Suppose we have a ball factory where we have n balls numbered from l to r (both inclusive) and have an infinite number of boxes numbered from 1 to infinity. So if we put each ball in the box with a number same to the sum of digits of the ball's number. (As an example, the ball number 123 will be put in the box number 1 + 2 + 3 = 6). So if we have two values l and r, we have to find the number of balls in the box with the most balls.
So, if the input is like l = 15 r = 25, then the output will be 2 because
The ball number 15 will be put inside 1+5 = 6
The ball number 16 will be put inside 1+6 = 7
The ball number 17 will be put inside 1+7 = 8
The ball number 18 will be put inside 1+8 = 9
The ball number 19 will be put inside 1+9 = 10
The ball number 20 will be put inside 2+0 = 2
The ball number 21 will be put inside 2+1 = 3
The ball number 22 will be put inside 2+2 = 4
The ball number 23 will be put inside 2+3 = 5
The ball number 24 will be put inside 2+4 = 6
The ball number 25 will be put inside 2+5 = 7
so box 6 and 7 contains maximum number of balls, that's why answer is 2
To solve this, we will follow these steps −
dict:= a new map
for i in range l to r, do
total:= 0
for each digit j of i, do
total := total + j
if total is not present in dict, then
dict[total] := 0
dict[total] := dict[total] + 1
return maximum of all values for all keys in dict
Example (Python)
Let us see the following implementation to get better understanding −
def solve(l, r):
dict={}
for i in range(l, r+1):
total=0
for j in str(i):
total += int(j)
if(total not in dict):
dict[total] = 0
dict[total] += 1
return max([dict[i] for i in dict])
l = 15
r = 25
print(solve(l, r))Input
15, 25
Output
1