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How to implement coin change problem using topDown approach using C#?
CoinChangeTopDownApproach takes 4 parameters, n is the amount, coins array contains the coins from which the amount needs to be calculated, t is the total number of coins, dp array will store all the pre calculated values. If amount is 0 then return 0. If the value is already calculated then return from the dp array. if the value is not calculated then call the CoinChangeTopDownApproach recursively.
Time complexity − O(N)
Space complexity − O(N)
Example
public class DynamicProgramming{
public int CoinChangeTopDownApproach(int n,int[] coins,int t,int[] dp){
if (n == 0){
return 0;
}
if (dp[n] != 0){
return dp[n];
}
int ans = int.MaxValue;
for (int i = 0; i < t; i++){
if (n - coins[i] >= 0){
int subprob = CoinChangeTopDownApproach(n - coins[i], coins, t, dp);
ans = Math.Min(ans, subprob + 1);
}
}
dp[n] = ans;
return dp[n];
}
}
static void Main(string[] args){
DynamicProgramming dp = new DynamicProgramming();
int N = 15;
int[] coins = { 1, 7, 10 };
int[] dp1 = new int[100];
int t = coins.Count();
int res = dp.CoinChangeTopDownApproach(15, coins, t, dp1);
Console.WriteLine(res);
}Output
3
Updated on: 17-Aug-2021
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