Algorithm
Problem Name: 564. Find the Closest Palindrome
Given a string n
representing an integer, return the closest integer (not including itself), which is a palindrome. If there is a tie, return the smaller one.
The closest is defined as the absolute difference minimized between two integers.
Example 1:
Input: n = "123" Output: "121"
Example 2:
Input: n = "1" Output: "0" Explanation: 0 and 2 are the closest palindromes but we return the smallest which is 0.
Constraints:
1 <= n.length <= 18
n
consists of only digits.n
does not have leading zeros.n
is representing an integer in the range[1, 1018 - 1]
.
Code Examples
#1 Code Example with Javascript Programming
Code -
Javascript Programming
/**
* @param {bigint | string} n
* @return {string}
*/
const nearestPalindromic = function(n) {
let bigInt = null
if (typeof n === 'bigint') bigInt = n
if (typeof n === 'string') bigInt = BigInt(n)
if (typeof n == null) throw new Error('unknown input type')
// take the number, keep adding 1 to it, then check if it's a palindrome
const prevPalindrome = getPrevPalindrome(bigInt)
const nextPalindrome = getNextPalindrome(bigInt)
const scalarPrev = bigInt - prevPalindrome
const scalarNext = nextPalindrome - bigInt
if (scalarPrev <= scalarNext) return prevPalindrome.toString()
else return nextPalindrome.toString()
}
/**
*
* @param {bigint} number
*/
function getPrevPalindrome(number) {
const decrementedNumber =
typeof number === 'bigint' ? number - BigInt(1) : BigInt(number) - BigInt(1)
if (decrementedNumber.toString().length === 1) return decrementedNumber
const leftSide = getLeftSideNumber(decrementedNumber)
const palindromedLeft = getPalindromeAsString(leftSide)
const rightSide = getRightSideNumberAsString(decrementedNumber)
const comparison = compareTwoValues(BigInt(palindromedLeft), BigInt(rightSide))
if (comparison === 0) {
// the right side is already the palindromedLeft - return the incrementedNumber
return decrementedNumber
}
if (comparison === 1) {
// this means the right side is already too far advanced (going downwards) compared to the palindromedLeft,
// you need to take the leftSideWithBorder, decrement by 1, then return this new number concatenated with
// the leftSide's palindrome - this is the answer
const leftWithBorder = getLeftSideNumberWithBorder(decrementedNumber)
const decremented = leftWithBorder - BigInt(1)
if (decremented === BigInt(0)) return BigInt(9)
const newWhole = BigInt(decremented.toString() + getRightSideNumberAsString(decrementedNumber))
const newLeft = getLeftSideNumber(newWhole)
const palindromedNewLeft = getPalindromeAsString(newLeft)
return BigInt(decremented.toString() + palindromedNewLeft.toString())
}
if (comparison === -1) {
// this means the right side can naturally increment to the palindromedLeft,
// so you can just return the leftSideWithBorder concatenated with the palindromedLeft
const leftSideWithBorder = getLeftSideNumberWithBorder(decrementedNumber)
return BigInt(leftSideWithBorder.toString() + palindromedLeft)
}
}
/**
*
* @param {bigint} number
* @returns {*}
*/
function getNextPalindrome(number) {
const incrementedNumber =
typeof number === 'bigint' ? number + BigInt(1) : BigInt(number) + BigInt(1)
if (incrementedNumber.toString().length === 1) return incrementedNumber
const leftSide = getLeftSideNumber(incrementedNumber)
const palindromedLeft = getPalindromeAsString(leftSide)
const rightSide = getRightSideNumberAsString(incrementedNumber)
const comparison = compareTwoValues(BigInt(palindromedLeft), BigInt(rightSide))
if (comparison === 0) {
// the right side is already the palindromedLeft - return the incrementedNumber
return incrementedNumber
}
if (comparison === 1) {
// this means the right side can naturally increment to the palindromedLeft,
// so you can just return the leftSideWithBorder concatenated with the palindromedLeft
const leftSideWithBorder = getLeftSideNumberWithBorder(incrementedNumber)
const leftAsString = leftSideWithBorder.toString()
const combined = leftAsString + palindromedLeft
return BigInt(combined)
}
if (comparison === -1) {
// this means the right side is already too far advanced compared to the palindromedLeft,
// you need to take the leftSideWithBorder, increment by 1, then return this new number concatenated with
// the leftSide's palindrome - this is the answer
const leftWithBorder = getLeftSideNumberWithBorder(incrementedNumber)
const incrementedLeftWithBorder = leftWithBorder + BigInt(1)
const newWhole = BigInt(
incrementedLeftWithBorder.toString() + getRightSideNumberAsString(incrementedNumber)
)
const newLeft = getLeftSideNumber(newWhole)
const palindromedNewLeft = getPalindromeAsString(newLeft)
return BigInt(incrementedLeftWithBorder.toString() + palindromedNewLeft.toString())
}
}
/**
*
* @param {bigint} number
*/
function getLeftSideNumber(number) {
const numberAsText = number.toString()
const numCharsInLeftSide = Math.floor(numberAsText.length / 2)
return BigInt(numberAsText.slice(0, numCharsInLeftSide))
}
/**
*
* @param {bigint} number
* @returns {bigint}
*/
function getLeftSideNumberWithBorder(number) {
const numberAsText = number.toString()
const hasOddNumChars = numberAsText.length % 2 === 1
const left = getLeftSideNumber(number)
// should return the left side only, if it's an even-digited number
// else, return the left side together with the border number (since it's an odd-digited number)
if (hasOddNumChars) {
const middleChar = numberAsText.charAt(Math.floor(numberAsText.length / 2))
return BigInt(left.toString() + middleChar)
} else {
return BigInt(left.toString())
}
}
/**
*
* @param {bigint} number
* @returns {string}
*/
function getRightSideNumberAsString(number) {
const numberAsText = number.toString()
const numCharsInRightSide = Math.floor(numberAsText.length / 2)
return numberAsText.slice(numberAsText.length - numCharsInRightSide)
}
/**
*
* @param {bigint} number
* @returns {string}
*/
function getPalindromeAsString(number) {
const numberAsText = number.toString()
return numberAsText
.split('')
.reverse()
.join('')
}
/**
*
* @param {bigint} number1
* @param {bigint} number2
* @returns {number}
*/
function compareTwoValues(number1, number2) {
if (number1 < number2) return -1
if (number1 === number2) return 0
if (number1 > number2) return 1
}
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#2 Code Example with Python Programming
Code -
Python Programming
class Solution:
def nearestPalindromic(self, S):
K = len(S)
candidates = [str(10**k + d) for k in (K-1, K) for d in (-1, 1)]
prefix = S[:(K+1)//2]
P = int(prefix)
for start in map(str, (P-1, P, P+1)):
candidates.append(start + (start[:-1] if K%2 else start)[::-1])
def delta(x):
return abs(int(S) - int(x))
ans = None
for cand in candidates:
if cand != S and not cand.startswith('00'):
if (ans is None or delta(cand) < delta(ans) or
delta(cand) == delta(ans) and int(cand) < int(ans)):
ans = cand
return ans
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