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三个数比大小的c语言程序三个数比大小的C语言程序在编程领域中，比较大小是一项常见的操作。
比较大小的程序可以用来判断给定的三个数中哪个数最大或最小。
本文将介绍一个用C 语言编写的程序，用于比较三个数的大小。
我们需要定义三个变量来存储这三个数。
我们可以使用整型来表示这些数，例如：```cint num1, num2, num3;```接下来，我们需要从用户那里获取这三个数的值。
为了简化程序，我们可以通过键盘输入来实现。
使用C语言的`scanf`函数可以实现这一功能，例如：```cprintf("请输入三个整数：\n");scanf("%d %d %d", &num1, &num2, &num3);```在上述代码中，`printf`函数用于输出提示信息，而`scanf`函数用于接收输入的三个整数。
接下来，我们需要编写比较大小的逻辑。
首先，我们可以使用`if`语句来判断`num1`是否大于`num2`和`num3`。
如果是，则`num1`是最大的数；否则，我们需要继续比较`num2`和`num3`的大小。
代码如下所示：```cif (num1 > num2 && num1 > num3) {printf("最大的数是：%d\n", num1);}else {if (num2 > num3) {printf("最大的数是：%d\n", num2);}else {printf("最大的数是：%d\n", num3);}}```在上述代码中，我们使用了嵌套的`if`语句来实现比较大小的逻辑。
首先，我们判断`num1`是否大于`num2`和`num3`，如果是，则输出`num1`是最大的数。
否则，我们继续判断`num2`是否大于`num3`，如果是，则输出`num2`是最大的数；否则，输出`num3`是最大的数。
经典c程序100例(1--10)【程序1】题目：有1、2、3、4个数字，能组成多少个互不相同且无重复数字的三位数？都是多少？1.程序分析：可填在百位、十位、个位的数字都是1、2、3、4。
组成所有的排列后再去掉不满足条件的排列。
2.程序源代码：[code=c]main(){int i,j,k;printf("\n");for(i=1;i<5;i++)／*以下为三重循环*/for(j=1;j<5;j++)for (k=1;k<5;k++){if (i!=k&&i!=j&&j!=k) /*确保i、j、k三位互不相同*/printf("%d,%d,%d\n",i,j,k);}}[/code]==============================================================【程序2】题目：企业发放的奖金根据利润提成。
利润(I)低于或等于10万元时，奖金可提10%；利润高于10万元，低于20万元时，低于10万元的部分按10%提成，高于10万元的部分，可可提成7.5%；20万到40万之间时，高于20万元的部分，可提成5%；40万到60万之间时高于40万元的部分，可提成3%；60万到100万之间时，高于60万元的部分，可提成1.5%，高于100万元时，超过100万元的部分按1%提成，从键盘输入当月利润I，求应发放奖金总数？1.程序分析：请利用数轴来分界，定位。
注意定义时需把奖金定义成长整型。
2.程序源代码：[code=c]main(){long int i;int bonus1,bonus2,bonus4,bonus6,bonus10,bonus;scanf("%ld",&i);bonus1=100000*0.1;bonus2=bonus1+100000*0.75;bonus4=bonus2+200000*0.5;bonus6=bonus4+200000*0.3;bonus10=bonus6+400000*0.15;if(i<=100000)bonus=i*0.1;else if(i<=200000)bonus=bonus1+(i-100000)*0.075;else if(i<=400000)bonus=bonus2+(i-200000)*0.05;else if(i<=600000)bonus=bonus4+(i-400000)*0.03;else if(i<=1000000)bonus=bonus6+(i-600000)*0.015;elsebonus=bonus10+(i-1000000)*0.01;printf("bonus=%d",bonus);}[/code]==============================================================【程序3】题目：一个整数，它加上100后是一个完全平方数，再加上168又是一个完全平方数，请问该数是多少？1.程序分析：在10万以内判断，先将该数加上100后再开方，再将该数加上268后再开方，如果开方后的结果满足如下条件，即是结果。
三数排序c++语言
以下是使用c++语言实现的三个数的排序：
1. 定义三个变量a、b、c分别表示三个数。
2. 使用cin输入三个数的值。
3. 使用if语句和swap函数实现排序：
a. 比较a和b的大小，如果a>b，则交换a和b的值。
b. 比较b和c的大小，如果b>c，则交换b和c的值。
c. 再次比较a和b的大小，如果a>b，则交换a和b的值（确保a 是最小的数）。
4. 使用cout分别输出三个数的值，即为从小到大排序后的结果。
以下是完整代码：
```
#include<iostream>
using namespace std;
int main(){
int a, b, c;
cin >> a >> b >> c;
if (a > b){
swap(a, b);
}
if (b > c){
swap(b, c);
}
if (a > b){
swap(a, b);
}
cout << a << " " << b << " " << c << endl;
return 0;
} ```。
