coin_problem.py

def coinProblem(coins, total):
    dp = [0] * (total + 1)
    coins.sort()
    
    for subtotal in range(1, total + 1):
        best = float('inf')
        
        for c in coins:
            if c <= subtotal:
                option = 1 + dp[subtotal - c]
                
                if option < best:
                    best = option  
            else:
                break
                
        dp[subtotal] = best                
    
    return dp[total]