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289 lines (272 loc) · 6.8 KB
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/*
* 算法第三章作业
* 刘景亮
*/
#include <iostream>
#include <math.h>
using namespace std;
/*
* 3. 顺时针打印趣味矩阵
*/
void Q3()
{
int arr[100][100] = { 0 };
int n = 5;
int count = 1;
cout << "输入一个数 n : ";
cin >> n;
for (int i = 0; i < n / 2; ++i)
{
// 上
for (int j = i; j < n - i; ++j)
{
arr[i][j] = count++;
}
// 右
for (int j = i + 1; j <= n - i - 1; ++j)
{
arr[j][n - i - 1] = count++;
}
// 下
for (int j = n - i - 2; j >= i; --j)
{
arr[n - i - 1][j] = count++;
}
// 左
for (int j = n - i - 2; j >= i + 1; --j)
{
arr[j][i] = count++;
// cout << j << "," << i << endl;
}
}
if (n % 2 == 1)
{
// cout << "---" << (n+1)/2 << endl;
arr[2][2] = n * n;
}
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < n; ++j)
{
cout << arr[i][j] << "\t";
}
cout << endl;
}
}
/*
* 7. 计算 ackermann 函数 ack(m, n) 的递归函数
*/
int ack(int m, int n)
{
if (m < 0 || n < 0)
{
return 0;
}
if (m == 0)
{
return n + 1;
}
if (n == 0)
{
return ack(m - 1, 1);
}
return ack(m - 1, ack(m, n - 1));
}
/*
* 11. 求 1*2*3*...*n 所得结果的末尾有多少个 0 (100 < n < 10000).
*/
void countZero()
{
int i = 0;
cout << "输入 n (1000 < n < 10000) : ";
cin >> i;
int n = i;
int count = 0;
while (n >= 5)
{
if (n % 5 == 0)
{
int ret = n;
while (ret % 5 == 0)
{
count++;
ret = ret / 5;
}
}
n--;
}
cout << i << "! 的末尾有 " << count << " 个 0." << endl;
}
/*
* 13. 推断竞赛名次
*/
void Q13()
{
cout << "ABCDE五个人可能的名次为 : " << endl;
int a, b, c, d, e;
for (a = 1; a <= 5; ++a)
{
for (b = 1; b <= 5; b++)
{
for (c = 1; c <= 5; c++)
{
for (d = 1; d <= 5; d++)
{
for (int e = 1; e <= 5; e++)
{
if ((b == 3 || c == 5)
&& (d == 2 || e == 4)
&& (b == 1 || e == 4)
&& (c == 1 || b == 2)
&& (d == 2 || a == 3)
&& (
a != b && a != c && a != d && a != e
&& b != c && b != d && b != e
&& c != d && c != e
&& d != e
))
{
cout << a << b << c << d << e << endl;
}
}
}
}
}
}
}
/*
* 16. 判断能否被 4，7，9 整除
*/
void Q16()
{
int n = 0;
cout << "请输入一个整数 n : ";
cin >> n;
int k = (n % 4 == 0) + (n % 7 == 0) * 2 + (n % 9 == 0) * 4;
// null->0
// 4->1 7->2 9->4
// 4*7->3 4*9->5 7*9->6
// 4*7*9->7
switch (k)
{
case 0:
cout << "都不行" << endl;
break;
case 1:
cout << "只能被 4 整除" << endl;
break;
case 2:
cout << "只能被 7 整除" << endl;
break;
case 3:
cout << "能被 4，7 整除" << endl;
break;
case 4:
cout << "只能被 9 整除" << endl;
break;
case 5:
cout << "能被 4，9 整除" << endl;
break;
case 6:
cout << "能被 7，9 整除" << endl;
break;
case 7:
cout << "都可以" << endl;
default:
break;
}
// cout << 4*7*9 << endl;
// cout << k << endl;
}
/*
* 18. 求两个数据: 5位数 = 2*4位数，9个数字互不相同
*/
void Q18()
{
for (int i = 1000; i < 10000; i++)
{
int a = i / 10 % 10, b = i / 100 % 10, c = i / 1000 % 10, d = i / 1 % 10, e = 0;
bool x = a != b && a != c && a != d
&& b != c && b != d
&& c != d;
if (x)
{
// cout << i << endl;
// cout << a << "," << b << "," << c << "," << d << endl;
int j = i * 2;
int aa = j / 10 % 10, bb = j / 100 % 10, cc = j / 1000 % 10, dd = j / 1 % 10, ee = j / 10000 % 10;
bool y = aa != bb && aa != cc && aa != dd && aa != ee
&& bb != cc && bb != d && bb != ee
&& cc != dd && cc != ee
&& d != ee;
if (y
&& aa != a && aa != b && aa != c && aa != d
&& bb != a && bb != b && bb != c && bb != d
&& cc != a && cc != b && cc != c && cc != d
&& dd != a && dd != b && dd != c && dd != d
&& ee != a && ee != b && ee != c && ee != d)
{
cout << "4 : " << i << " , ";
cout << "5 : " << j << endl;
}
}
}
}
/*
* 23. 对一个 5 位数以内的数
* 1. 判断是几位数
* 2. 按顺序输出各位数字
* 3. 逆序输出各位数字
*/
void Q23()
{
int n = 0;
cout << "输入一个5位数以内的正整数 : ";
cin >> n;
char arr[10] = { 0 };
int tmp = n;
int cnt = 0;
while (tmp)
{
arr[cnt] = '0' + tmp % 10;
tmp /= 10;
cnt++;
}
cout << "这是一个 " << cnt << " 位数字" << endl;
cout << "正序 : ";
while (cnt)
{
cout << arr[--cnt];
}
cout << endl;
cout << "逆序 : ";
cout << arr << endl;
}
int main()
{
cout << "3. 顺时针打印趣味矩阵" << endl;
Q3();
cout << "---------------------" << endl;
cout << "7. 计算 ackermann 函数 ack(m, n) 的递归函数" << endl;
int m, n;
cout << "请输入 m 和 n : ";
cin >> m >> n;
cout << ack(m, n) << endl;
cout << "---------------------" << endl;
cout << "11. 求 1*2*3*...*n 所得结果的末尾有多少个 0 (100 < n < 10000)." << endl;
countZero();
cout << "---------------------" << endl;
cout << "13. 推断竞赛名次" << endl;
Q13();
cout << "---------------------" << endl;
cout << "16. 判断能否被 4，7，9 整除" << endl;
Q16();
cout << "---------------------" << endl;
cout << "18. 求两个数据: 5位数 = 2*4位数，9个数字互不相同" << endl;
Q18();
cout << "---------------------" << endl;
cout << "23. 对一个 5 位数以内的数" << endl;
Q23();
cout << "---------------------" << endl;
return 0;
}