10个经典的C语言基础算法及代码1.冒泡排序算法冒泡排序是一种简单但效率较低的排序算法，在每一轮遍历中比较相邻的两个元素，如果顺序不正确则交换它们，直到整个数组有序为止。
```cvoid bubbleSort(int arr[], int n)for (int i = 0; i < n-1; i++)for (int j = 0; j < n-1-i; j++)if (arr[j] > arr[j+1])int temp = arr[j];arr[j] = arr[j+1];arr[j+1] = temp;}}}```2.选择排序算法选择排序是一种简单直观的排序算法，它每次从待排序的数组中选择最小（或最大）的元素，并放到已排序的数组末尾。
```cvoid selectionSort(int arr[], int n)for (int i = 0; i < n-1; i++)int min_index = i;for (int j = i+1; j < n; j++)if (arr[j] < arr[min_index])min_index = j;}}int temp = arr[i];arr[i] = arr[min_index];arr[min_index] = temp;}```3.插入排序算法插入排序的基本思想是将数组分为已排序和未排序两部分，每次将未排序的元素插入到已排序的合适位置。
```cvoid insertionSort(int arr[], int n)for (int i = 1; i < n; i++)int key = arr[i];int j = i - 1;while (j >= 0 && arr[j] > key)arr[j+1] = arr[j];j--;}arr[j+1] = key;}```4.快速排序算法快速排序使用分治法的思想，每次选择一个基准元素，将小于基准的元素放到左边，大于基准的元素放到右边，然后递归地对左右两个子数组进行排序。
C语言常用算法程序汇总C语言是一门广泛应用于计算机编程的语言，具有较高的效率和灵活性。
在C语言中，常见的算法程序包括排序算法、查找算法、递归算法等等。
以下是一些常用的C语言算法程序的汇总：1.排序算法：-冒泡排序：通过多次迭代比较相邻元素并交换位置，将最大的元素逐渐移动到正确的位置。
-插入排序：将待排序的元素与已排序的部分依次比较并插入到正确的位置。
-选择排序：每次从待排序的元素中选择最小的元素并与已排序的部分交换位置。
-快速排序：通过选择一个基准元素，将数组划分为两个子数组进行递归排序。
2.查找算法：-顺序查找：逐个比较数组中的元素，直到找到目标元素或到数组末尾。
-二分查找：通过比较目标元素与数组中间元素的大小，逐步缩小范围，直到找到目标元素。
-哈希查找：通过散列函数将目标元素映射到哈希表的索引位置进行查找。
3.递归算法：-阶乘：通过递归调用自身计算一个正整数的阶乘。
-斐波那契数列：通过递归调用自身计算斐波那契数列的第n个数。
-二叉树遍历：通过递归调用自身遍历二叉树的各个节点。
4.图算法：- 最短路径算法：如Dijkstra算法和Floyd算法，用于计算图中两个节点之间的最短路径。
-拓扑排序：通过对有向无环图进行排序，使得所有的边从排在前面的节点指向排在后面的节点。
- 最小生成树：如Prim算法和Kruskal算法，用于找到图中连接所有节点的最小子树。
5.动态规划：-最长公共子序列：通过寻找两个字符串中的最长公共子序列，解决字符串匹配问题。
-背包问题：通过动态规划解决在给定容量下选取物品使得总价值最大的问题。
-最大子序列和：通过动态规划解决一个数组中选取连续子序列使得和最大的问题。
以上只是一些C语言中常用的算法程序的汇总，实际上，还有很多其他的算法，如逆波兰表达式、霍夫曼编码、最小割等等。
通过学习这些算法，可以更好地理解C语言的应用和开发。
实验六函数及其使用1 学时4学时2 实验目的与要求学习函数的编写。
理解数学中的函数、自变量、函数在某一点的取值与 C++中的自定义函数、函数参数、函数调用及其返回值之间的联系，掌握 C++对数学函数功能的实现方式。
3 实验环境WINDOWS XP 或WINDOWS SERVER 2000Microsoft Visual C++ 6.04 准备工作安装好Microsoft Visual C++6.05 实验内容（一）．输入三个数，编写一个程序求这三个数的最大值和最小值。
要求把求最大值和最小值编写成函数。
#include <iostream.h>double max(double a,double b,double c);double min(double a,double b,double c);int main (){int a,b,c;cout <<"请输入三个数: " <<endl;cin >>a;cin >>b;cin >>c;cout <<"最大数的为: " <<max(a,b,c) <<endl;cout <<"最小的数为: " <<min(a,b,c) <<endl;return 0;}double max(double a,double b,double c){if (a>b && a>c) return a;if (b>a && b>c) return b;return c;}double min(double a,double b,double c){if (a<b && a<c) return a;if (b<a && b<c) return b;return c;}（二）编制如下自定义函数，实现指定功能。
