第十章 函数的进阶与应用.docx

第十章 函數的進階與應用10-1 函數的重載(overloading)何謂重載:相同的函數名稱被重複用於不同函數的宣告與定義,稱為overloading範例:i. 參數的資料型態不同int Max(int,int);float Max(float,float);ii. 參數的數目不一樣double Area(double x);double Area(double x, double y);範例程式:試撰寫程式,由鍵盤輸入選擇,比較兩個數或三個數,然後自動判斷找出最大值Step1.先撰寫一個具備比較兩個數的程式Step2.再增加可以比較三個數的函數注意:函數名稱相同,但變數不同程式碼:#include using std:cin;using std:cout;using std:endl;double min(double, double);double min(double, double, double);int main()int n;double x,y,z;couthow many number you want to compare:(2 or 3)n;if ( n =2) coutPlease input two integers, first integer:x; cout The second integer:y; coutThe minimum value is min(x,y)endl; else if (n =3) coutPlease input three integers, first integer:x; cout The second integer:y; cout The third integer:z; coutThe minimum value is min(x,y,z)endl; else coutYou input a wrong numberendl;return 0;double min(double a, double b)return (ab)temp = b;if (temp c); temp = c;return temp;10-2 參數的預設值函數的參數可以做預設值,例如declaration float Area(float width, float length=12.0)definition float Area(float width, float length) return width*length ;call A=Area(6.5) 代表width=6.5, length已預設為12.0 A=Area(6.5,15) width=6.5,length=15.0 練習:將上述宣告,定義及呼叫撰寫成程式10-4 亂數的取得(random numbers)一、 準亂數產生器(pseudo-random number generator)每次執行起始值都一樣declaration#include /C+ standard library .cout rand(); /產生一個亂數介於032767之間如果想要產生有範圍的亂數,必須做縮尺(scaling),例如 i = rand() % 6 ;練習1.建立一個45的二維陣列,陣列每個元素介於1到6之間i =( rand() % 6 + 1 );主要程式碼 (program:10-4-1.cpp)int main() for(int i = 0 ; i 4 ; i+) for(int j = 0; j 4 ; j+) arrayij=( rand() % 6 + 1 ); coutsetw(10)arrayij; coutendl;程式碼:#include using std:endl;using std:cout;using std:cin;#include using std:setw;#include int main()const int m = 4; const int n = 5;int Amn=0;int temp = 1; while (temp = 1) for (int i = 0; i m; i+)for (int j = 0; j n; j+)Aij=(1+rand()%6);for (int ii = 0; ii m; ii+)for (int jj = 0; jj n; jj+)coutsetw(10)Aiijj;coutendl;coutDo you want to try again(1 for yes)temp; return 0;練習2.擲一骰子遊戲,骰子之數值介於16之間,試統計擲6000次之後,16每一個數字出現的機率次數程式撰寫方法先定義16發生機率次數為0再用for迴圈配合switch指令進行統計程式主要架構 (program 10-4-2.cpp)int main() int f1=0, f2=0, f3=0, f4=0, f5=0, f6=0 ; for(int roll = 0 ; roll 4 ; roll+) face=1 + rand() % 6 ; switch(face)case 1: +f1; break;case 2: +f2; break;case 3: +f3; break;case 4: +f4; break;case 5: +f5; break;case 6: +f6; break;default: coutProgram never get here.;return 0 ;程式碼:#include using std:endl;using std:cout;using std:cin;#include int main()int f6 = 0;int face;for (int roll = 1; roll =6000; roll+) face = 1+rand()%6; switch(face) case 1:+f0;break;case 2:+f1;break;case 3:+f2;break;case 4:+f3;break;case 5:+f4;break;case 6:+f5;break; default:coutProgram never get here!endl; coutThe times of die is:endl;for (int j = 0; j 6; j+)coutface =j+1, the times is:fjendl;coutnThe probability of die is :endl;for (int k = 0; k 6; k+)coutface =k+1, the times is:double(fk)/6000endl;return 0;二、 將pseudo-random number改為randomize1. 