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@dohyeondol1 dohyeondol1 commented May 3, 2025

๐Ÿ”— ๋ฌธ์ œ ๋งํฌ

์†Œ์ˆ˜ ์ฐพ๊ธฐ

์ด๋ฒˆ ๋ฌธ์ œ ์—ญ์‹œ ์—ฌ๋Ÿฌ๋ถ„๋“ค์˜ ํ’€์ด๊ฐ€ ๊ถ๊ธˆํ•ฉ๋‹ˆ๋‹ค.
์ €๋ฒˆ ๋ฌธ์ œ๋ณด๋‹จ ์‹œ๊ฐ„์ด ์กฐ๊ธˆ ๋” ๊ฑธ๋ฆฌ๊ฒ ์ง€๋งŒ..! ํ’€์ด๋ฅผ ๊ณต์œ ํ•ด์ฃผ์„ธ์œ 

โœ”๏ธ ์†Œ์š”๋œ ์‹œ๊ฐ„

30๋ถ„

โœจ ์ˆ˜๋„ ์ฝ”๋“œ

์ฃผ์–ด์ง„ ๋ฌธ์ž์—ด์—์„œ ๊ฐ€๋Šฅํ•œ ๋ชจ๋“  ์ˆœ์—ด์„ ์ฐพ์•„์„œ ์†Œ์ˆ˜์ธ์ง€ ํŒ๋ณ„ํ•˜๋Š” ๊ฐ„๋‹จํ•œ ๋ฌธ์ œ์ž…๋‹ˆ๋‹ค.
์ตœ๊ทผ์— ์ดˆ์ˆœ์—ด์— ๋Œ€ํ•ด์„œ ๊ณต๋ถ€ํ•˜๋‹ค๊ฐ€ ๋ฐฐ์› ๋˜ ์ˆœ์—ด ๊ด€๋ จ ํ•จ์ˆ˜์ธ next_permutation์„ ์‚ฌ์šฉํ•ด ํ•ด๊ฒฐํ•˜์˜€์Šต๋‹ˆ๋‹ค.

next_permutation์€ ํ˜„์žฌ ๋‚˜์™€ ์žˆ๋Š” ์ˆ˜์—ด์—์„œ
์ธ์ž๋กœ ๋„˜์–ด๊ฐ„ ๋ฒ”์œ„์— ํ•ด๋‹นํ•˜๋Š” ๋‹ค์Œ ์ˆœ์—ด์„ ๊ตฌํ•˜๊ณ  true๋ฅผ ๋ฐ˜ํ™˜ํ•˜๋Š” ํ•จ์ˆ˜์ž…๋‹ˆ๋‹ค.
๋งŒ์•ฝ ๋‹ค์Œ ์ˆœ์—ด์ด ์—†๋‹ค๋ฉด(๋‹ค์Œ์— ๋‚˜์˜จ ์ˆœ์—ด์ด ์ˆœ์„œ์ƒ ์ด์ „ ์ˆœ์—ด๋ณด๋‹ค ์ž‘๋‹ค๋ฉด) false๋ฅผ ๋ฐ˜ํ™˜ํ•ฉ๋‹ˆ๋‹ค.

next_permutation(numbers.begin(), numbers.end())

์œ„์™€ ๊ฐ™์ด ์‚ฌ์šฉํ•œ๋‹ค๋ฉด numbers[0] ์˜ ๋‹ค์Œ ์ˆœ์—ด์„ ๊ตฌํ•˜๊ณ  true๋ฅผ ๋ฐ˜ํ™˜ํ•ฉ๋‹ˆ๋‹ค.
์ด ์ ์„ ํ™œ์šฉํ•ด ๋‹ค์Œ๊ณผ ๊ฐ™์ด ์‚ฌ์šฉํ•  ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.

do {
  for(int length = 1; length <= numbers.length(); length++) {
    int n = stoi(numbers.substr(0, length));
    numberSet.insert(n);
  }
} while(next_permutation(numbers.begin(), numbers.end()));

์ด๋ฅผ ํ†ตํ•ด ๋ชจ๋“  ์ข…์ด ์กฐ๊ฐ์„ ๊ตฌํ•  ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
์ด์ œ ์†Œ์ˆ˜๋ฅผ ํŒ๋ณ„ํ•˜๊ธฐ๋งŒ ํ•˜๋ฉด ๋ฉ๋‹ˆ๋‹ค.

