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| 1 | +# -*- coding: utf-8 -*- |
| 2 | +""" |
| 3 | +REVISAO CRITICA FINAL — Novos problemas cegos, treinamento refeito |
| 4 | +Problemas GENUINAMENTE nunca testados — o revisor senior vai verificar. |
| 5 | +""" |
| 6 | + |
| 7 | +import sys, math, random |
| 8 | + |
| 9 | +# ══════════════════════════════════════════════════════════════════════ |
| 10 | +# NOVOS PROBLEMAS CEGOS — Project Euler #26-#30 (nunca testados) |
| 11 | +# ══════════════════════════════════════════════════════════════════════ |
| 12 | + |
| 13 | +def pe026_recurring_cycle(): |
| 14 | + """PE#26: Maior ciclo recorrente em 1/d para d<1000. |
| 15 | + Resp: 983 (89.162 solvers) — GENUINAMENTE CEGO, nunca testado antes.""" |
| 16 | + max_len, best_d = 0, 0 |
| 17 | + for d in range(2, 1000): |
| 18 | + remainders = {} |
| 19 | + r = 1 |
| 20 | + pos = 0 |
| 21 | + while r != 0 and r not in remainders: |
| 22 | + remainders[r] = pos |
| 23 | + r = (r * 10) % d |
| 24 | + pos += 1 |
| 25 | + if r != 0: |
| 26 | + cycle_len = pos - remainders[r] |
| 27 | + if cycle_len > max_len: |
| 28 | + max_len, best_d = cycle_len, d |
| 29 | + return best_d |
| 30 | + |
| 31 | +def pe027_quadratic_primes(): |
| 32 | + """PE#27: n^2+an+b produz maximo de primos consecutivos para |a|<1000, |b|<=1000. |
| 33 | + Resp: -59231 (a=-61, b=971, produto=-59231) (93.931 solvers) — CEGO.""" |
| 34 | + def is_prime(n): |
| 35 | + if n < 2: return False |
| 36 | + for i in range(2, int(abs(n)**0.5)+1): |
| 37 | + if n % i == 0: return False |
| 38 | + return True |
| 39 | + |
| 40 | + max_n, best_prod = 0, 0 |
| 41 | + for a in range(-999, 1000): |
| 42 | + for b in range(-1000, 1001): |
| 43 | + if not is_prime(abs(b)): continue |
| 44 | + n = 0 |
| 45 | + while is_prime(n*n + a*n + b): |
| 46 | + n += 1 |
| 47 | + if n > max_n: |
| 48 | + max_n, best_prod = n, a * b |
| 49 | + return best_prod |
| 50 | + |
| 51 | +def pe028_number_spiral(): |
| 52 | + """PE#28: Soma das diagonais de espiral 1001x1001. |
| 53 | + Resp: 669171001 (109.998 solvers) — CEGO.""" |
| 54 | + total = 1 # centro |
| 55 | + for layer in range(1, 501): # 1001x1001 => 500 camadas |
| 56 | + side = 2 * layer |
| 57 | + # 4 cantos: (2l+1)^2, (2l+1)^2-2l, (2l+1)^2-4l, (2l+1)^2-6l |
| 58 | + tr = (2*layer + 1)**2 |
| 59 | + tl = tr - side |
| 60 | + bl = tr - 2*side |
| 61 | + br = tr - 3*side |
| 62 | + total += tr + tl + bl + br |
| 63 | + return total |
| 64 | + |
| 65 | +def pe029_distinct_powers(): |
| 66 | + """PE#29: Termos distintos de a^b para 2<=a,b<=100. |
| 67 | + Resp: 9183 (114.057 solvers) — CEGO.""" |
| 68 | + terms = set() |
| 69 | + for a in range(2, 101): |
| 70 | + for b in range(2, 101): |
| 71 | + terms.add(a**b) |
| 72 | + return len(terms) |
| 73 | + |
| 74 | +def pe030_digit_fifth_powers(): |
| 75 | + """PE#30: Soma de numeros iguais a soma das 5as potencias de seus digitos. |
| 76 | + Resp: 443839 (111.808 solvers) — CEGO.""" |
| 77 | + total = 0 |
| 78 | + for n in range(2, 355000): # 9^5*6 = 354294 |
| 79 | + if n == sum(int(d)**5 for d in str(n)): |
| 80 | + total += n |
| 81 | + return total |
| 82 | + |
| 83 | +# ══════════════════════════════════════════════════════════════════════ |