目录2）一元二次方程求解............................................3）1-100之间所有整数的和，能被某数整除的所有整数的和，积......4）闰年的判断..................................................5）水仙花数....................................................6）简单计算器..................................................7）一维数组的声明、初始化、赋值、遍历（求数组所有元素的和，积，最大值，最小值等统计数值）...................................................8）二维数组的声明、初始化、赋值、遍历（求数组所有元素的和，积，最大值，最小值等统计数值）...................................................9）圆台的体积..................................................10）三角形的三边，求三角形的面积...............................11）乘法口诀表.................................................12）字符串的统计（大写，小写字母，数字的个数）.................13）数值类型的转换：数值-字符串，字符串-数字，数值类型之间的显示转换，隐式转换.............................................................14）遍历窗体上的组件...........................................15）随机数发生器的用法.........................................16）用判断成绩等级，改变窗体的背景颜色.........................17）用和求1-100之间所有整数的和，积等.........................18）类的创建和使用（类的声明，字段，属性和方法的添加，生成类的实例和使用其成员）...........................................................19）的用法.....................................................1）1( , e)s = (1());(s >= 90 s <= 100)("优秀");(s >= 80 s < 90)("良好");(s >= 70 s < 80)("中");(s >= 60 s < 70)("与格");("不与格");2）一元二次方程求解1( , e)a = (),b = (),c = ();(a 0)("方程的根是： " + ( / b)());= (b, 2) - 4 * a * c;( >= 0)X1 = ( + (, 0.5)) / 2 * a;X2 = ( - (, 0.5)) / 2 * a;= "X1="1()+"\r\2="2();("没有实数根！");3）1-100之间所有整数的和，能被某数整除的所有整数的和，积 1( , e)= 0;( i = 0; i <= 100; i = i + 1)= + i;1 = ();求1~100之内所有偶数的和= 0;( i = 0; i <= 100; i = i + 2)= + i;1 = ();1( , e)= 0;a;( i = 0; i <= 100; )a = i % 7;(a 0)= + i;1 = ();4）闰年的判断1( , e)a = 32(1);((a %40 a %1000) a %400 0)("是闰年");("不是闰年");或办法a = (1 );s = (a % 4 0 ? "该年份是闰年 ": "该年份是平年 " );(s )5）水仙花数1( , e)s = "水仙花数:"+"\r\n";( i = 100; i < 1000; )= i % 10;= i / 10 % 10;= i / 100;(i * * + * * + * * )s () + "\r\n";(s,"你好漂亮");6）简单计算器1( , e)1 = 32(1);2 = 32(3);(2 ("+"))((12)());(2 ("-"))((12)());(2 ("*"))((1*2)());(2 ("/"))((12)());(2 ("%"))((12)());("运算符出错");或办法a = (1);b = (3);s = 2;c = (s "+" ? a + b : (s "-" ? a - b : (s "*" ? a * b : (s "/" ? a / b :a % b))));7）一维数组的声明、初始化、赋值、遍历（求数组所有元素的和，积，最大值，最小值等统计数值）1( , e)1 "原数组为：" + "\r\n";[] a = [5];( i = 0; i < ; )a[i] = (0, 100);1 a[i]() + " ";= a[0], = a[0]; s = 0; = 0;( i = 0; i < ; )(a[i] > )= a[i];(a[i] < )= a[i];s a[i]; = s / ;1 ("\r\n最大值为{0}\r\n最小值为{1}\r\n均值为{2}\r\n和为{3}", , , , s);8）二维数组的声明、初始化、赋值、遍历（求数组所有元素的和，积，最大值，最小值等统计数值）2( , e)2 "原数组为：" + "\r\n";[,] b = [3, 4];( i = 0; i < 3; )( j = 0; j < 4; )b[i, j] = (-100,100);2 b[i, j]() + " , ";= b[0, 0], = b[0, 0]; s = 0; = 0;( i = 0; i < 3; )( j = 0; j < 4; )b[i, j] = (-100, 100);(b[i, j] > ) = b[i, j];(b[i, j] < ) = b[i, j];s b[i, j];= s / (3 * 4);2 ("\r\n最大值为{0}\r\n最小值为a{1}\r\n平均值为{2}\r\n和为{3}", , , , s);9）圆台的体积圆台体积计算公式V＝π*h*(R^2 + ^2)/3即：v = *h*（R*R + R* r *r）/31( , e)R = (1),r = (2),h = (3);π = 3.14;X1 = π * h * ((R, 