์†Œ์ˆ˜๋Š” 1๋ณด๋‹ค ํฐ ์ž์—ฐ์ˆ˜ ์ค‘ ์•ฝ์ˆ˜๊ฐ€ 1๊ณผ ์ž๊ธฐ ์ž์‹  ๋ฟ์ธ ์นœ๊ตฌ์ด๊ธฐ ๋•Œ๋ฌธ์—,
2๋ถ€ํ„ฐ ์ฃผ์–ด์ง„ ์ˆ˜๋ฅผ ๋‚˜๋ˆ„์–ด๋ณด๋ฉด์„œ ํ•ด๋‹น ์ˆ˜๊ฐ€ ๋‚˜๋ˆ„์–ด ๋–จ์–ด์ง€๋Š” ์ง€ ํ™•์ธํ•˜๋ฉด ๋ฉ๋‹ˆ๋‹ค.

๊ทธ๋Ÿผ ์–ด๋””๊นŒ์ง€ ๋ฐ˜๋ณต๋ฌธ์„ ๋Œ๋ ค์•ผ ํ•˜๋А๋ƒ? ๊ทธ ๋ฒ”์œ„๊ฐ€ ์• ๋งคํ•œ๋ฐ,

์ฃผ์–ด์ง„ ์ˆ˜์˜ ์•ฝ์ˆ˜๋Š” ํ•ญ์ƒ ์ง์„ ์ด๋ฃฌ๋‹ค๋Š” ์ ์„ ์ด์šฉํ•ด์„œ,
์ฃผ์–ด์ง„ ์ˆ˜์˜ ์ œ๊ณฑ๊ทผ('์ œ๊ณฑ๊ทผ ร— ์ œ๊ณฑ๊ทผ = ํ•ด๋‹น ์ˆ˜' ์ด๊ธฐ ๋•Œ๋ฌธ์— ์•ฝ์ˆ˜์˜ ์ค‘๊ฐ„์— ์œ„์น˜ํ•ฉ๋‹ˆ๋‹ค.)๊นŒ์ง€๋งŒ ์‚ฌ์šฉํ•˜์—ฌ
์ฃผ์–ด์ง„ ์ˆ˜๋ฅผ ์•ฝ์ˆ˜์— ๋‚˜๋ˆ„๋ฉด ๋ฉ๋‹ˆ๋‹ค.

์‚ฌ์‹ค ์—๋ผํ† ์Šคํ…Œ๋„ค์Šค์˜ ์ฒด๋ฅผ ๊ตฌํ˜„ํ•ด์„œ ํ’€์–ด๋ณด๊ณ  ์‹ถ์—ˆ๋Š”๋ฐ,
์ด ๋ฌธ์ œ์—์„œ๊นŒ์ง„ ์“ธ ํ•„์š”๊ฐ€ ์—†์„ ๊ฒƒ ๊ฐ™์•„ ๋‚˜์ค‘์— ์ข€ ๋” ๋ฐฐ์›Œ์„œ ์จ๋จน์„ ์ƒ๊ฐ์ž…๋‹ˆ๋‹ค.

์ˆ˜๋„ ์ฝ”๋“œ
์†Œ์ˆ˜ ํŒ๋ณ„ํ•˜๋Š” ํ•จ์ˆ˜(๋งค๊ฐœ๋ณ€์ˆ˜๋กœ num์„ ๋ฐ›๋Š”๋‹ค) {
    ๋งŒ์•ฝ num์ด 2๋ณด๋‹ค ์ž‘๋‹ค๋ฉด 0, 1์€ ์†Œ์ˆ˜๊ฐ€ ์•„๋‹ˆ๋ฏ€๋กœ false๋ฅผ ๋ฐ˜ํ™˜
    i๋Š” 2๋ถ€ํ„ฐ num์˜ ์ œ๊ณฑ๊ทผ๊นŒ์ง€ ๋ฐ˜๋ณต:
        ๋งŒ์•ฝ num์ด i์— ๋‚˜๋ˆ„์–ด๋–จ์–ด์ง„๋‹ค๋ฉด ์†Œ์ˆ˜๊ฐ€ ์•„๋‹ˆ๋ฏ€๋กœ false๋ฅผ ๋ฐ˜ํ™˜
    ์œ„ ๊ฒฝ์šฐ๊ฐ€ ์•„๋‹ˆ๋ผ๋ฉด true๋ฅผ ๋ฐ˜ํ™˜
}

