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29-InSange #98

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@InSange InSange commented Aug 25, 2024

๐Ÿ”— ๋ฌธ์ œ ๋งํฌ

Find the Closest Palindrome

โœ”๏ธ ์†Œ์š”๋œ ์‹œ๊ฐ„

ํ•˜๋ฃจ

โœจ ์ˆ˜๋„ ์ฝ”๋“œ

๋ฌธ์ œ ๊ฐœ์š”

ํŒฐ๋ฆฐ๋“œ๋กฌ์ธ๋ฐ ์ฃผ์–ด์ง€๋Š” ๋ฌธ์ž์—ด์ด ์ˆซ์ž์ž…๋‹ˆ๋‹ค.
๋ฌธ์ž์—ด ์ˆซ์ž n์„ ์ž…๋ ฅ ๋ฐ›์•˜์„ ๋•Œ ํŒฐ๋ฆฐ๋“œ๋กฌ์„ ๊ตฌ์„ฑํ•˜๋Š” ์ˆซ์ž๋ฅผ ์ฐพ์œผ์‹œ์˜ค.
์ˆซ์ž๋Š” n์—์„œ ๊ฐ€๊นŒ์šด ์ˆซ์ž์ด์—ฌ์•ผ ํ•˜๋ฉฐ ๋งŒ์•ฝ ๊ฐ€๊นŒ์šด ํŒฐ๋ฆฐ๋“œ๋กฌ ์ˆซ์ž๊ฐ€ 2๊ฐœ(n๋ณด๋‹ค ์ž‘๊ฑฐ๋‚˜ ํฐ ๊ฒฝ์šฐ)์ผ ๊ฒฝ์šฐ ๋” ์ž‘์€ ๊ฐ’์„ ๋‹ต์œผ๋กœ ํ•œ๋‹ค.
ํŒฐ๋ฆฐ๋“œ๋กฌ์€ ์ค‘๊ฐ„์„ ๊ธฐ์ ์œผ๋กœ ์ขŒ, ์šฐ๊ฐ€ ๋˜‘๊ฐ™์•„์•ผ ํ•ฉ๋‹ˆ๋‹ค.

์ ‘๊ทผ ๋ฐฉ์‹

๋ฌธ์ œ์—์„œ๋Š” intํ˜•์ด๋ผ ๋˜์–ด ์žˆ์ง€๋งŒ ์กฐ๊ฑด์„ ๋ณด๋ฉด length๊ฐ€ 18๋กœ ์ •์ˆ˜ํ˜•์œผ๋กœ ํ‘œํ˜„ํ•  ์ˆ˜ ์—†๋‹ค.
๊ทธ๋Ÿผ long longํ˜•์œผ๋กœ ๋ณ€ํ™˜ํ•œ ๋’ค ์™„์ „ ํƒ์ƒ‰์€ ์–ด๋–จ๊นŒ?
๋งŒ์•ฝ ์ตœ๋Œ€ ๊ธธ์ด์ธ 18์ผ ๊ฒฝ์šฐ
123456789987878787 ์ผ ๋•Œ 123456789987654321์ด ๊ฐ€๊นŒ์šด ๋‹ต์ด๋ผ๊ณ  ์ •ํ•˜์˜€์„ ๊ฒฝ์šฐ 224,466 ๋ฒˆ 1์„ ๋นผ์ค˜์•ผ ํ•œ๋‹ค.
์ถฉ๋ถ„ํ•  ๊ฒƒ ๊ฐ™์ง€๋งŒ
๋งŒ์•ฝ ์šฐ๋ฆฌ๊ฐ€ ์• ๋งคํ•œ ์ˆซ์ž ์ผ ๋•Œ ์ •์ˆ˜ n๋ณด๋‹ค ์ž‘์€ ๊ฐ€๊นŒ์šด ์ˆซ์ž์™€ ํฐ ๊ฐ€๊นŒ์šด ์ˆซ์ž๋ฅผ ์ฐพ์•„์•ผํ•˜๊ธฐ ๋•Œ๋ฌธ์— ๋„ˆ๋ฌด ๋น„ํšจ์œจ์ ์ธ ๊ฒƒ์„ ํ™•์ธํ•  ์ˆ˜ ์žˆ๋‹ค.