2) + (r, 2) + R * r) / 3;v = "圆台体积是：" + X1();(v);10）三角形的三边，求三角形的面积1( , e)A = (1);B = (2);C = (3);d; f; s;(A + B > C & A + C > B & B + C > A & A - B < C & A - C < B &B -C < A)d = (A * A + C * C - B * B) / (2 * A * C);f = ((1 - d * d), 0.5);s = 0.5 * A * C * f;("三角形面积是："());("输入数据有误");11）乘法口诀表1( , e)= ""; = 0;199 = "";( i = 1; i < 10; )( j = 1; j <= i; )= i * j;( >= 10)199 + "\n";12）字符串的统计（大写，小写字母，数字的个数）1( , e)a = 1;( t a)(t >= '0' t <='9')(t >= 'a' t <= 'z')(t >= 'A' t <= 'Z')3 = ();4 = ();5 = ();13）数值类型的转换：数值-字符串，字符串-数字，数值类型之间的显示转换，隐式转换类型转换、隐式转换、显示转换、类的用法、方法主要以隐式转换为例(其他的类似求解)补充：1）何时使用隐式和显示转换？答：隐式转换一般发生在数据进行混合运算的情况下，是编译系统自动进行的，不需要加以声明;显示转换，又称为强制类型转换，该方式需要用户明确的指定转换的目标类型，该类型一般形式为: (类型说明符) （需要转换的表达式）二、类型转换隐式转换a; b; c; d; f; g; h; y;1( , e)b = 1;c = b;d = c; f = d; g = f;((), "转换1");2( , e)a = 2; c = a; d = c; f = d; g = f;((), "转换2");显示转换a; b; c; d; f; g; h; y;1( , e)a; b;a = 1.1111f;b = ()a;((), "郭浩);2( , e)a; b;a = 2.3m;b = ()a;3( , e)a; b;a = 1;b = ()a;31( , e)a; b;a = 94;b = (a);类的用法1( , e)a = "123";b = 32(a);2( , e)a = "456";3( , e)a = "789";b = (a);4( , e)a = "0";b = (a);方法a (1)(() );14）遍历窗体上的组件遍历组件代码如下= 0;= 0;= 0;= 0;( c )(c )= + 1;(c )= + 1;(c )= + 1;(c )= + 1;= "的数量：" + + "\r\n"+ "的数量：" + + "\r\n"+ "的数量：" + + "\r\n"+ "的数量：" + + "\r\n";(, "遍历组件", , , 1);运行截图15）随机数发生器的用法求浮点型数组最大元素1 = "生成数组：" + "\r\n";[] a = [5];r = ();( i = 0; i < ; )a[i] = (0, 1000);1 a[i]() + " ";= a[0], = a[0];( i = 0; i < ; )(a[i] > )= a[i];(a[i] < )= a[i];2 "最大值" + ();16）用判断成绩等级，改变窗体的背景颜色 1( , e)(s >= 0 s <= 100)(s / 10)0:1:2:3:4:5:("不与格");6:( "与格");10:( "优秀");("请输入正确的分数"); ( "请输入正确的分数");1( , e)s = 1;(s)"红":"黄":"蓝":"黑":"白":"绿":。
三整数排序c语言程序三整数排序C语言程序是一种常见的编程问题，通过编写程序可以将给定的三个整数按照从小到大的顺序进行排序。
下面是一个简单的示例程序：```c#include<stdio.h>//函数声明void sortNumbers(int*a,int*b,int*c);int main(){int a,b,c;//读取三个整数printf("请输入三个整数：");scanf("%d%d%d",&a,&b,&c);//调用排序函数sortNumbers(&a,&b,&c);//输出排序结果printf("排序结果为：%d%d%d\n",a,b,c);return0;}//函数定义void sortNumbers(int*a,int*b,int*c){ int temp;//使用冒泡排序法进行排序if(*a>*b){temp=*a;*a=*b;*b=temp;}if(*a>*c){temp=*a;*a=*c;*c=temp;}if(*b>*c){temp=*b;*b=*c;*c=temp;}}```以上是一个简单的使用冒泡排序法实现的三整数排序C语言程序。
程序首先通过`scanf`函数读取三个整数，并将它们传递给`sortNumbers`函数进行排序。
`sortNumbers`函数使用冒泡排序法对三个整数进行排序，最后将排序结果输出到屏幕上。
通过运行这个程序，可以得到输入的三个整数按照从小到大的顺序得到排序结果。
希望以上内容能够帮到你，如果有任何问题，请随时向我提问。