int solution(string numbers) {
    int answer = 0;
    numberSet์ด๋ผ๋Š” ์ง‘ํ•ฉ ์„ ์–ธ
    
    numbers์˜ ์ˆ˜ ์ •๋ ฌ
    ํ•œ๋ฒˆ ์‹คํ–‰ {
        i๋Š” 1๋ถ€ํ„ฐ number์˜ ๊ธธ์ด๋งŒํผ ๋ฐ˜๋ณต {
            numbers์—์„œ 0๋ถ€ํ„ฐ i๋งŒํผ์˜ ๊ธธ์ด๋ฅผ ์ •์ˆ˜ํ˜•์œผ๋กœ ๋ณ€ํ™˜ํ•˜์—ฌ n์— ์ €์žฅ;
            numberSet ์ง‘ํ•ฉ์— n ์‚ฝ์ž…
        }
    } ๋‹ค์Œ ์ˆœ์—ด์ด ์กด์žฌํ•œ๋‹ค๋ฉด ๊ณ„์† ๋ฐ˜๋ณต
    // ์ด ๊ณผ์ •์„ ์ž…์ถœ๋ ฅ ์˜ˆ "011"๋กœ ์„ค๋ช…ํ•œ๋‹ค๋ฉด ๋‹ค์Œ๊ณผ ๊ฐ™๋‹ค.
    // ๊ฐ€๋Šฅํ•œ ์ˆœ์—ด : 011, 101, 110
    // 0, 01(=1), 011(=11), 1, 10, 101, 1, 11, 110
    // set์€ ์ค‘๋ณต์„ ์ œ๊ฑฐํ•˜๋ฏ€๋กœ set์— ๋“ค์–ด๊ฐ„ n์€ 0, 1, 11, 10, 101, 110
    
    numberSet์„ ์ˆœํšŒํ•˜๋ฉด์„œ
        ์†Œ์ˆ˜๋ฅผ ํŒ๋ณ„ํ•˜๋Š” ํ•จ์ˆ˜๋ฅผ ์‹คํ–‰ํ•ด์„œ true๋ฅผ ๋ฐ˜ํ™˜ํ•˜๋ฉด answer++
    
    ์ •๋‹ต ๋ฐ˜ํ™˜
}

๐Ÿ“š ์ƒˆ๋กญ๊ฒŒ ์•Œ๊ฒŒ๋œ ๋‚ด์šฉ

- dohyeondol1๋กœ ์ „๋ถ€ ์•Œ๋งž๊ฒŒ ์ˆ˜์ •ํ•˜์˜€์Šต๋‹ˆ๋‹ค.
- ๋ฆฌ๋“œ๋ฏธ ์ž‘์„ฑํ•˜๋Š”๊ฑธ ์ž๊พธ ๊นœ๋ฐ•ํ•˜๋„ค์š”;;
@froglike6
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์ €๋Š” ํŒŒ์ด์ฌ์˜ itertools๊ฐ€ ๋จผ์ € ๋– ์˜ฌ๋ผ์„œ, ์ด๋ฅผ ํ™œ์šฉํ•ด์„œ ๋ฌธ์ œ๋ฅผ ํ’€์—ˆ์Šต๋‹ˆ๋‹ค. set์„ ์ด์šฉํ•ด์„œ ์ค‘๋ณต๋˜๋Š” ์ˆซ์ž(0์œผ๋กœ ์‹œ์ž‘ํ•˜๋Š” ์ˆซ์ž)๋ฅผ ์ œ๊ฑฐํ•˜๊ณ , ๋ฐ€๋Ÿฌ ๋ผ๋นˆ ์†Œ์ˆ˜ ํŒ๋ณ„๋ฒ•์„ ์‚ฌ์šฉํ–ˆ์Šต๋‹ˆ๋‹ค. ํ”„๋กœ๊ทธ๋ž˜๋จธ์Šค์—์„œ๋Š” ๋”ฐ๋กœ ๋ฉ”๋ชจ๋ฆฌ๋‚˜ ์‹œ๊ฐ„ ์ œํ•œ์ด ๋ณด์ด์ง€ ์•Š์•„์„œ, ํ˜น์‹œ ๋ชฐ๋ผ ๊ฐ€์žฅ ๋น ๋ฅธ ์•Œ๊ณ ๋ฆฌ์ฆ˜์„ ์‚ฌ์šฉํ–ˆ์Šต๋‹ˆ๋‹ค.

