# Program to find lexicographically smallest string after applying operations in Python

PythonServer Side ProgrammingProgramming

Suppose we have a string s with only numeric digits and also have two values a and b. We can apply any one of the following two operations any number of times and in any order on s −

• Add 'a' to all odd positioned items of s(0-indexed). If digit is 9, then by adding something with it will be cycled back to 0.

• Rotate 's' to the right by b positions.

So we have to find the lexicographically smallest string we can get by applying the above operations any number of times on s.

So, if the input is like s = "5323" a = 9 b = 2, then the output will be 2050 because if we follow

• Rotate: "5323"
• Rotate: "2151"

To solve this, we will follow these steps −

• seen := a new set
• deq := a new queue with one element 's'
• while deq is not empty, do
• curr := first deleted element of deq
• insert curr into seen set
• if ad is not in seen, then
• insert ad at the end of deq
• insert ad into seen set
• ro := perform rotate operation on curr
• if ro is not in seen, then
• insert ro at the end of deq
• insert ro into seen set
• return minimum of seen

## Example

Let us see the following implementation to get better understanding −

from collections import deque
res = ''
for idx, i in enumerate(s):
if idx % 2 == 1:
num = (int(i) + a) % 10
res += str(num)
else:
res += i

return res

def rotate_(s, b):
idx = len(s)-b
res = s[idx:] + s[0:idx]
return res

def solve(s, a, b):
seen = set()
deq = deque([s])

while deq:
curr = deq.popleft()

ro = rotate_(curr, b)
if ro not in seen:
deq.append(ro)

return min(seen)

s = "5323"
a = 9
b = 2
print(solve(s, a, b))

## Input

"5323", 9, 2


## Output

2050