etemp=e;e=d;if(fabs(p)>=fabs(0.5*q*etemp)||p<=q*(a-x)||p>=q*(b-x)) d=CGOLD*(e=(x>=xm?a-x:b-x));The above conditions determine the acceptability of the parabolicfit.Here we take the golden section step into the larger of the two segments.else{d=p/q;Take the parabolic step.u=x+d;if(u-a<tol2||b-u<tol2)d=SIGN(tol1,xm-x);}}else{d=CGOLD*(e=(x>=xm?a-x:b-x));}u=(fabs(d)>=tol1?x+d:x+SIGN(tol1,d));fu=(*f)(u);This is the one function evaluation per iteration.if(fu<=fx){Now decide what to do with our func-tion evaluation.if(u>=x)a=x;else b=x;SHFT(v,w,x,u)Housekeeping follows:SHFT(fv,fw,fx,fu)}else{if(u<x)a=u;else b=u;if(fu<=fw||w==x){v=w;w=u;fv=fw;fw=fu;}else if(fu<=fv||v==x||v==w){v=u;fv=fu;}}Done with housekeeping.Back foranother iteration.}nrerror("Too many iterations in brent");*xmin=x;Never get here.return fx;}CITED REFERENCES AND FURTHER READING:Brent,R.P.1973,Algorithms for Minimization without Derivatives(Englewood Cliffs,NJ:Prentice-Hall),Chapter5.[1]Forsythe,G.E.,Malcolm,M.A.,and Moler,C.B.1977,Computer Methods for Mathematical Computations(Englewood Cliffs,NJ:Prentice-Hall),§8.2.10.3One-Dimensional Search with FirstDerivativesHere we want to accomplish precisely the same goal as in the previous section,namely to isolate a functional minimum that is bracketed by the triplet of abscissas(a,b,c),but utilizing an additional capability to compute the function’s first derivative as well as its value.Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press. P rograms Copyright (C) 1988-1992 by Numerical Recipes Software. Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copying of machine-readable files (including this one) to any server c omputer, is strictly prohibited. To order Numerical Recipes books, d iskettes, or CDROMs visit website or call 1-800-872-7423 (North America only), o r send email to trade@ (outside North America).In principle,we might simply search for a zero of the derivative,ignoring the function value information,using a rootfinder like rtflsp or zbrent(§§9.2–9.3). It doesn’t take long to reject that idea:How do we distinguish maxima from minima? Where do we go from initial conditions where the derivatives on one or both of the outer bracketing points indicate that“downhill”is in the direction out of thebracketed interval?We don’t want to give up our strategy of maintaining a rigorous bracket on the minimum at all times.The only way to keep such a bracket is to update it using function(not derivative)information,with the central point in the bracketing triplet always that with the lowest function value.Therefore the role of the derivatives can only be to help us choose new trial points within the bracket.One school of thought is to“use everything you’ve got”:Compute a polynomial of relatively high order(cubic or above)that agrees with some number of previous function and derivative evaluations.For example,there is a unique cubic that agrees with function and derivative at two points,and one can jump to