image
์šฐ๋ฆฌ๋Š” ๋ฌธ์ œ๊ฐ€ ์›ํ•˜๋Š” ๋‹ต์ด ํŒฐ๋ฆฐ๋“œ๋กฌ์„ ๊ตฌ์„ฑํ•œ๋‹ค.
๊ทธ๋Ÿผ ์ค‘๊ฐ„์„ ๊ธฐ์ ์œผ๋กœ ์•ž์ž๋ฆฌ๋ฅผ ๋’ท์ž๋ฆฌ๋กœ ์ฑ„์›Œ์ฃผ๋ฉด ๊ฐ€์žฅ ๊ฐ€๊นŒ์šด ๊ฐ’์ด์ง€ ์•Š์„๊นŒ ์ƒ๊ฐํ–ˆ๋‹ค.
์˜ˆ๋ฅผ ๋“ค์–ด
123456789 ๋ผ๋Š” ์ˆซ์ž๊ฐ€ ์žˆ์„ ๋•Œ 5๊ฐ€ ์ค‘๊ฐ„์„ ์ฐจ์ง€ํ•œ๋‹ค.
์•ž์ž๋ฆฌ๋ฅผ ๋’ท์ž๋ฆฌ๋กœ ๊ต์ฒดํ–ˆ์„ ๊ฒฝ์šฐ 987656789
๋’ท์ž๋ฆฌ๋ฅผ ์•ž์ž๋ฆฌ๋กœ ๊ต์ฒดํ–ˆ์„ ๊ฒฝ์šฐ 123454321
๋ˆ„๊ฐ€ ๋ด๋„ 123456789์— ๊ฐ€๊นŒ์šด ๊ฒƒ์€ 123454321์ธ ๊ฒƒ์„ ํ™•์ธํ•  ์ˆ˜ ์žˆ๋‹ค.
๊ทธ๋Ÿผ 987654321์ผ ๋•Œ๋„ ๋’ท์ž๋ฆฌ๋ฅผ ์•ž์ž๋ฆฌ๋กœ ๋ฐ”๊พธ์—ˆ์„ ๋•Œ 987656789์ด ๋” ๊ฐ€๊นŒ์šด ๊ฒƒ์„ ํ™•์ธํ•  ์ˆ˜ ์žˆ๋‹ค.

long long Convert(long long& num)
    {
        string s = to_string(num);
        int n = s.length();
        int l = (n-1) / 2;
        int r = n / 2;
        while(l >= 0) s[r++] = s[l--];
        return stoll(s);
    }

์ข‹๋‹ค. ์•ž์ž๋ฆฌ๋ฅผ ๋ฐ”ํƒ•์œผ๋กœ ๋’ท์ž๋ฆฌ๋ฅผ ๋ณ€ํ™˜์‹œํ‚ค๋Š” ํ•จ์ˆ˜๋ฅผ ๋งŒ๋“ค์—ˆ๋‹ค.

ํ•˜์ง€๋งŒ ์˜ˆ์™ธ๊ฐ€ ์žˆ๋‹ค.
199์˜ ๊ฒฝ์šฐ 191๋ณด๋‹ค๋Š” 202๊ฐ€ ๋” ๊ฐ€๊น๊ธฐ์— ๊ฐ’์„ ๋น„๊ตํ•ด์ฃผ๊ธดํ•ด์•ผ ํ•˜๋Š”๋ฐ

์ผ์ผ์ด ๋‹ค ๋ฐฉ๋ฌธํ•˜๊ธฐ๋Š” ๋น„ํšจ์œจ์ ์ด๋‹ˆ
์ด์ง„ ํƒ์ƒ‰์„ ํ†ตํ•ด ์ฐพ๋Š” ๋ฐฉ์‹์„ ํƒํ•˜์˜€๋‹ค.

long long UpPal(long long num)
    {
        long long left = 0;
        long long right = num;
        long long ans = INT_MIN;
        
        while(left <= right)
        {
            long long mid = (right + left)/2;
            long long palin = Convert(mid);
            if(palin < num) 
            {
                ans = palin;
                left = mid + 1;
            }
            else
            {
                right = mid - 1;
            }
        }
        
        return ans;
    }
    
    long long DownPal(long long num)
    {
        long long left = num;
        long long right = 1e18;
        long long ans = INT_MIN;
        
        while(left <= right) {
            long long mid = (right + left) / 2;
            long long palin = Convert(mid);
            if(palin > num)
            {
                ans = palin;
                right = mid - 1;
            }
            else 
            {
                left = mid + 1;
            }
        }
        
