coin_change_topdown.cpp File Reference

Minimum coins change problem is a problem used to find the minimum number of coins required to completely reach a target amount. More...

#include <iostream>
#include <vector>
#include <cassert>
#include <climits>

Include dependency graph for coin_change_topdown.cpp:

Namespaces
	dynamic_programming
	Dynamic Programming algorithms.
	mincoins_topdown
	Functions for minimum coin exchange problem.

Functions
template<typename T >
int64_t	dynamic_programming::mincoins_topdown::mincoins (const T &n, const std::vector< T > &coins, const int16_t &t, std::vector< T > dp)
	This implementation is for finding minimum number of coins . More...
static void	test ()
	Test implementations. More...
int	main ()
	Main function. More...

Detailed Description

Minimum coins change problem is a problem used to find the minimum number of coins required to completely reach a target amount.

This problem can be solved using 2 methods:

1. Top down approach
2. Bottom up appraoch Top down approach involves a vector with all elements initialised to 0. It is based on optimal substructure and overlapping subproblems. Overall time complexity of coin change problem is O(n*t) For example: example 1:- Coins: {1,7,10} Target:15 Therfore minimum number of coins required = 3 of denomination 1,7 and 7.

   Author

   Divyansh Kushwaha

Function Documentation

main()

int main

(

void

)

Main function.

Returns

0 on exit

           {
    test(); // execute the test
    return 0;
}

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mincoins()

template<typename T >

int64_t dynamic_programming::mincoins_topdown::mincoins	(	const T &	n,
		const std::vector< T > &	coins,
		const int16_t &	t,
		std::vector< T >	dp
	)

This implementation is for finding minimum number of coins .

Parameters

T	template-type to use any kind of value
n	amount to be reached
coins	vector of coins
t	deontes the number of coins
dp	initilised to 0

Returns

minimum number of coins

                                                                                              {
        if(n==0){
            return 0;
        }
        if(dp[n]!=0){
            return dp[n];
        }
        int ans=INT_MAX;    //variable to store min coins
        for(int i=0;i<t;i++){
            if(n-coins[i]>=0){  //if after subtracting the current denomination is it greater than 0 or not
                int sub=mincoins(n-coins[i],coins,t,dp);
                ans=std::min(ans,sub+1);
            }
        }
        dp[n]=ans;
        return dp[n];   //returns minimum number of coins
    }

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test()

static void test ( )

static

Test implementations.

Returns

void

                   {
    // example 1: number of coins=3 and minimum coins required=3(7,7,1)
    const int64_t n1 = 15;
    const int8_t t1=3, a1=0;
    std::cout << "\nTest 1...";
    std::vector<int64_t> arr1 {1,7,10};
    std::vector<int64_t> dp1 (n1+1);
    fill(dp1.begin(),dp1.end(),a1);
    assert(dynamic_programming::mincoins_topdown::mincoins(n1, arr1, t1, dp1)==3);
    std::cout << "Passed\n";
}

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