μ‹œλ¦¬μ¦ˆ

🍎2661번: μ’‹μ€μˆ˜μ—΄

20161019
BOJ
PS

(뭐가 μ’‹λ‹€λŠ” κ±΄μ§€λŠ” λͺ¨λ₯΄κ² μ§€λ§Œ)

문제λ₯Ό 읽어보면 λ°±νŠΈλž˜ν‚Ήμ„ ν•˜λ©΄ 100% ν’€λ¦°λ‹€λŠ” 것은 ν™•μ‹€ν•˜μ§€λ§Œ N = 80 이라
κ·Έλƒ₯ μ†μœΌλ‘œ 해보고 μ‹Άλ‹€λŠ” 생각이 λ“ λ‹€.


두 가지 쑰건을 만쑱 μ‹œμΌœμ•Ό ν•œλ‹€. 

1. μΈμ ‘ν•œ 두 개의 μˆ˜μ—΄μ΄ 같지 μ•ŠμœΌλ©΄μ„œ 
2. μ •μˆ˜λ‘œ λ‚˜νƒ€λƒˆμ„ λ•Œ κ°€μž₯ μˆ˜κ°€ μž‘λ„λ‘ λ§Œλ“€μ–΄ μ£Όμ–΄μ•Όν•œλ‹€.

2번 쑰건을 μœ„ν•΄μ„œλŠ” μ•žμͺ½μ— μž‘μ€ μˆ˜κ°€ μ˜€λ„λ‘ ν•΄μ•Ό ν•œλ‹€.

λ”°λΌμ„œ 길이가 i인 κ°€μž₯ μž‘μ€ 쒋은 μˆ˜μ—΄μ„ S(i) 라고 ν•˜λ©΄

S(1) = 1 이닀.

i = 2μΌλ•Œμ—λŠ” 1번 쑰건에 μ˜ν•΄ 11은 될 수 μ—†κ³  κ·Έ λ‹€μŒ μž‘μ€ 수인 12κ°€ λœλ‹€.

κ³„μ†ν•΄μ„œ S(i-1) 의 맨 뒀에 1 2 3 μˆœμ„œλŒ€λ‘œ λ„£μ–΄λ³΄λ©΄μ„œ 1. 2. 번 쑰건을 만쑱 μ‹œν‚€λŠ” 수λ₯Ό 찾으면 μ’‹μ€μˆ˜μ—΄μ„ 계속 μ°Ύμ•„λ‚˜κ°ˆ 수 μžˆλ‹€. 
S(2) = 12
S(3) = 121
S(4) = 1213
S(5) = 12131
S(6) = 121312
S(7) = 1213121

이 방법은 i = 8 μΌλ•Œ λ§‰νžˆκ²Œ λ˜λŠ”λ° 
12131211 12131212  12131213 λͺ¨λ‘ 1번 쑰건을 λ§Œμ‘±μ‹œν‚€μ§€ λͺ»ν•œλ‹€.

μ—¬κΈ°μ„œ λ§‰λ§‰ν•˜μ§€λ§Œ μ°¨κ·Όμ°¨κ·Ό λŒμ•„κ°€μ„œ 생각해보면
i = 7 μΌλ•Œ 1213121 λŒ€μ‹  1213123 이 κ°€λŠ₯함을 μ•Œ 수 μžˆλ‹€.
λ”°λΌμ„œ 
S(8) = 1213123 1
S(9) = 1213123 12
S(10) = 1213123 121
S(11) = 1213123 1213
S(12) = 1213123 12131
S(13) = 1213123 121312
S(14) = 1213123 1213121

i = 15 일 λ•Œ μ•„κΉŒμ™€ λ§ˆμ°¬κ°€μ§€λ‘œ

S(15) = 1213123 1213123 1 을 ν•˜κ²Œ 되면 또 1번 쑰건을 λ§Œμ‘±μ‹œν‚€μ§€ λͺ»ν•œλ‹€.

........
.......

μ—¬κΈ°κΉŒμ§€λ§Œ ν•˜μž.
μ—¬κΈ°μ„œ κ·œμΉ™μ°ΎκΈ°λ₯Ό ν¬κΈ°ν•˜κ³  λ°±νŠΈλž˜ν‚Ήμ„ ν•˜κΈ°λ‘œ 결심.


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#include <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;
int n,a['ae'];
void dfs(int here)
{
    for(int i = 1; i <= here/2 ; i++)
    {
        if(equal(a+here-i, a+here, a+here-i-i)) return;
    }
    if(here == n)
    {
        for(int i =  0; i < n ; i++)
            cout<<a[i];
        cout<<'\n';
        exit(0);
    }
    for(int candi = 1 ; candi <= 3; candi++)
    {
        a[here] = candi;
        dfs(here+1);
    }
}
int main()
{
    cin>>n;
    dfs(0);
    return 0;
}

equal(f1, l1, f2)λŠ” f1κ°€ l1κΉŒμ§€ μ¦κ°€ν•˜λŠ” λ™μ•ˆ f2도 증가할 λ•Œ f1, f2κ°€ 가리킨 두 μˆ˜μ—΄μ΄ 같은지 μ—¬λΆ€λ₯Ό λ¦¬ν„΄ν•œλ‹€.

μ΄μƒν•˜κ²Œ equalλ‘œλŠ” μž˜λ˜λŠ”λ° strncmp둜 ν’€λ €κ³  ν•˜λ©΄ WAκ°€ λ‚˜μ˜¨λ‹€.
Upsolving이 ν•„μš”ν•œ 문제

.

piano (press key Q)

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