        return ans;
    }

0์—์„œ n๋ณด๋‹ค ์ž‘์€ ํŒฐ๋ฆฐ๋“œ๋กฌ ๊ฐ’์„ ์ฐพ๊ธฐ ์œ„ํ•ด ์˜ฌ๋ผ๊ฐ€๋Š” UpPal๊ณผ ๊ธธ์ด 18๋ณด๋‹ค ๋” ๊ธด 10์— 18์Šน์—์„œ ์ ์  ๋‚ด๋ ค์˜ค๋Š” DownPal์„ ํ†ตํ•ด ๊ฐ๊ฐ n๋ณด๋‹ค ํฐ ํŒฐ๋ฆฐ๋“œ๋กฌ๊ณผ, ์ž‘์€ ํŒฐ๋ฆฐ๋“œ๋กฌ์„ ์ฐพ๋Š” ๋ฐฉ์‹์„ ์ˆ˜ํ–‰ํ•˜์˜€๋‹ค.
image

๋‹ค๋ฅธ ๋ฐฉ์‹ ํ’€์ด

์ฒซ ํ’€์ด ๋ฐฉ์‹์œผ๋กœ ๋ฏธ๋ฃจ์–ด ๋ณด์•˜์„ ๋•Œ
์ค‘๊ฐ„ ๊ฐ’์„ ๋ฐ”ํƒ•์œผ๋กœ ํŒฐ๋ฆฐ๋“œ๋กฌ์„ ๋งŒ๋“ค ์ˆ˜ ์žˆ๋‹ค.
์ค‘๊ฐ„ ๊ฐ’์„ ๋งŒ๋“ค์—ˆ์„ ๋•Œ
168์˜ ๊ฒฝ์šฐ 161๋กœ ๋งŒ๋“ค์–ด์ง€์ง€๋งŒ 171์˜ ํŒฐ๋ฆฐ๋“œ๋กฌ ๊ฐ’์ด 168๊ณผ ๊ฐ€์žฅ ๊ฐ€๊นŒ์šด ํŒฐ๋ฆฐ๋“œ๋กฌ์ด๋‹ค.
์ฆ‰ ์ค‘๊ฐ„๊ฐ’์— 1์„ ๋”ํ–ˆ์„ ๊ฒฝ์šฐ๋ฅผ ํ™•์ธํ•ด์•ผํ•˜๋ฉฐ
์ด ๋ฐ˜๋Œ€์ธ 1์„ ๋บ์„ ๊ฒฝ์šฐ๋„ ํ™•์ธํ•ด์•ผํ•œ๋‹ค.
751์˜ ๊ฒฝ์šฐ 757 ๋ณด๋‹ค๋Š” 747์ด ๋” ๊ฐ€๊น๋‹ค.

์ฆ‰ ์ค‘๊ฐ„๊ฐ’, ์ค‘๊ฐ„๊ฐ’ +1, ์ค‘๊ฐ„๊ฐ’ -1 ์„ ํ™•์ธํ•ด์•ผ ํ•œ๋‹ค.

์—ฌ๊ธฐ์—
999์˜ ๊ฒฝ์šฐ ๊ฐ€์žฅ ๊ฐ€๊นŒ์šด ๊ฐ’์€ 1001์ด ๋˜๊ณ 
1000์˜ ๊ฒฝ์šฐ 1001๊ณผ 999๊ฐ€ ๋˜๊ธฐ ๋•Œ๋ฌธ์— ๋” ์ž‘์€ ๊ฐ’์ธ 999๊ฐ€ ๋œ๋‹ค.

๊ณ ๋กœ ๋งจ ์•ž์ด 1์ด๊ณ  ๋์ด 1, ์ค‘๊ฐ„์ด 0์ธ ๊ฒฝ์šฐ๋ฅผ ํ™•์ธํ•ด์•ผํ•˜๊ณ 
9๋กœ ์ด๋ฃจ์–ด์ง„ ๊ฒฝ์šฐ๋„ ํ™•์ธ์„ ํ•ด์•ผํ•œ๋‹ค.

