Arr map(int, input split meaning in python)

This has not much to do with dynamic programming itself.

n, S = map(int, input().split())

will query the user for input, and then split it into words, convert these words in integers, and unpack it into two variables n and S. This thus will succeed when the user enters two numbers (not more, not less).

It works as follows:

1. input() will query the user for input, and read one line of user input;
2. .split() will split that input into a list of "words";
3. map(int, ...) will call int on each word, it will to that lazily (although that is not important here); and
4. n, S = ... will unpack the expression into two elements, and assign the first one to n and the second one to S.

For example:

>>> n, S = map(int, input().split())
14 25
>>> n
14
>>> S
25

But it will error if you pass only one number, three numbers, etc. like:

>>> n, S = map(int, input().split())
14
Traceback (most recent call last):
  File "", line 1, in 
ValueError: not enough values to unpack (expected 2, got 1)
>>> n, S = map(int, input().split())
14 25 37
Traceback (most recent call last):
  File "", line 1, in 
ValueError: too many values to unpack (expected 2)
>>> n, S = map(int, input().split())
foo bar
Traceback (most recent call last):
  File "", line 1, in 
ValueError: invalid literal for int() with base 10: 'foo'

The line:

w = list(map(int, input().split()))

does more or less the same thing, but instead takes as input from the user a sequence of numbers. There can be zero, one or more numbers. w will store a list of numbers. The list(..) part forces Python to evaluate the map(..) eagerly.

dp = [0] * (S + 1)

Here we will construct a list with S + 1 zeros. In Python, you can multiply a list (and tuple) with an integer n. The result is a list (or tuple) that is n times as large as the original list, and it repeats the elements. For example:

>>> [1,4,2,5] * 3
[1, 4, 2, 5, 1, 4, 2, 5, 1, 4, 2, 5]

Since here the given list contains one zero, it will thus produce a list that contains S+1 zeros.

Finally

dp[0] = 0

will set the first element to zero. But since that was already the case, this line is not very useful.

Let's break it down:

• input() gets user input and returns a string, e.g. "1 2 3 4 5"

• input().split() splits that input on whitespaces, e.g. ["1", "2", "3", ...]

• int() converts a string to a integer, e.g. "1" -> 1

• map(fn, sequence) applies the function fn to each element in the sequence, e.g. fn(sequence[0]), fn(sequence[1]), ...

• map(int, input().split()) applies int to each string element in the input, e.g. ["1", "2", "3", ...] -> int("1"), int("2"), ...

• list() turns any iterator/generator to a list, e.g. int("1"), int("2"), ... => [1, 2, 3, ...]

Example:

In []:
list(map(int, input().split()))

Input:
1 2 3 4 5

Out[]:
[1, 2, 3, 4, 5]

Note: this is the same as, which may be easier to read:

In []:
[int(n) for n in input().split()]

Input:
1 2 3 4 5

Out[]:
[1, 2, 3, 4, 5]

You don't create an array this way, you create an object that will provide you the objects once you iterate over them. Meaning as in a for loop

for v in arr:
    do something with v

or when you would create another sequence from it, like with list()

my_list = list(arr)

the point is that with a list you create a structure in RAM that will hold all the items upfront, which is often not what you actually need per se, so map allows you to simply define what you want (that takes no CPU or extra storage space) and only performs the actions when needed. If you do you need this as a list then a comprehension is preferable over map:

mylist = [int(n) for n in input.split()]

Sidenote: Python doesn't have a regular 'array', it has lists for ordered sequences that can be indexed. It does have specialized array for numerical values of a specific type but that's more oriented for low-level applications or for interfacing to other systems that need those kind of statically typed arrays.

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