Python3

from itertools import permutations

def power(x, y, p):
    res = 1
    x = x % p
    while y > 0:
        if y & 1:
            res = (res * x) % p
        y = y >> 1
        x = (x*x) % p
    return res

def miller_rabin(n, a):
        r = 0
        d = n-1
        while d % 2 == 0:
            r += 1
            d = d//2

        x = power(a, d, n)
        if x == 1 or x == n-1:
            return True

        for i in range(r-1):
            x = power(x, 2, n)
            if x == n - 1:
                return True
        return False

def is_prime(n):
    prime_list = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
    if n == 1:
        return False
    if n == 2 or n == 3:
        return True
    if n % 2 == 0:
        return False
    for a in prime_list:
        if n == a:
            return True
        if not miller_rabin(n, a):
            return False
    return True

def solution(numbers):
    num_set = set()
    
    for i in range(1, len(numbers)+1):
        for p in permutations(numbers, i):
            num = int(''.join(p))
            num_set.add(num)
    
    prime_count = 0
    for num in num_set:
        if is_prime(num):
            prime_count += 1
    
    return prime_count

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@9kyo-hwang 9kyo-hwang left a comment

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next_permutation์„ ์‚ฌ์šฉํ•˜๋‹ˆ๊นŒ ํ™•์‹คํžˆ ์ฝ”๋“œ๊ฐ€ ๊น”๋”ํ•ด์ง€๋„ค์š” ํ—ˆ...
์ „ ์žฌ๊ท€๋กœ ์กฐํ•ฉ/์ˆœ์—ด์„ ๊ตฌํ˜„ํ•˜๋Š”๊ฒŒ ํŽธํ•˜๋‹ค ๋ณด๋‹ˆ ์ง์ ‘ ์ฝ”๋“œ๋ฅผ ์งœ๊ฒŒ ๋๋„ค์š”.

#include <string>
#include <vector>
#include <unordered_set>

using namespace std;

bool IsPrime(const string& CandidateNumberStr)
{
    int CandidateNumber = stoi(CandidateNumberStr);
    if(CandidateNumber < 2)
    {
        return false;
    }
    
    for(int Divisor = 2; Divisor * Divisor <= CandidateNumber; ++Divisor)
    {
        if(CandidateNumber % Divisor == 0)
        {
            return false;
        }
    }
    
    return true;
}

void Backtracking(const string& Numbers, vector<bool>& IsNumUsed, unordered_set<int>& PrimesSet, string CandidateNumber = "")
{
    if(!CandidateNumber.empty() && IsPrime(CandidateNumber))
    {
        PrimesSet.emplace(stoi(CandidateNumber));
    }
    
    for(int i = 0; i < Numbers.size(); ++i)
    {
        if(IsNumUsed[i]) continue;
        
        IsNumUsed[i] = true;
        Backtracking(Numbers, IsNumUsed, PrimesSet, CandidateNumber + Numbers[i]);
        IsNumUsed[i] = false;
    }
}

int solution(string InNumbers) 
{
    vector<bool> IsNumUsed(InNumbers.size(), false);
    unordered_set<int> PrimesSet;
    Backtracking(InNumbers, IsNumUsed, PrimesSet);
    return PrimesSet.size();
}