採用srand(),程式輸入一個unsigned integer為seed,可使rand函數產生不同系列的亂數Example: (program 10-4-3.cpp)unsigned int seed;coutseed;srand(seed);for(int i= 1;i =10; i+)coutsetw(10)1+rand()%6;if(i%5=0)coutendl;練習:將上述片段程式寫成完整程式碼,然後輸入不同seed2. 取用系統時間為亂數,較為簡易,需加上下列指令#includeusing std:time;.srand( time(0) );.練習:將上題程式碼之seed改為time(0) (program 10-4-4.cpp)10-5遞迴函數(recursive function)何謂遞迴函數:函數不斷呼叫自己,直到termination condition產生才停止一、 階乘函數(factorial function)n!n!=n(n-1)(n-2).321函數寫法1. 遞迴(10-5-2.cpp)int Factorial(int N) if(N=1) return 1; else return N*Factorial(N-1);2. 迴圈(10-5-1.cpp)int Factorial(int N) int temp=1; for(int i= 1;i =N; i+) temp *= i; return temp;練習:寫一個遞迴函數計算n!程式碼:1. 採用迴圈方式寫#include using std:endl;using std:cout;using std:cin;unsigned long Factorial(int); int main()int N;coutPlease input a integer bigger than 1N; coutThe value of N! is Factorial(N)endl;return 0;unsigned long Factorial (int Num)int temp=1;for (int i = 1; i = Num; i+)temp *=i; return temp;2. 採用遞迴方式撰寫#include using std:endl;using std:cout;using std:cin;unsigned long Factorial(int); int main()int N;coutPlease input a integer bigger than 1N; coutThe value of N! is Factorial(N)endl;return 0;unsigned long Factorial (int Num)if (Num =1)return 1;/termination conditionelse return Num*Factorial(Num-1);/recursive condition二、 Gretest Common Divider(GCD)找兩個整數的最大公因數程式碼:1. 遞迴(10-5-3.cpp)int GCD(int M, int N) if(M%N)=0) return N; else return GCD( N, M%N );程式碼:#include using std:endl;using std:cout;using std:cin;int GCD(int,int); int main()int M,N;coutPlease input two integer bigger than 1, the first value isN; coutThe second value is M;cout The greatest common divider is :GCD(M,N)1) if(M%N)=0) temp=1; else temp=M%N; M=N; N=temp; return N;程式碼:#include using std:endl;using std:cout;using std:cin;int GCD(int,int); int main()int M,N;coutPlease input two integer bigger than 1, the first value isN; coutThe second value is M;cout The greatest common divider is :GCD(M,N)1)if (M%N)=0) temp = 1; else temp = M%N;M = N;N = temp; return N;練習:使用遞迴撰寫程式,求兩個整數之最大公因數*第十章 作業*Topic 1. 函數的重載(overloading):相同函數名稱被重複用於不同函數的宣告和定義A. 試寫出一程式，內含函數，以重載方式使程式能經由輸入一整數或浮點數值，回傳此數值的平方。B. 利用函數重載功能，寫出兩個同樣名為Max( )的函數，分別可以找出二個數中之最大值及三個數中之最大值。Topic 2. 亂數(random numbers)取得A. 寫一程式，能以亂數跑出一組樂透彩卷號碼。Topic 3. 遞迴(recursion )函數A. 寫一程式，能以遞迴方式計算，再以迴圈方式計算一次。B. 以遞迴方式計算兩數之最大公約數。C. 已知費式級數(Fibonacci number)之定義如下：故為0、1、1、2、3、5、8、13 ，試以遞迴演算法(recursive algorithm) ，計算 之值。D.已知binomial coefficient定義為，有如下特性：，且當，試寫一遞迴