catalogue

Example 3-7 enter two integers and sum the squares

For example, calculate 4! The two phases of the project:

# Nested calls to functions

# Nested Call

# Example 3-7 enter two integers and sum the squares

#include <iostream> using namespace std; int fun2(int m) { return m * m; } int fun1(int x,int y) { return fun2(x) + fun2(y); } int main() { int a, b; cout<<"Please enter two integers (a and b): "; cin >> a >> b; cout << "The sum of square of a and b: " << fun1(a, b) << endl; return 0; }

# Recursive call of function

# definition

l} functions that call themselves directly or indirectly are called recursive calls.

# Example: calculate n!

l) formula 1: n= n × (n-1) × (n-2) × (n-3) ×...× two × one

l) formula 2:

# For example, calculate 4! The two phases of the project:

l) recurrence:

l) regression:

# Example 3-8 find n!

### Source code:

#include <iostream> using namespace std; unsigned fac(int n){ unsigned f; if (n == 0) f = 1; else f = fac(n - 1) * n; return f; } int main() { unsigned n; cout << "Enter a positive integer:"; cin >> n; unsigned y = fac(n); cout << n << "! = " << y << endl; return 0; }

Operation results:

Enter a positive integer:8 8! = 40320

# Example 3-9 calculate the number of different combinations of k people selected from n people to form a committee by recursive method.

## analysis

number of combinations selected from n individuals = number of combinations selected from n-1 individuals + number of combinations selected from n-1 individuals;

• when n = k or k = 0, the number of combinations is 1.

## Source code:

#include<iostream> using namespace std; int comm(int n, int k) { if (k > n) return 0; else if (n == k || k == 0) return 1; else return comm(n - 1, k) + comm(n - 1, k - 1); } int main() { int n, k; cin >> n >> k; cout << "C(n, k) = " << comm(n, k) << endl; return 0; }

## Operation results:

18 5 8568

# Example 3-10 Hanoi Tower

There are three needles A, B and C. There are n plates on needle A, the large one is lower and the small one is upper. It is required to move the N plates from needle A to needle C. during the movement, needle B can be used to move only one plate at A time, and the large plate is lower and the small plate is upper on the three needles during the movement.

l) moving n plates from pin A to pin C can be divided into three steps:

N. move n-1 plates on A to pin B (with the help of pin C);

n. move the remaining plate on pin A to pin C;

N. move n-1 plates from pin B to pin C (with the help of pin A).

## Source code:

#include <iostream> using namespace std; //Move the top plate of src needle to dest needle void move(char src, char dest) { cout << src << " --> " << dest << endl; } //Move n plates from src needle to dest needle, and use medium needle as transfer void hanoi(int n, char src, char medium, char dest) { if (n == 1) move(src, dest); else { hanoi(n - 1, src, dest, medium); move(src, dest); hanoi(n - 1, medium, src, dest); } } int main() { int m; cout << "Enter the number of diskes: "; cin >> m; cout << "the steps to moving " << m << " diskes:" << endl; hanoi(m, 'A', 'B', 'C'); return 0; }

## Operation results:

Enter the number of diskes:3 the steps to moving 3 diskes: A --> C A --> B C --> B A --> C B --> A B --> C A --> C

# Parameter passing of function

- The storage unit of the formal parameter is allocated only when the function is called
- Arguments can be constants, variables, or expressions
- Argument type must match formal parameter
- Value transfer is the transfer of parameter values, that is, one-way transfer
- Reference passing can achieve two-way passing
- Constant reference as a parameter can ensure the security of argument data