Given a number N. The task is to find the smallest and largest palindromic number possible with N digits.
Input: N = 4 Output: Smallest Palindrome = 1001 Largest Palindrome = 9999 Input: N = 5 Output: Smallest Palindrome = 10001 Largest Palindrome = 99999
Smallest N-digit Palindromic Number: On observing carefully, you will observe that for N = 1, the smallest palindromic number will be 0. And for any other value of N, the smallest palindrome will have the first and last digits as 1 and all of the digits in between as 0.
- Case 1 : If N = 1 then answer will be 0.
- Case 2 : If N != 1 then answer will be (10(N-1)) + 1.
Largest N-digit Palindromic Number: Similar to the above approach, you can see that the largest possible palindrome number with N-digits can be obtained by appending 9 for N times. Therefore, largest N digits palindrome number will be 10N – 1.
Below is the implementation of the above approach:
Smallest Palindrome: 1001 Largest Palindrome: 9999
Time Complexity: O(1)
- Make largest palindrome by changing at most K-digits
- Next smallest prime palindrome
- N'th palindrome of K digits
- Given a number, find the next smallest palindrome
- Construct lexicographically smallest palindrome
- Make a lexicographically smallest palindrome with minimal changes
- Largest palindrome which is product of two n-digit numbers
- Smallest x such that 1*n, 2*n, ... x*n have all digits from 1 to 9
- Smallest odd digits number not less than N
- Smallest odd number with N digits
- Smallest even digits number not less than N
- Smallest Even number with N digits
- Smallest number with at least n digits in factorial
- Smallest number with sum of digits as N and divisible by 10^N
- Smallest multiple of 3 which consists of three given non-zero digits
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