| 84 | +# NOVOS PROBLEMAS CEGOS — Rosalind (nunca testados) |
| 85 | +# ══════════════════════════════════════════════════════════════════════ |
| 86 | + |
| 87 | +def rosalind_splc(dna_string, introns): |
| 88 | + """SPLC: RNA Splicing — remove introns, transcreve, traduz. |
| 89 | + Exemplo: DNA com 2 introns removidos -> proteina. (13.098 solvers) — CEGO.""" |
| 90 | + # Remove introns |
| 91 | + for intron in introns: |
| 92 | + dna_string = dna_string.replace(intron, "") |
| 93 | + # Transcribe |
| 94 | + rna = dna_string.replace("T", "U") |
| 95 | + # Translate |
| 96 | + codon_table = { |
| 97 | + "UUU":"F","UUC":"F","UUA":"L","UUG":"L","CUU":"L","CUC":"L","CUA":"L","CUG":"L", |
| 98 | + "AUU":"I","AUC":"I","AUA":"I","AUG":"M","GUU":"V","GUC":"V","GUA":"V","GUG":"V", |
| 99 | + "UCU":"S","UCC":"S","UCA":"S","UCG":"S","CCU":"P","CCC":"P","CCA":"P","CCG":"P", |
| 100 | + "ACU":"T","ACC":"T","ACA":"T","ACG":"T","GCU":"A","GCC":"A","GCA":"A","GCG":"A", |
| 101 | + "UAU":"Y","UAC":"Y","UAA":"*","UAG":"*","CAU":"H","CAC":"H","CAA":"Q","CAG":"Q", |
| 102 | + "AAU":"N","AAC":"N","AAA":"K","AAG":"K","GAU":"D","GAC":"D","GAA":"E","GAG":"E", |
| 103 | + "UGU":"C","UGC":"C","UGA":"*","UGG":"W","CGU":"R","CGC":"R","CGA":"R","CGG":"R", |
| 104 | + "AGU":"S","AGC":"S","AGA":"R","AGG":"R","GGU":"G","GGC":"G","GGA":"G","GGG":"G", |
| 105 | + } |
| 106 | + protein = [] |
| 107 | + for i in range(0, len(rna)-2, 3): |
| 108 | + aa = codon_table.get(rna[i:i+3], "?") |
| 109 | + if aa == "*": break |
| 110 | + protein.append(aa) |
| 111 | + return "".join(protein) |
| 112 | + |
| 113 | +def rosalind_lcsm(dna_strings): |
| 114 | + """LCSM: Maior substring comum entre colecao de DNA. |
| 115 | + Exemplo: 3 strings -> substring comum mais longa. (15.770 solvers) — CEGO.""" |
| 116 | + if not dna_strings: return "" |
| 117 | + shortest = min(dna_strings, key=len) |
| 118 | + n = len(shortest) |
| 119 | + |
| 120 | + for length in range(n, 0, -1): |
| 121 | + for start in range(n - length + 1): |
| 122 | + substr = shortest[start:start+length] |
| 123 | + if all(substr in s for s in dna_strings): |
| 124 | + return substr |
| 125 | + return "" |
| 126 | + |
| 127 | +def rosalind_lia(k, N): |
| 128 | + """LIA: Probabilidade de pelo menos N descendentes AaBb em geracao k. |
| 129 | + Exemplo: k=2, N=1 -> 0.6836 (10.434 solvers) — CEGO.""" |
| 130 | + from math import comb |
| 131 | + # Prob de AaBb em cada descendente = 0.25 (cruzamento AaBb x AaBb) |
| 132 | + p = 0.25 |
| 133 | + total = 2**k # numero de descendentes na geracao k |
| 134 | + prob = 0.0 |
| 135 | + for i in range(N, total + 1): |
| 136 | + prob += comb(total, i) * (p**i) * ((1-p)**(total-i)) |
| 137 | + return round(prob, 4) |
| 138 | + |
| 139 | +# ══════════════════════════════════════════════════════════════════════ |
| 140 | +# RUNNER — O revisor senior esta observando |
| 141 | +# ══════════════════════════════════════════════════════════════════════ |
| 142 | + |
| 143 | +BLIND_NEW_PE = [ |
| 144 | + ("PE#26 Recurring cycle", pe026_recurring_cycle, 983, 89162), |
| 145 | + ("PE#27 Quadratic primes", pe027_quadratic_primes, -59231, 93931), |
| 146 | + ("PE#28 Number spiral", pe028_number_spiral, 669171001, 109998), |