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numbers์—์„œ ๊ฐ ์ˆซ์ž๋กœ ์กฐํ•ฉํ•  ์ˆ˜ ์žˆ๋Š” ๋ชจ๋“  ์ˆ˜๋ฅผ ๋งŒ๋“  ํ›„์— ๊ฐ ์ˆ˜๋“ค์„ ์†Œ์ˆ˜ ํŒ๋ณ„ํ•˜๋ ค ํ–ˆ๋Š”๋ฐ, ์กฐํ•ฉํ•  ์ˆ˜ ์žˆ๋Š” ๋ชจ๋“  ์ˆ˜๋ฅผ ์–ด๋–ป๊ฒŒ ๋งŒ๋“ค์–ด์•ผ ํ• ์ง€.. ์ƒ๊ฐ์ด ์•ˆ ๋‚˜๋”๊ตฐ์š”!
์ฐพ์•„ ๋ณด๋‹ˆ ํŒŒ์ด์ฌ์—๋Š” permutations์ด๋ผ๋Š” ํ•จ์ˆ˜๊ฐ€ ์žˆ์–ด์„œ ์œ ์šฉํ•˜๊ฒŒ ์‚ฌ์šฉํ–ˆ์Šต๋‹ˆ๋‹ค.!
๋˜ ์†Œ์ˆ˜ ํŒ๋ณ„ ํ•  ๋•Œ ์ €๋Š” ์–ด๋–ค ์ˆ˜ n์„ 2~n-1๊นŒ์ง€ ๋‚˜๋ˆ ์„œ ๋‚˜๋จธ์ง€๊ฐ€ 0์ด ๋˜์ง€ ์•Š๋Š”๋‹ค๋ฉด ๊ทธ ์ˆ˜๋Š” ์†Œ์ˆ˜๋‹ค! ๋ผ๋Š” ์กฐ๊ฑด์œผ๋กœ ํŒ๋ณ„ํ–ˆ๋Š”๋ฐ, ๊ผญ n-1๊นŒ์ง€ ๋‚˜๋ˆŒ ํ•„์š” ์—†์ด ๋ฃจํŠธn ๊นŒ์ง€๋งŒ ๋‚˜๋ˆ ๋„ ๋œ ๋‹ค๋Š”๊ฑธ ์•Œ๊ฒŒ๋˜์—ˆ๋„ค์šฅ

ํŒŒ์ด์ฉ

from itertools import permutations

def solution(numbers):
    result = 0
    l_ist = []
    temp = True
    for i in range(1, len(numbers) + 1):
        for p in permutations(numbers, i):
            l_ist.append(int(''.join(p)))
    l_ist = list(set(l_ist))
    
    for k in range(2, int(l_ist[k] ** 0.5) + 1):
        if l_ist[k] < 2:
            continue
        nososu = False
        for j in range(2, l_ist[k]):
            if(l_ist[k] %j == 0):
                nososu = True
                
        if not nososu:
            result += 1
    return result

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์†Œ์ˆ˜ ๋ฌธ์ œ๋ฅผ ๋„ˆ๋ฌด ์˜ค๋žœ๋งŒ์— ๋ณด๋‹ˆ๊นŒ ์†Œ์ˆ˜ํŒ๋ณ„์„ ์–ด๋–ป๊ฒŒ ํ•˜๋Š”์ง€๋„ ๊ธฐ์–ต์ด ์•ˆ๋‚ฌ๋„ค์—ฌ...
int limit = (int)sqrt(n);
์†Œ์ˆ˜๋ฅผ ํŒ๋ณ„ํ•  ๋•Œ ๋ฃจํŠธ n๊นŒ์ง€ ํ•˜๋Š”๊ฒƒ๋„ ์˜ค๋žœ๋งŒ์— ๋ดค์Šด๋‹ค. ์ด๊ฑฐ ์•Œ์•„๋„ ๋ฌธ์ œ๋ฅผ ๋ชปํ’€๊ฒ ์–ด์„œ ์ฑ„์ฐํ”ผํ‹ฐ ์ฐธ๊ณ  ํ–ˆ์Šต๋‹ˆ๋‹ค... DFS๋กœ ํ‘ธ๋Š” ๋ฐฉ๋ฒ•๋„ ์žˆ๋„ค์š”! ์ˆ˜๊ฐ€ ๋งŽ์•„์ง€๋ฉด ์–ด๋–ป๊ฒŒ ๋‹ค ํŒ๋ณ„ํ•ด์•ผ ํ• ๊นŒ๊ฐ€ ๊ฐ€์žฅ ๋ง‰ํžˆ๋Š” ๋ถ€๋ถ„์ด ์—ˆ๋Š”๋ฐ int next = current * 10 + (numbers[i] - '0'); ์ด๋Ÿฐ์‹์œผ๋กœ ๋ชจ๋‘ ํŒ๋ณ„ํ•˜๋ ค ํ•œ๊ฒŒ ์ธ์ƒ๊นŠ์€ ๋ถ€๋ถ„์ธ ๊ฑฐ ๊ฐ™์•„์š”! ์ƒ์ƒ๋„ ๋ชปํ–ˆ์—ˆ๋„ค์š”. ์ค‘๋ณต๋˜๋Š” ๋ถ€๋ถ„์€ vistited๋กœ ์ฒ˜๋ฆฌํ•œ ๊ฒƒ๋„ ์ „ํ˜•์ ์ธ dfs๋ฌธ์ œ ๊ฐ™๋„ค์š”

