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Program to find numbers with same consecutive differences in Python
Suppose we have to find an array of size N such that the absolute difference between every two consecutive digits is K. Every number in the answer must not have leading zeros except for the number 0 itself.
So, if the input is like N = 4 K = 7, then the output will be [1818, 2929, 7070, 8181, 9292], here 0707 is not valid as it has leading 0.
To solve this, we will follow these steps −
if N is same as 1, then
return a new list from range 0 to 9
queue := make a queue with all elements from 1 to 9
for n in range 0 to N - 2, do
len_queue := size of queue
for j in range 0 to len_queue - 1, do
num := left item of queue, and delete it from queue
lsd := num mod 10
if lsd - K >= 0, then
insert num * 10 + lsd - K at the end of queue
if K and lsd + K <= 9, then
insert num * 10 + lsd + K at the end of queue
return elements of queue
Example
Let us see the following implementation to get better understanding −
from collections import deque
def solve(N, K):
if N == 1:
return list(range(10))
queue = deque(list(range(1, 10)))
for n in range(N - 1):
len_queue = len(queue)
for j in range(len_queue):
num = queue.popleft()
lsd = num % 10
if lsd - K >= 0:
queue.append( num * 10 + lsd - K )
if K and lsd + K <= 9:
queue.append( num * 10 + lsd + K )
return list(queue)
N = 4
K = 7
print(solve(N, K))
Input
4, 7
Output
[1818, 2929, 7070, 8181, 9292]
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