins: "` `+ F);` ` ` `Console.WriteLine(` `"Count of 2 valueds coins: "` `+ T);` ` ` `Console.WriteLine(` `"Count of 1 valueds coins: "` `+ O);` `}` `// Driver Code` `public` `static` `void` `Main(String []args)` `{` ` ` `int` `N = 8;` ` ` `find(N);` `}` `}` `// This code is contributed by 29AjayKumar` |

## Javascript

`<script>` `// Javascript program to implement ` `// the above approach ` `// Function to find minimum count of {1, 2, 5}` `// valued coins required to make a change of` `// all values in the range [1, N]` `function` `find(N)` `{ ` ` ` `var` `T, F, O;` ` ` `// Number of 5 valueds coins required` ` ` `F = parseInt((N - 4) / 5);` ` ` `// Number of 1 valued coins required` ` ` `if` `(((N - 5 * F) % 2) == 0)` ` ` `{` ` ` `O = 2;` ` ` `}` ` ` `else` ` ` `{` ` ` `O = 1 ;` ` ` `}` ` ` `// Number of 2 valued coins required` ` ` `T = Math.floor((N - 5 * F - O)/2);` ` ` `document.write( ` `"Count of 5 valueds coins: "` `+ F + ` `"<br>"` `);` ` ` `document.write( ` `"Count of 2 valueds coins: "` `+ T + ` `"<br>"` `);` ` ` `document.write( ` `"Count of 1 valueds coins: "` `+ O + ` `"<br>"` `);` `}` `var` `N = 8;` `find(N);` `// This code is contributed by SoumikMondal.` `</script>` |

**Output:**

Count of 5 valueds coins: 0 Count of 2 valueds coins: 3 Count of 1 valueds coins: 2

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