๊ทธ๋Ÿผ ๋‚˜์˜ค๋Š” ๊ฒฝ์šฐ์˜ ์ˆ˜๋Š”

์ค‘๊ฐ„ ๊ฐ’ ๊ธฐ์ค€ ํŒฐ๋ฆฐ๋“œ๋กฌ
์ค‘๊ฐ„ ๊ฐ’ + 1 ๊ธฐ์ค€ ํŒฐ๋ฆฐ๋“œ๋กฌ
์ค‘๊ฐ„ ๊ฐ’ - 1 ๊ธฐ์ค€ ํŒฐ๋ฆฐ๋“œ๋กฌ
n๋ณด๋‹ค ํฐ 10^length + 1๋กœ ์ด๋ฃจ์–ด์ง„ ํŒฐ๋ฆฐ๋“œ๋กฌ
length๋ณด๋‹ค ์งง์€ 9๋กœ๋งŒ ์ด๋ฃจ์–ด์ง„ ํŒฐ๋ฆฐ๋“œ๋กฌ

์ธ ๊ฒƒ์„ ํ™•์ธํ•  ์ˆ˜ ์žˆ๋‹ค.

class Solution {
public:
    string nearestPalindromic(string n) {
        if(n.length()==1)
            return to_string(stoi(n)-1);
        
        int d = n.length();
        vector<long> candidates;
        candidates.push_back(pow(10,d-1)-1);
        candidates.push_back(pow(10,d)+1);

        int mid = (d+1)/2;
        long prefix = stol(n.substr(0,mid));
        vector<long> v = {prefix,prefix+1, prefix-1};
        for(long i : v)
        {
            string postfix = to_string(i);
            if(d%2!=0)
                postfix.pop_back();
            reverse(postfix.begin(), postfix.end());
            string c = to_string(i)+postfix;
            candidates.push_back(stol(c));
        }
        long mindiff = LONG_MAX;
        long result;
        long num = stol(n);
        for(int i=0;i<5;i++)
        {
            if(candidates[i]!=num && abs(candidates[i]-num)<mindiff)
            {
                mindiff = abs(candidates[i]-num);
                result = candidates[i];
            }
            else if(abs(candidates[i]-num)==mindiff)
                result = min(result, candidates[i]);
        }
        return to_string(result);
    }
};

ํ›„๊ธฐ

์ฒ˜์Œ์—๋Š” ๋นก๊ตฌํ˜„์œผ๋กœ ๋ธŒ๋ฃจํŠธํฌ์Šค ๋ฐฉ์‹์„ ๊ณ ์ง‘ํ•˜์˜€๋‹ค.
ํ•œ ์ž๋ฆฌ ํ•œ์ž๋ฆฌ ๋น„๊ตํ•ด๋ณด๋Š” ๋ฐฉ์‹์œผ๋กœ ๊ทธ๋ฆฌ๋”” ๋ฐฉ์‹๋„ ์ ‘๊ทผํ•ด๋ณผ๋ ค๊ณ  ํ–ˆ์ง€๋งŒ ๋„ˆ๋ฌด ์˜ˆ์™ธ ๋ฒ”์ฃผ๊ฐ€ ํด ๋ฟ๋”๋Ÿฌ ์—„๋‘๊ฐ€ ๋‚˜์ง€ ์•Š์•˜๋‹ค.
ํžŒํŠธ๋“ค์„ ์ฐธ๊ณ ํ•ด๋ณด์•˜์ง€๋งŒ ์–ด๋ ค์›€์ด ์—†์ž–์•„ ์žˆ์—ˆ์œผ๋ฉฐ ํŒฐ๋ฆฐ๋“œ๋กฌ ํŠน์„ฑ์„ ๊ฐ€์ง€๊ณ  ์ ‘๊ทผ์„ ์‹œ๋„ํ•˜์˜€์„๋•Œ๋Š” ๊ดœ์ฐฎ์•˜๋˜ ๊ฒƒ ๊ฐ™๋‹ค.

์ƒ๊ฐ์„ ๋งŽ์ด ํ•ด๋ณผ ์ˆ˜ ์žˆ๋Š” ๋ฌธ์ œ์ด๊ธฐ๋„ํ•˜๋ฉฐ ํ‰์†Œ ํŒฐ๋ฆฐ๋“œ๋กฌ์„ ์ž˜ ์ ‘ํ•˜์ง€ ์•Š๋‹ค๋ณด๋‹ˆ ์˜ค๋žœ๋งŒ์— ์žฌ๋ฏธ๋ฅผ ๋ณผ ์ˆ˜ ์žˆ์—ˆ๋˜ ๊ฒƒ ๊ฐ™๋‹ค.

๐Ÿ“š ์ƒˆ๋กญ๊ฒŒ ์•Œ๊ฒŒ๋œ ๋‚ด์šฉ

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