本次记录的题目是:4, 8, 9, 11, 12, 14, 29, 34, 35, 36。
4.
C++: #include <iostream> #include <stdlib.h> using namespace std; bool is_palindromic(int number){ static char index[]="0123456789"; char str[6] = {NULL}; int i = 0; do{ str[i++] = index[number%(unsigned)10]; number /= 10; } while(number); for (int t = 0; t < i / 2; t++) if (str[t] != str[i - t - 1]) return false; return true; } int main(int argc, const char * argv[]) { int * palindromic = (int *)malloc(sizeof(int) * 10000); int x = 0; for (int i = 999; i >= 100; i--) { for (int t = 999; t >= 100; t--) { if (is_palindromic(i*t)) { palindromic[x] = i*t; x++; } } } qsort_b((void *)palindromic, x, sizeof(int), ^int(const void * p1, const void *p2) { return *(int*)p2 - *(int*)p1; }); printf("%dn",palindromic[0]); }
8.
C++: #include <iostream> using namespace std; int main(int argc, const char * argv[]) { long long max = 0; static const char * digits = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450"; for (int pos = 0; pos < 988; pos++) { long long num[14] = {NULL}; num[13] = 1; for (int i = 0; i < 13; i++) num[13] *= digits[pos + i] - '0'; if (num[13] > max) max = num[13]; } printf("%lldn",max); }
9.
C++: #include <iostream> using namespace std; int main(int argc, const char * argv[]) { for (long long c = 997; c > 2; c--) { for (long long b = c - 1; b > 0; b--) { long long a = 1000 - c - b; if (a > 0 && c*c == a*a + b*b) { printf("%lldn",a*b*c); return 0; } } } }
11.
C++: #include <iostream> using namespace std; int grid[20][20] = {{ 8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8}, {49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0}, {81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65}, {52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91}, {22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80}, {24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50}, {32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70}, {67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21}, {24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72}, {21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95}, {78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92}, {16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57}, {86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58}, {19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40}, { 4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66}, {88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69}, { 4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36}, {20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16}, {20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54}, { 1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48}}; long long max_in_row(int row){ long long max = 0; for (int pos = 0; pos < 17; pos++) { long long tmp = 1; for (int i = 0; i < 4; i++) tmp *= grid[row][pos+i]; if (max < tmp) max = tmp; } return max; } long long max_in_column(int column){ long long max = 0; for (int pos = 0; pos < 17; pos++) { long long tmp = 1; for (int i = 0; i < 4; i++) tmp *= grid[pos+i][column]; if (max < tmp) max = tmp; } return 0; } long long max_in_diagonally(int row, int column, bool direction){ /*! * @brief direction * * true: false: * x___ ___x * _x__ __x_ * __x_ _x__ * ___x x___ * */ long long res = 1; if (direction) for (int x = 0, y = 0; x < 4 && y < 4; x++,y++) res *= grid[row + x][column + y]; else for (int x = 0, y = 0; x < 4 && y < 4; x++,y++) res *= grid[row + x][column - y]; return res; } int main(int argc, const char * argv[]) { long long max = 0; for (int row = 0; row < 20; row++) { long long row_m = max_in_row(row); if (max < row_m) max = row_m; } for (int column = 0; column < 20; column++) { long long column_m = max_in_column(column); if (max < column_m) max = column_m; } for (int row = 0; row < 17; row++) { for (int column = 0; column < 17; column++) { long long diagonally_t_m = max_in_diagonally(row, column, true); long long diagonally_f_m = max_in_diagonally(row, column, false); if (max < diagonally_t_m) max = diagonally_t_m; if (max < diagonally_f_m) max = diagonally_f_m; } } printf("%lldn",max); }
12.
Mathematica: triangular = 1; For[step = 2, step < Infinity, step++, {If[Length[Divisors[triangular]] >= 500, Break[]], triangular += step} ]; Print[triangular];
14.
Mathematica: num = 0; max = 0; For[number = 999999, number > 0, number--, {tmp = 0; n = number; While[n != 1, {If[EvenQ[n], n /= 2, n = 3*n + 1], tmp++} ], If[max < tmp, {max = tmp, num = number}] } ] Print[num]
29.
Mathematica: Length[ DeleteDuplicates[ ArrayReshape[ Table[a^b, {a, 2, 100}, {b, 2, 100}], {1, 9801} ][[1]] ] ]
34.
C++: #include <iostream> using namespace std; int main(int argc, char *argv[]) { static const int factorial[10] = {1,1,2,6,24,120,720,5040,40320,362880}; long long count = 0; // 9! + 9! + 9! + 9! + 9! + 9! + 9! = 2540160 // However, 9999999 is much bigger than 2540160 for (int i = 3; i < 2540160; i++) { int p = i; int res = 0; while (p != 0) { res += factorial[p % 10]; p /= 10; } if (res == i) count+=i; } printf("%lldn",count); }
35.
Mathematica: Export["primes.txt", Table[Prime[n], {n, 1, 78498}]]; C++: #include <iostream> #include <string> #include <fstream> #include <map> using namespace std; map<int, int> prime_m; int* rotate(const char * prime){ size_t length = strlen(prime); int * result = (int *)malloc(sizeof(int) * length); char * tmp = (char *)malloc(sizeof(char) * length * 2); for (int pos = 0; pos < length * 2; pos++) { tmp[pos] = prime[pos % length]; } for (int offset = 1; offset < length; offset++) { char * tmp2 = (char *)malloc(sizeof(char) * length); for (int p = 0; p < length; p++) tmp2[p] = tmp[offset + p]; int r_p = atoi(tmp2); result[offset-1] = r_p; free(tmp2); } free(tmp); return result; } int main(int argc, const char * argv[]) { ifstream primes("primes.txt"); if(!primes) return 1; string prime; while(getline(primes, prime)) prime_m[atoi(prime.c_str())] = 1; primes.clear(); primes.seekg(0, ios::beg); int count = 0; while(getline(primes, prime)) { int * rotations = rotate(prime.c_str()); int count_i = 0; for (int i = 0; i < prime.length() - 1; i++) if (prime_m[rotations[i]] == 1) count_i++; if (count_i == prime.length() - 1) count++; } printf("%dn",count); return 0; }
36.
C++: #include <iostream> #include <bitset> using namespace std; bool is_palindromic_binary(bitset<20> number){ int start = 19; for (; start > 0; start--) if (number.test(start)) break; for (int i = start; i > (start / 2); i--) { if (number.test(i) != number.test(start - i)) return false; } return true; } bool is_palindromic_decimal(int number){ static char index[]="0123456789"; char str[7] = {NULL}; int i = 0; do{ str[i++] = index[number%(unsigned)10]; number /= 10; } while(number); for (int t = 0; t < i / 2; t++) if (str[t] != str[i - t - 1]) return false; return true; } int main(int argc, const char * argv[]) { int count = 0; for (int i = 0; i < 1000000; i++) if (is_palindromic_binary(i) && is_palindromic_decimal(i)) count+=i; printf("%dn",count); }