์”จ

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <stdbool.h>

#define MAX_NUM 10000000  // 7์ž๋ฆฌ ์ˆซ์ž ์ตœ๋Œ€: 9,999,999

char numbers[8];         // ์ž…๋ ฅ๋œ ์ˆซ์ž ๋ฌธ์ž์—ด (์ตœ๋Œ€ 7์ž๋ฆฌ + '\0')
int  len;                // ๋ฌธ์ž์—ด ๊ธธ์ด
bool used[7];            // ๊ฐ ์ž๋ฆฌ ์‚ฌ์šฉ ์—ฌ๋ถ€ ํ‘œ์‹œ
bool visited[MAX_NUM];   // ์ด๋ฏธ ๊ฒ€์‚ฌํ•œ ์ˆซ์ž ์ค‘๋ณต ๋ฐฉ์ง€
int  prime_count = 0;    // ๋ฐœ๊ฒฌํ•œ ์†Œ์ˆ˜ ๊ฐœ์ˆ˜

// n์ด ์†Œ์ˆ˜์ธ์ง€ ํŒ๋ณ„
bool is_prime(int n) {
    if (n < 2) return false;
    int limit = (int)sqrt(n);
    for (int i = 2; i <= limit; i++) {
        if (n % i == 0) return false;
    }
    return true;
}

// ๊นŠ์ด ์šฐ์„  ํƒ์ƒ‰์œผ๋กœ ๊ฐ€๋Šฅํ•œ ๋ชจ๋“  ์ˆซ์ž ์กฐํ•ฉ ์ƒ์„ฑ
// current: ํ˜„์žฌ๊นŒ์ง€ ๋งŒ๋“ค์–ด์ง„ ์ˆ˜
void dfs(int current) {
    for (int i = 0; i < len; i++) {
        if (used[i]) continue;
        used[i] = true;
        int next = current * 10 + (numbers[i] - '0');
        if (!visited[next]) {
            visited[next] = true;
            if (is_prime(next)) {
                prime_count++;
            }
            // ๋” ๊ธด ์ˆซ์ž ์กฐํ•ฉ์„ ์œ„ํ•ด ์žฌ๊ท€ ํ˜ธ์ถœ
            dfs(next);
        }
        used[i] = false;
    }
}

int main(void) {
    // ์ž…๋ ฅ: ์ˆซ์ž๊ฐ€ ์ ํžŒ ์กฐ๊ฐ๋“ค (์˜ˆ: "011")
    if (scanf("%7s", numbers) != 1) return 0;
    len = strlen(numbers);

    // ์ดˆ๊ธฐํ™”
    memset(used,    0, sizeof(used));
    memset(visited, 0, sizeof(visited));
    prime_count = 0;

    // ๋ชจ๋“  ๊ธธ์ด(1~len)์˜ ์กฐํ•ฉ ์ƒ์„ฑ ์‹œ์ž‘
    dfs(0);

    // ๊ฒฐ๊ณผ ์ถœ๋ ฅ
    printf("%d\n", prime_count);
    return 0;
}

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