From e37b1b1544b8dab24b41dfa4c26fa0d07b0e71bb Mon Sep 17 00:00:00 2001 From: arthur Date: Tue, 11 Nov 2025 11:10:17 -0300 Subject: [PATCH] feat: added alternative solution and TLE solution to decode-ways problem, wrote the tutorial file and added some more manual test cases --- decode-ways/decode-ways-tutorial.pdf | Bin 0 -> 73477 bytes decode-ways/decode-ways-tutorial.tex | 51 +++++++++++++++++++++++++++ decode-ways/decode-ways.pdf | Bin 139713 -> 67071 bytes decode-ways/input/10 | 4 +-- decode-ways/input/100 | 4 +-- decode-ways/input/101 | 4 +-- decode-ways/input/102 | 4 +-- decode-ways/input/103 | 4 +-- decode-ways/input/104 | 4 +-- decode-ways/input/105 | 4 +-- decode-ways/input/106 | 4 +-- decode-ways/input/107 | 4 +-- decode-ways/input/108 | 2 ++ decode-ways/input/109 | 2 ++ decode-ways/input/11 | 4 +-- decode-ways/input/110 | 2 ++ decode-ways/input/12 | 4 +-- decode-ways/input/13 | 4 +-- decode-ways/input/15 | 4 +-- decode-ways/input/16 | 4 +-- decode-ways/input/17 | 4 +-- decode-ways/input/18 | 2 +- decode-ways/input/19 | 4 +-- decode-ways/input/20 | 4 +-- decode-ways/input/21 | 4 +-- decode-ways/input/22 | 2 +- decode-ways/input/23 | 4 +-- decode-ways/input/24 | 4 +-- decode-ways/input/25 | 2 +- decode-ways/input/26 | 4 +-- decode-ways/input/27 | 2 +- decode-ways/input/28 | 4 +-- decode-ways/input/29 | 4 +-- decode-ways/input/30 | 2 +- decode-ways/input/31 | 2 +- decode-ways/input/32 | 2 +- decode-ways/input/33 | 4 +-- decode-ways/input/34 | 4 +-- decode-ways/input/35 | 4 +-- decode-ways/input/36 | 4 +-- decode-ways/input/37 | 4 +-- decode-ways/input/38 | 4 +-- decode-ways/input/39 | 4 +-- decode-ways/input/40 | 4 +-- decode-ways/input/41 | 2 +- decode-ways/input/42 | 4 +-- decode-ways/input/43 | 4 +-- decode-ways/input/44 | 4 +-- decode-ways/input/45 | 4 +-- decode-ways/input/46 | 4 +-- decode-ways/input/47 | 4 +-- decode-ways/input/48 | 4 +-- decode-ways/input/49 | 4 +-- decode-ways/input/5 | 4 +-- decode-ways/input/50 | 4 +-- decode-ways/input/51 | 4 +-- decode-ways/input/52 | 4 +-- decode-ways/input/53 | 4 +-- decode-ways/input/54 | 4 +-- decode-ways/input/55 | 4 +-- decode-ways/input/56 | 4 +-- decode-ways/input/57 | 4 +-- decode-ways/input/58 | 4 +-- decode-ways/input/59 | 4 +-- decode-ways/input/6 | 4 +-- decode-ways/input/60 | 4 +-- decode-ways/input/61 | 4 +-- decode-ways/input/62 | 2 +- decode-ways/input/63 | 4 +-- decode-ways/input/64 | 4 +-- decode-ways/input/65 | 4 +-- decode-ways/input/66 | 4 +-- decode-ways/input/67 | 4 +-- decode-ways/input/68 | 4 +-- decode-ways/input/69 | 4 +-- decode-ways/input/7 | 4 +-- decode-ways/input/70 | 4 +-- decode-ways/input/71 | 4 +-- decode-ways/input/72 | 4 +-- decode-ways/input/73 | 4 +-- decode-ways/input/74 | 4 +-- decode-ways/input/75 | 4 +-- decode-ways/input/76 | 4 +-- decode-ways/input/77 | 4 +-- decode-ways/input/78 | 4 +-- decode-ways/input/79 | 4 +-- decode-ways/input/8 | 4 +-- decode-ways/input/80 | 4 +-- decode-ways/input/81 | 4 +-- decode-ways/input/82 | 4 +-- decode-ways/input/83 | 4 +-- decode-ways/input/84 | 4 +-- decode-ways/input/85 | 4 +-- decode-ways/input/86 | 4 +-- decode-ways/input/87 | 4 +-- decode-ways/input/88 | 4 +-- decode-ways/input/89 | 4 +-- decode-ways/input/9 | 4 +-- decode-ways/input/90 | 4 +-- decode-ways/input/91 | 4 +-- decode-ways/input/92 | 4 +-- decode-ways/input/93 | 4 +-- decode-ways/input/94 | 4 +-- decode-ways/input/95 | 4 +-- decode-ways/input/96 | 4 +-- decode-ways/input/97 | 4 +-- decode-ways/input/98 | 4 +-- decode-ways/input/99 | 4 +-- decode-ways/output/100 | 2 +- decode-ways/output/101 | 2 +- decode-ways/output/102 | 2 +- decode-ways/output/103 | 2 +- decode-ways/output/104 | 2 +- decode-ways/output/105 | 2 +- decode-ways/output/106 | 2 +- decode-ways/output/107 | 2 +- decode-ways/output/108 | 1 + decode-ways/output/109 | 1 + decode-ways/output/110 | 1 + decode-ways/output/12 | 2 +- decode-ways/output/13 | 2 +- decode-ways/output/15 | 2 +- decode-ways/output/16 | 2 +- decode-ways/output/17 | 2 +- decode-ways/output/19 | 2 +- decode-ways/output/20 | 2 +- decode-ways/output/25 | 2 +- decode-ways/output/29 | 2 +- decode-ways/output/32 | 2 +- decode-ways/output/33 | 2 +- decode-ways/output/34 | 2 +- decode-ways/output/36 | 2 +- decode-ways/output/39 | 2 +- decode-ways/output/40 | 2 +- decode-ways/output/41 | 2 +- decode-ways/output/42 | 2 +- decode-ways/output/43 | 2 +- decode-ways/output/45 | 2 +- decode-ways/output/46 | 2 +- decode-ways/output/47 | 2 +- decode-ways/output/48 | 2 +- decode-ways/output/5 | 2 +- decode-ways/output/50 | 2 +- decode-ways/output/51 | 2 +- decode-ways/output/52 | 2 +- decode-ways/output/53 | 2 +- decode-ways/output/54 | 2 +- decode-ways/output/55 | 2 +- decode-ways/output/56 | 2 +- decode-ways/output/57 | 2 +- decode-ways/output/58 | 2 +- decode-ways/output/59 | 2 +- decode-ways/output/6 | 2 +- decode-ways/output/60 | 2 +- decode-ways/output/61 | 2 +- decode-ways/output/62 | 2 +- decode-ways/output/63 | 2 +- decode-ways/output/64 | 2 +- decode-ways/output/65 | 2 +- decode-ways/output/66 | 2 +- decode-ways/output/67 | 2 +- decode-ways/output/68 | 2 +- decode-ways/output/69 | 2 +- decode-ways/output/7 | 2 +- decode-ways/output/70 | 2 +- decode-ways/output/71 | 2 +- decode-ways/output/72 | 2 +- decode-ways/output/73 | 2 +- decode-ways/output/74 | 2 +- decode-ways/output/75 | 2 +- decode-ways/output/76 | 2 +- decode-ways/output/77 | 2 +- decode-ways/output/78 | 2 +- decode-ways/output/79 | 2 +- decode-ways/output/8 | 2 +- decode-ways/output/80 | 2 +- decode-ways/output/81 | 2 +- decode-ways/output/82 | 2 +- decode-ways/output/83 | 2 +- decode-ways/output/84 | 2 +- decode-ways/output/85 | 2 +- decode-ways/output/86 | 2 +- decode-ways/output/87 | 2 +- decode-ways/output/88 | 2 +- decode-ways/output/89 | 2 +- decode-ways/output/90 | 2 +- decode-ways/output/91 | 2 +- decode-ways/output/92 | 2 +- decode-ways/output/93 | 2 +- decode-ways/output/94 | 2 +- decode-ways/output/95 | 2 +- decode-ways/output/96 | 2 +- decode-ways/output/97 | 2 +- decode-ways/output/98 | 2 +- decode-ways/output/99 | 2 +- decode-ways/problem.json | 4 +-- decode-ways/src/TLE.cpp | 40 +++++++++++++++++++++ decode-ways/src/alternative_ac.cpp | 45 +++++++++++++++++++++++ decode-ways/src/generator.cpp | 3 ++ decode-ways/statement/tutorial.tex | 37 +++++++++++++++++++ 200 files changed, 466 insertions(+), 281 deletions(-) create mode 100644 decode-ways/decode-ways-tutorial.pdf create mode 100644 decode-ways/decode-ways-tutorial.tex create mode 100644 decode-ways/input/108 create mode 100644 decode-ways/input/109 create mode 100644 decode-ways/input/110 create mode 100644 decode-ways/output/108 create mode 100644 decode-ways/output/109 create mode 100644 decode-ways/output/110 create mode 100644 decode-ways/src/TLE.cpp create mode 100644 decode-ways/src/alternative_ac.cpp diff --git a/decode-ways/decode-ways-tutorial.pdf