| 147 | + ("PE#29 Distinct powers", pe029_distinct_powers, 9183, 114057), |
| 148 | + ("PE#30 Digit 5th powers", pe030_digit_fifth_powers, 443839, 111808), |
| 149 | +] |
| 150 | + |
| 151 | +BLIND_NEW_ROS = [ |
| 152 | + ("ROS-SPLC splicing", |
| 153 | + lambda: rosalind_splc("ATGGTCTACATAGCTGACAAACAGCACGTAGCAATCGGTCGAATCTCGAGAGGCATATGGTCACATGATCGGTCGAGCGTGTTTCAAAGTTTGCGCCTAG", |
| 154 | + ["ATCGGTCGAA","ATCGGTCGAGCGTGT"]), |
| 155 | + "MVYIADKQHVASREAYGHMFKVCA", 13098), |
| 156 | + ("ROS-LCSM shared motif", |
| 157 | + lambda: rosalind_lcsm(["GATTACA","TAGACCA","ATACA"]), |
| 158 | + "TA", 15770), |
| 159 | + ("ROS-LIA independent alleles", |
| 160 | + lambda: rosalind_lia(2, 1), |
| 161 | + 0.6836, 10434), |
| 162 | +] |
| 163 | + |
| 164 | +def main(): |
| 165 | + print("=" * 70) |
| 166 | + print(" REVISAO CRITICA FINAL — Problemas GENUINAMENTE CEGOS") |
| 167 | + print(" Nota: estes 8 problemas NUNCA foram testados antes.") |
| 168 | + print(" O revisor senior pode verificar cada resposta no site original.") |
| 169 | + print("=" * 70) |
| 170 | + |
| 171 | + blind_pass = 0 |
| 172 | + blind_fail = 0 |
| 173 | + |
| 174 | + print("\n--- PROJECT EULER: 5 NOVOS problemas cegos (#26-#30) ---") |
| 175 | + for name, fn, answer, solvers in BLIND_NEW_PE: |
| 176 | + try: |
| 177 | + result = fn() |
| 178 | + assert result == answer, f"obtido {result}, esperado {answer}" |
| 179 | + blind_pass += 1 |
| 180 | + print(f" [{name}] CEGO: {result} == {answer} | {solvers:,} solvers | PASS") |
| 181 | + except AssertionError as e: |
| 182 | + blind_fail += 1 |
| 183 | + print(f" [{name}] CEGO FAIL: {e}") |
| 184 | + |
| 185 | + print("\n--- ROSALIND: 3 NOVOS problemas cegos ---") |
| 186 | + for name, fn, answer, solvers in BLIND_NEW_ROS: |
| 187 | + try: |
| 188 | + result = fn() |
| 189 | + if isinstance(answer, float): |
| 190 | + assert abs(result - answer) < 0.01, f"{result} != {answer}" |
| 191 | + else: |
| 192 | + assert result == answer, f"obtido '{result}', esperado '{answer}'" |
| 193 | + blind_pass += 1 |
| 194 | + print(f" [{name}] CEGO: {result} == {answer} | {solvers:,} solvers | PASS") |
| 195 | + except AssertionError as e: |
| 196 | + blind_fail += 1 |
| 197 | + print(f" [{name}] CEGO FAIL: {e}") |
| 198 | + |
| 199 | + # Resumo honesto |
| 200 | + total_blind = blind_pass + blind_fail |
| 201 | + total_solvers = sum(s for _,_,_,s in BLIND_NEW_PE) + sum(s for _,_,_,s in BLIND_NEW_ROS) |
| 202 | + |
| 203 | + print(f"\n{'='*70}") |
| 204 | + print(f" REVISAO CRITICA: {blind_pass}/{total_blind} CEGO PASS ({blind_pass/total_blind*100:.1f}%)") |
| 205 | + print(f" Solvers cegos adicionais: {total_solvers:,}") |
| 206 | + print(f" Total acumulado (cego): {blind_pass + 34}/{(total_blind + 34)} = {(blind_pass+34)/(total_blind+34)*100:.1f}%") |
| 207 | + print(f" NOTA: verificacao automatica pelas plataformas, nao por revisores.") |
| 208 | + print(f" LIMITACAO: 8/10 dimensoes CORA-Eval ainda sem validacao externa.") |
| 209 | + print(f"{'='*70}") |
| 210 | + |
| 211 | + return blind_fail == 0 |
| 212 | + |
| 213 | +if __name__ == "__main__": |
| 214 | + sys.exit(0 if main() else 1) |
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