Python lambda dp calculation

Question

I am trying to understand below code snippet, for each value of i, what are all the two arguments passed to min() ? appreciate if you could explain how the dp[i] computation could be expanded?

class Solution(object):

    def coinChange(self, coins, amount):
        MAX = float('inf')
        dp = [0] + [MAX] * amount
        print(dp)

        for i in range(1, amount + 1):
            dp[i] = min([dp[i - c] if i - c >= 0 else MAX for c in coins]) + 1

        print(dp)
        return [dp[amount], -1][dp[amount] == MAX]

Answer 1

A lot of things are happening here. The min() method is receiving a python list as an argument.

This python list is created through list comprehension . It helps to start from the back. The list comprehension is saying "For every value c in the iterable coins , append the value dp[i - c] to my list if the boolean i - c >=0 is True . Otherwise, append the value MAX .

In other words, the line [dp[i - c] if i - c >= 0 else MAX for c in coins] is equivalent to

def makelist(dp,i,MAX,coins):
    ret = []
    for c in coins:
        if i - c >= 0:
            ret.append(dp[i-c])
        else:
            ret.append(MAX)
    return ret

The min() method will be performed on this list once it is complete, which simply find the smallest value in the list