题目：http://lx.lanqiao.cn/problemset.page?code=BASIC-&userid=188230
一、数列排序
time：0ms
#include<iostream> #include<vector> #include<algorithm> using namespace std; int main() { int g, item; cin >> g; vector<int> v; while (g--) { cin >> item; v.push_back(item); } sort(v.begin(), v.end()); for (int i = 0; i < v.size(); ++i) cout << v[i] << " "; cout << endl; return 0; }
二、十六进制转八进制
思路：将16进制先转为2进制，然后将2进制再转为8进制
time：46ms
#include<iostream> #include<string> using namespace std; int main() { int n; cin >> n; while (n--) { string in_out, t; cin >> in_out; for (int i = 0; i < in_out.size(); ++i) { switch (in_out[i]) { case '0':t += "0000"; break; case '1':t += "0001"; break; case '2':t += "0010"; break; case '3':t += "0011"; break; case '4':t += "0100"; break; case '5':t += "0101"; break; case '6':t += "0110"; break; case '7':t += "0111"; break; case '8':t += "1000"; break; case '9':t += "1001"; break; case 'A':t += "1010"; break; case 'B':t += "1011"; break; case 'C':t += "1100"; break; case 'D':t += "1101"; break; case 'E':t += "1110"; break; case 'F':t += "1111"; break; } } if (t.length() % 3 == 1) t = "00" + t; if (t.length() % 3 == 2) t = "0" + t; bool key = false; for (int i = 0; i <= t.length() - 3; i+=3) { int num = 4 * (t[i] - '0') + 2 * (t[i+1] - '0') + t[i+2] - '0'; if (num) key = true; if (key) cout << num; } cout << endl; } return 0; }
三、十六进制与八进制互转
这里我们可以写一个函数，用于m进制转n进制
两个题都可以直接套统一的算法模板
算法模板
void Exchange_JZ(string str1, string& str2, int form, int to) { int i, len, k; int t[maxn] = { 0 }, A[maxn] = { 0 }; len = str1.size(); for (i = len - 1; i >= 0; i--) { t[len - 1 - i] = str1[i] - (str1[i]<58 ? 48 : str1[i]<97 ? 55 : 61); } for (k = 0; len;) { for (i = len - 1; i >= 1; i--) { t[i - 1] += t[i] % to*form; t[i] /= to; } A[k++] = t[0] % to; t[0] /= to; while (len>0 && !t[len - 1]) { len--; } } for (i = k - 1; i >= 0; i--) str2 += A[i] + (A[i]<10 ? 48 : A[i]<36 ? 55 : 61); }
此算法更适用于大数任意进制之间的转换
上一题不能用此算法的原因是，8进制与16进制均为2进制的组合，利用此关系求解更为快捷
time：十六->十进制：0ms 十->十六进制：15ms
int main() { string str1, str2; cin >> str1; Exchange_JZ(str1, str2, 10, 16); cout << str2 << endl; return 0; }
四、特殊回文数
遍历构造解
time：0ms
#include<iostream> using namespace std; int main() { int n; cin >> n; for (int i = 10; i < 100; ++i) { int sum = 2 * (i % 10 + i / 10); if (n < sum)continue; else if (n - sum>=10)continue; else cout << i << n - sum << i % 10 << i / 10 << endl; } for (int i = 100; i < 1000; ++i) if (n == 2 * (i % 10 + i / 100 + i / 10 % 10)) cout << i << i % 10 << i / 10 % 10 << i / 100 << endl; return 0; }
五、回文数
遍历构造解
time：0ms
#include<iostream> using namespace std; int main() { for (int i = 10; i < 100; ++i) cout << i << i % 10 << i / 10 << endl; }
六、特殊的数字
水仙花数
遍历构造解
time：0ms
#include<iostream> using namespace std; int fun(int x) { int a = x % 10; int b = x / 10 % 10; int c = x / 100; return a*a*a + b*b*b + c*c*c; } int main() { for (int i = 100; i < 1000; ++i) if (i == fun(i)) cout << i << endl; return 0; }
七、杨辉三角
time：15ms
直角三角形式
#include<iostream> using namespace std; const int MAX = 50; int N[MAX][MAX]; int f(int r, int c) { if (c == 0 || r == c) N[r][c] = 1; if (N[r][c] == 0) N[r][c] = f(r - 1, c - 1) + f(r - 1, c); return N[r][c]; } int main() { int n; while (cin >> n) { for (int i = 0; i < n; i++) for (int j = 0; j <= i; j++) { cout << f(i, j); if (j == i)cout << endl; else cout << " "; } } return 0; }
等腰三角形式
#include<iostream> using namespace std; const int MAX = 50; int N[MAX][MAX]; int f(int r, int c) { if (c == 0 || r == c) N[r][c] = 1; if (N[r][c] == 0) N[r][c] = f(r - 1, c - 1) + f(r - 1, c); return N[r][c]; } int main() { int n; while (cin >> n) { for (int i = 0; i < n; i++) { for (int k = 0; k < n - i; ++k) cout << " "; for (int j = 0; j <= i; j++) { cout << f(i, j); if (j == i)cout << endl; else cout << " "; } } } return 0; }
八、查找整数
遍历
time：0ms
#include<iostream> #include<vector> using namespace std; int main() { int num, tar; cin >> num; vector<int> V; while (num--) { int i; cin >> i; V.push_back(i); } cin >> tar; vector<int>::iterator it = V.begin(); while (it != V.end()) { if (*it == tar) { cout << it - V.begin() + 1 << endl; break; } it++; } if (it == V.end())cout << -1 << endl; return 0; }
九、数列特征
排序+遍历求和
time：15ms
#include<iostream> #include<algorithm> #include<vector> using namespace std; int main() { int num, result = 0; cin >> num; vector<int>V; while (num--) { int i; cin >> i; V.push_back(i); } sort(V.begin(), V.end()); cout << *(V.end() - 1) << endl << *V.begin() << endl; for (int i = 0; i < V.size(); ++i) result += V[i]; cout << result << endl; return 0; }
十、字母图形
双端队列
time：15ms
#include<iostream> #include<deque> using namespace std; void fun(deque<char>& V) { char ch = V[0] + 1; V.pop_back(); V.push_front(ch); } int main() { deque<char> v; int n, m; cin >> n >> m; for (int i = 'A'; i < 'A' + m; ++i) v.push_back(i); for (int i = 0; i < n; ++i) { for (int i = 0; i < v.size(); ++i) cout << v[i]; fun(v); cout << endl; } return 0; }
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