human
Can you provide a code to count numbers ( smaller than or equal to N ) with given digit sum and the other steps required given the following:
Count numbers ( smaller than or equal to N ) with given digit sum | N can be max 10 ^ 18 and hence digitsum will be 162 maximum ..
If sum_so_far equals to given sum then return 1 else 0.
Our constructed number should not become greater than N ..
If tight is true then it will also be true for ( i + 1 ) digit ..
Driver code"
How can the above be solved in Python?
assistant
#Here is code to count numbers ( smaller than or equal to N ) with given digit sum and the other steps required.
 def solve ( i , tight , sum_so_far , Sum , number , length ) :
	if i == length :
		if sum_so_far == Sum :
			return 1
		else :
			return 0
	ans = dp [ i ] [ tight ] [ sum_so_far ]
	if ans != - 1 :
		return ans
	ans = 0
	for currdigit in range ( 0 , 10 ) :
		currdigitstr = str ( currdigit )
		if not tight and currdigitstr > number [ i ] :
			break
		ntight = tight or currdigitstr < number [ i ]
		nsum_so_far = sum_so_far + currdigit
		ans += solve ( i + 1 , ntight , nsum_so_far , Sum , number , length )
	return ans
if __name__ == " _ _ main _ _ " :
	count , Sum = 0 , 4
	number = "100"
	dp = [ [ [ - 1 for i in range ( 162 ) ] for j in range ( 2 ) ] for k in range ( 18 ) ]
	print ( solve ( 0 , 0 , 0 , Sum , number , len ( number ) ) )