b/decode-ways/decode-ways-tutorial.pdf new file mode 100644 index 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+\begin{document} +\maketitle +O problema pode ser resolvido utilizando uma abordagem de \textbf{programação dinâmica}, na qual calculamos, passo a passo, o número de formas possíveis de decodificar a sequência até cada posição. + +A ideia é que cada dígito (ou par de dígitos consecutivos) da sequência pode representar uma letra do alfabeto latino, desde que o valor correspondente esteja entre $1$ e $26$. Assim, precisamos contar todas as maneiras válidas de interpretar a sequência numérica. + +Definimos uma estrutura de DP com dois estados para cada posição $i$: +\begin{itemize} + \item $dp[i][0]$: número de mensagens possíveis terminando no caractere $i$ \textbf{quando o dígito atual não é concatenado} com o anterior; + \item $dp[i][1]$: número de mensagens possíveis terminando no caractere $i$ \textbf{quando o dígito atual é concatenado} com o anterior. +\end{itemize} + +A transição entre os estados é definida da seguinte forma: +\begin{itemize} + \item Se o dígito atual $s[i]$ está entre $1$ e $9$, ele pode ser interpretado como uma letra individual. Logo: + \[ + dp[i][0] = dp[i - 1][0] + dp[i - 1][1] + \] + \item Se a combinação dos dois últimos dígitos $s[i-1]s[i]$ forma um número entre $10$ e $26$, então esses dois dígitos podem ser interpretados como uma única letra: + \[ + dp[i][1] = dp[i - 2][0] + dp[i - 2][1] + \] +\end{itemize} + +A base da recorrência é: +\[ +dp[0][0] = 1, \quad dp[0][1] = 0, \quad dp[1][0] = 1, \quad dp[1][1] = 0 +\] +pois antes de processar qualquer caractere há exatamente uma maneira “vazia” de formar uma mensagem válida, e o primeiro dígito pode, no máximo, representar uma única letra isolada. + +O resultado final é dado pela soma: + +\[ +dp[n][0] + dp[n][1] +\] + +onde $n$ é o comprimento da sequência de entrada. + +Essa solução possui complexidade de tempo e espaço $O(n)$, podendo ser otimizada para $O(1)$ espaço se armazenarmos apenas os últimos dois estados necessários para o cálculo. +\end{document} diff --git a/decode-ways/decode-ways.pdf b/decode-ways/decode-ways.pdf index 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z{O)I2o@pmX=e?(siw9@(!E}CK@!aa(4es8*Td$(1>!acIaK5HlbXLDA>SpvarmzX+ z$pAa~)AVl#_7HLj~>0Jp9wv` z>Bf&Q=0j|r%K-mBe9IL7lMy5nlZhz|mIDD5e>N~(3NKS>dSxIsFbXeMAX_mYGaxZt z3NKP`Z*(9vHy|(|QVK6gZf0*FH8>zJAW{l1Nkkx9JUKH(I59CsFhw;+GDR^%Ha0gh zLoqf(L_$F~GBPCkMKwk;MKMD*Ha9XuF*ZX)LP0k&GC4ChK3xhg zlfExAe;v;~Y64Ld#qo3AOmvb_N1aUkh~Ek}Hq*NWTT2VU#wtay%@$&jC1f>e0ygPg zfFM{{1byc=KmL!)GzMt=TUy^yCR z$n(l`*?X=V&wtZ@8b6-!!xQD6_-Gp=F%}cL + +typedef long long ll; +using namespace std; + +int ways(string &s, int n, int idx = 0) +{ + if (idx > n) + return 1; + if (s[idx] == '0') + return 0; + + int count = ways(s, n, idx + 1); + if (idx + 1 < n) + { + int num = stoi(s.substr(idx, 2)); + if (num >= 10 && num <= 26) + count += ways(s, n, idx + 2); + } + + return count; +} + +vector used; +int numDecodings(string &s) +{ + int n = (int)s.size(); + used.resize(n, false); + return ways(s, n); +} + +int main() +{ + int n; + cin >> n; + string code; + cin >> code; + cout << numDecodings(code) << endl; + return 0; +} \ No newline at end of file diff --git a/decode-ways/src/alternative_ac.cpp b/decode-ways/src/alternative_ac.cpp new file mode 100644 index 0000000..ed6c711 --- /dev/null +++ b/decode-ways/src/alternative_ac.cpp @@ -0,0 +1,45 @@ +#include + +typedef long long ll; +using namespace std; + +ll numDecodings(string s) +{ + if (s[0] == '0') + return 0; + + int N = s.size(); + ll dp1 = 1, dp2 = 1; + for (int i = 2; i <= N; i++) + { + ll next = 0; + char current = s[i - 1], last = s[i - 2]; + string aux = ""; + aux += last; + aux += current; + if (current != '0') + { + next = dp2; + } + + int code = stoi(aux); + if (10 <= code && code <= 26) + { + next += dp1; + } + swap(dp1, dp2); + swap(dp2, next); + } + + return dp2; +} + +int main() +{ + int n; + cin >> n; + string code; + cin >> code; + cout << numDecodings(code) << endl; + return 0; +} \ No newline at end of file diff --git a/decode-ways/src/generator.cpp b/decode-ways/src/generator.cpp index e2b6f5b..e47a844 100644 --- a/decode-ways/src/generator.cpp +++ b/decode-ways/src/generator.cpp @@ -30,6 +30,9 @@ vector generate_sample_tests() { vector generate_manual_tests() { vector tests; tests.push_back(output_tc("101010101010")); + tests.push_back(output_tc("11111111111111111111")); + tests.push_back(output_tc("111111111111111111111111111111111111111111111")); + tests.push_back(output_tc("111111111111111111111000000000000000000000000")); tests.push_back(output_tc("123456789")); return tests; } diff --git a/decode-ways/statement/tutorial.tex b/decode-ways/statement/tutorial.tex index e69de29..fe2dc74 100644 --- a/decode-ways/statement/tutorial.tex +++ b/decode-ways/statement/tutorial.tex @@ -0,0 +1,37 @@ +O problema pode ser resolvido utilizando uma abordagem de \textbf{programação dinâmica}, na qual calculamos, passo a passo, o número de formas possíveis de decodificar a sequência até cada posição. + +A ideia é que cada dígito (ou par de dígitos consecutivos) da sequência pode representar uma letra do alfabeto latino, desde que o valor correspondente esteja entre $1$ e $26$. Assim, precisamos contar todas as maneiras válidas de interpretar a sequência numérica. + +Definimos uma estrutura de DP com dois estados para cada posição $i$: +\begin{itemize} + \item $dp[i][0]$: número de mensagens possíveis terminando no caractere $i$ \textbf{quando o dígito atual não é concatenado} com o anterior; + \item $dp[i][1]$: número de mensagens possíveis terminando no caractere $i$ \textbf{quando o dígito atual é concatenado} com o anterior. +\end{itemize} + +A transição entre os estados é definida da seguinte forma: +\begin{itemize} + \item Se o dígito atual $s[i]$ está entre $1$ e $9$, ele pode ser interpretado como uma letra individual. Logo: + \[ + dp[i][0] = dp[i - 1][0] + dp[i - 1][1] + \] + \item Se a combinação dos dois últimos dígitos $s[i-1]s[i]$ forma um número entre $10$ e $26$, então esses dois dígitos podem ser interpretados como uma única letra: + \[ + dp[i][1] = dp[i - 2][0] + dp[i - 2][1] + \] +\end{itemize} + +A base da recorrência é: +\[ +dp[0][0] = 1, \quad dp[0][1] = 0, \quad dp[1][0] = 1, \quad dp[1][1] = 0 +\] +pois antes de processar qualquer caractere há exatamente uma maneira “vazia” de formar uma mensagem válida, e o primeiro dígito pode, no máximo, representar uma única letra isolada. + +O resultado final é dado pela soma: + +\[ +dp[n][0] + dp[n][1] +\] + +onde $n$ é o comprimento da sequência de entrada. + +Essa solução possui complexidade de tempo e espaço $O(n)$, podendo ser otimizada para $O(1)$ espaço se armazenarmos apenas os últimos dois estados necessários para o cálculo.