【C/PTA —— 11.函数2（课外实践）】

一.函数题

6-1 计算A[n]=1/(1 + A[n-1])

float fun(int n)
{if (n == 1)return 1;return 1 / (1 + fun(n - 1));
}

6-2 递归实现顺序输出整数

void printdigits(int n)
{int count = 0;int num1 = 0;num1 = n;if (n == 0){printf("0");return 0;}while (n){n /= 10;count++;}int num[100] = { 0 };n = num1;int count1 = 0;while (n){num[count1++] = n % 10;n /= 10;}for (int i = count1 - 1; i >= 0; i--){printf("%d\n", num[i]);}
}

6-3 自然数的位数(递归版)

int NumDigit(int number)
{if (number == 0)return 0;else if (number / 10 == 0)return 1;elsereturn NumDigit(number / 10) + 1;
}

6-4 分治法求解金块问题

int max(int a[], int m, int n) {int i;int max = a[0];for (i = m; i < n + 1; i++) {if (a[i] > max) {max = a[i];}}return max;
}int min(int a[], int m, int n) {int i;int min = a[0];for (i = m; i < n + 1; i++) {if (a[i] < min) {min = a[i];}}return min;
}

6-5 汉诺塔

void hanoi(int n, char from, char to, char by)
{void move(char x, char y);if (n == 1)move(from, to);else{hanoi(n - 1, from, by, to);move(from, to);hanoi(n - 1, by, to, from);}
}void move(char x, char y)
{printf("%c->%c\n",x,y);
}

6-6 重复显示字符(递归版)

void Show(int number, char symbol)
{void Print(char ch);if (number <= 0)return;if (number == 1)Print(symbol);else{Show(number - 1, symbol);Print(symbol);}
}void Print(char ch)
{printf("%c", ch);
}

6-7 显示平行四边形(右)(递归版)

void RtPara(int width, int height, char symbol)
{void PrintSpace(int number);if (width <= 0 || height <= 0)return;else{PrintSpace(height - 1);Show(width, symbol);putchar('\n');RtPara(width, height - 1, symbol);}
}void PrintSpace(int number)
{if (number <= 0)return;else{printf(" ");PrintSpace(number - 1);}
}

二.编程题

7-2 N阶楼梯上楼问题

int ClimbStairs(int number)
{if (number == 1)return 1;else if (number == 2)return 2;else{int dp[number+1];dp[1] = 1;dp[2] = 2;int i = 0;for (i = 3; i <= number; i++){dp[i] = dp[i - 1] + dp[i - 2];}return dp[number];}
}int main()
{int n = 0;int ways = 0;scanf("%d", &n);ways = ClimbStairs(n);printf("%d\n", ways);
}