def change_greedy(t, n):
    """贪心策略"""

    m = [0 for _ in range(len(t))]

    for i, money in enumerate(t):
        m[i] = n // money
        n = n % money

    return f'找零: {m}，剩余 {n} 元找不开'

def change_recursion1(t, n):
    """递归"""

    min_coin = n

    # 递归基本结束条件
    if n in t:
        return 1
    else:
        for i in [c for c in t if c <= n]:
            # 递归，减小规模：每次减去一种面值，挑选最小数量
            num = 1 + change_recursion1(t, n - i)
            if num < min_coin:
                min_coin = num

    return min_coin

def change_recursion2(t, n):
    """递归 (改进版)"""

    # 记录最优解
    known = [0] * (n + 1)
    min_coin = n

    if n in t:
        known[n] = 1
        return 1
    # 查表成功，直接用最优解
    elif known[n] > 0:
        return known[n]
    else:
        for i in [c for c in t if c <= n]:
            num = 1 + change_recursion1(t, n - i)
            if num < min_coin:
                min_coin = num
                # 找到最优解，记录到表中
                known[n] = min_coin

    return min_coin

def change_dp(t, n):
    """动态规划"""

    # dp 记录每一步的最优解、trace 记录硬币组合
    dp = [0] * (n + 1)
    trace = [0] * (n + 1)

    # 从 1 到 n 逐个计算最少硬币数
    for money in range(1, n + 1):
        # 初始化一个最大值
        count = money
        # 初始化新硬币
        new_coin = 1
        # 减去每个面值，查找剩余数量的最优解，记录总的最少数
        for j in [c for c in t if c <= money]:
            if dp[money - j] + 1 < count:
                count = dp[money - j] + 1
                new_coin = j
        # 记录当前钱数的最优解，记录到表中
        dp[money] = count
        trace[money] = new_coin

    return dp[n], trace


def change_dp_traceback(t, n):

    dp, trace = change_dp(t, n)
    coin = n

    while coin > 0:
        curr = trace[coin]
        print(curr)
        coin -= curr