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2217. Find Palindrome With Fixed Length

Description

Given an integer array queries and a positive integer intLength, return an array answer where answer[i] is either the queries[i]th smallest positive palindrome of length intLength or -1 if no such palindrome exists.

A palindrome is a number that reads the same backwards and forwards. Palindromes cannot have leading zeros.

 

Example 1:

Input: queries = [1,2,3,4,5,90], intLength = 3
Output: [101,111,121,131,141,999]
Explanation:
The first few palindromes of length 3 are:
101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, ...
The 90th palindrome of length 3 is 999.

Example 2:

Input: queries = [2,4,6], intLength = 4
Output: [1111,1331,1551]
Explanation:
The first six palindromes of length 4 are:
1001, 1111, 1221, 1331, 1441, and 1551.

 

Constraints:

  • 1 <= queries.length <= 5 * 104
  • 1 <= queries[i] <= 109
  • 1 <= intLength <= 15

Solutions

Solution 1

Thinking

We need the \(q\)-th palindrome of length \(\textit{intLength}\). \(q\) can be \(10^9\) and the length up to \(15\), so listing palindromes is impossible. A palindrome is determined by its first half; the second half is the mirror.

The first half has length \(\lceil \textit{intLength}/2 \rceil\) and ranges from \(10^{l-1}\) to \(10^l-1\). Query \(q\) maps to \(v = 10^{l-1}+q-1\); if \(v\) overflows the answer is \(-1\), otherwise mirror \(v\)'s digits (dropping the middle copy when the length is odd).

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class Solution:
    def kthPalindrome(self, queries: List[int], intLength: int) -> List[int]:
        l = (intLength + 1) >> 1
        start, end = 10 ** (l - 1), 10**l - 1
        ans = []
        for q in queries:
            v = start + q - 1
            if v > end:
                ans.append(-1)
                continue
            s = str(v)
            s += s[::-1][intLength % 2 :]
            ans.append(int(s))
        return ans

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class Solution {
    public long[] kthPalindrome(int[] queries, int intLength) {
        int n = queries.length;
        long[] ans = new long[n];
        int l = (intLength + 1) >> 1;
        long start = (long) Math.pow(10, l - 1);
        long end = (long) Math.pow(10, l) - 1;
        for (int i = 0; i < n; ++i) {
            long v = start + queries[i] - 1;
            if (v > end) {
                ans[i] = -1;
                continue;
            }
            String s = "" + v;
            s += new StringBuilder(s).reverse().substring(intLength % 2);
            ans[i] = Long.parseLong(s);
        }
        return ans;
    }
}

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class Solution {
public:
    vector<long long> kthPalindrome(vector<int>& queries, int intLength) {
        int l = (intLength + 1) >> 1;
        long long start = pow(10, l - 1), end = pow(10, l) - 1;
        vector<long long> ans;
        for (int& q : queries) {
            long long v = start + q - 1;
            if (v > end) {
                ans.push_back(-1);
                continue;
            }
            string s = to_string(v);
            string s1 = s;
            reverse(s1.begin(), s1.end());
            s += s1.substr(intLength % 2);
            ans.push_back(stoll(s));
        }
        return ans;
    }
};

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func kthPalindrome(queries []int, intLength int) []int64 {
    l := (intLength + 1) >> 1
    start, end := int(math.Pow10(l-1)), int(math.Pow10(l))-1
    var ans []int64
    for _, q := range queries {
        v := start + q - 1
        if v > end {
            ans = append(ans, -1)
            continue
        }
        t := v
        if intLength%2 == 1 {
            t /= 10
        }
        for t > 0 {
            v = v*10 + t%10
            t /= 10
        }
        ans = append(ans, int64(v))
    }
    return ans
}

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function kthPalindrome(queries: number[], intLength: number): number[] {
    const isOdd = intLength % 2 === 1;
    const bestNum = 10 ** ((intLength >> 1) + (isOdd ? 1 : 0) - 1);
    const max = bestNum * 9;
    return queries.map(v => {
        if (v > max) {
            return -1;
        }
        const num = bestNum + v - 1;
        return Number(
            num +
                (num + '')
                    .split('')
                    .reverse()
                    .slice(isOdd ? 1 : 0)
                    .join(''),
        );
    });
}

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impl Solution {
    pub fn kth_palindrome(queries: Vec<i32>, int_length: i32) -> Vec<i64> {
        let is_odd = (int_length & 1) == 1;
        let best_num = i32::pow(10, (int_length / 2 + (if is_odd { 0 } else { -1 })) as u32);
        let max = best_num * 9;
        queries
            .iter()
            .map(|&num| {
                if num > max {
                    return -1;
                }
                let num = best_num + num - 1;
                format!(
                    "{}{}",
                    num,
                    num.to_string()
                        .chars()
                        .rev()
                        .skip(if is_odd { 1 } else { 0 })
                        .collect::<String>()
                )
                .parse()
                .unwrap()
            })
            .collect()
    }
}

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