the interpolated minimum of that cubic(if there is a minimum within the bracket).Suggested by Davidon and others,formulas for this tactic are given in[1].We like to be more conservative than this.Once superlinear convergence sets in,it hardly matters whether its order is moderately lower or higher.In practical problems that we have met,most function evaluations are spent in getting globally close enough to the minimum for superlinear convergence to commence.So we are more worried about all the funny“stiff”things that high-order polynomials can do (cf.Figure3.0.1b),and about their sensitivities to roundoff error.This leads us to use derivative information only as follows:The sign of the derivative at the central point of the bracketing triplet(a,b,c)indicates uniquely whether the next test point should be taken in the interval(a,b)or in the interval (b,c).The value of this derivative and of the derivative at the second-best-so-far point are extrapolated to zero by the secant method(inverse linear interpolation), which by itself is superlinear of order1.618.(The golden mean again:see[1],p.57.) We impose the same sort of restrictions on this new trial point as in Brent’s method. If the trial point must be rejected,we bisect the interval under scrutiny.Yes,we are fuddy-duddies when it comes to makingflamboyant use of derivative information in one-dimensional minimization.But we have met too many functions whose computed“derivatives”don’t integrate up to the function value and don’t accurately point the way to the minimum,usually because of roundoff errors, sometimes because of truncation error in the method of derivative evaluation.You will see that the following routine is closely modeled on brent in the previous section.#include<math.h>#include"nrutil.h"#define ITMAX100#define ZEPS1.0e-10#define MOV3(a,b,c,d,e,f)(a)=(d);(b)=(e);(c)=(f);float dbrent(float ax,float bx,float cx,float(*f)(float),float(*df)(float),float tol,float*xmin)Given a function f and its derivative function df,and given a bracketing triplet of abscissas ax, bx,cx[such that bx is between ax and cx,and f(bx)is less than both f(ax)and f(cx)], this routine isolates the minimum to a fractional precision of about tol using a modification of Brent’s method that uses derivatives.The abscissa of the minimum is returned as xmin,and Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press. P rograms Copyright (C) 1988-1992 by Numerical Recipes Software. Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copying of machine-readable files (including this one) to any server c omputer, is strictly prohibited. To order Numerical Recipes books, d iskettes, or CDROMs visit website or call 1-800-872-7423 (North America only), o r send email to trade@ (outside North America).Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press. P rograms Copyright (C) 1988-1992 by Numerical Recipes Software. Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copying of machine-readable files (including this one) to any server c omputer, is strictly prohibited. To order Numerical Recipes books, d iskettes, or CDROMs visit website or call 1-800-872-7423 (North America only), o r send email to trade@ (outside North America).the minimum function value is returned as dbrent ,the returned function value.{int iter,ok1,ok2;Will be used as flags for whether pro-posed steps are acceptable or not.float a,b,d,d1,d2,du,dv,dw,dx,e=0.0;float fu,fv,fw,fx,olde,tol1,tol2,u,u1,u2,v,w,x,xm;Comments following will point out only differences from the routine brent .Read that routine first.a=(ax <cx ?ax :cx);b=(ax >cx ?ax :cx);x=w=v=bx;fw=fv=fx=(*f)(x);dw=dv=dx=(*df)(x);All our housekeeping chores are dou-bled by the necessity of movingderivative values around as wellas function values.for (iter=1;iter<=ITMAX;iter++){xm=0.5*(a+b);tol1=tol*fabs(x)+ZEPS;tol2=2.0*tol1;if (fabs(x-xm)<=(tol2-0.5*(b-a))){*xmin=x;return fx;}if (fabs(e)>tol1){d1=2.0*(b-a);Initialize these d ’s to an out-of-bracket value.d2=d1;if (dw !=dx)d1=(w-x)*dx/(dx-dw);Secant method with one point.if (dv !=dx)d2=(v-x)*dx/(dx-dv);And the other.Which of these two estimates of d shall we take?We will insist that they be within the bracket,and on the side pointed to by the derivative at x :u1=x+d1;u2=x+d2;ok1=(a-u1)*(u1-b)>0.0&&dx*d1<=0.0;ok2=(a-u2)*(u2-b)>0.0&&dx*d2<=0.0;olde=e;Movement on the step before last.e=d;if (ok1||ok2){Take only an acceptable d ,and ifboth are acceptable,then takethe smallest one.if (ok1&&ok2)d=(fabs(d1)<fabs(d2)?d1:d2);else if (ok1)d=d1;elsed=d2;if (fabs(d)<=fabs(0.5*olde)){u=x+d;if (u-a <tol2||b-u <tol2)d=SIGN(tol1,xm-x);}else {Bisect,not golden section.d=0.5*(e=(dx >=0.0?a-x :b-x));Decide which segment by the sign of the derivative.}}else {d=0.5*(e=(dx >=0.0?a-x :b-x));}}else {d=0.5*(e=(dx >=0.0?a-x :b-x));}if (fabs(d)>=tol1){u=x+d;fu=(*f)(u);}else {u=x+SIGN(tol1,d);fu=(*f)(u);if (fu >fx){If the minimum step in the downhilldirection takes us uphill,then we are done.*xmin=x;return fx;}}du=(*df)(u);Now all the housekeeping,sigh. if(fu<=fx){if(u>=x)a=x;else b=x;MOV3(v,fv,dv,w,fw,dw)MOV3(w,fw,dw,x,fx,dx)MOV3(x,fx,dx,u,fu,du)}else{if(u<x)a=u;else b=u;if(fu<=fw||w==x){MOV3(v,fv,dv,w,fw,dw)MOV3(w,fw,dw,u,fu,du)}else if(fu<fv||v==x||v==w){MOV3(v,fv,dv,u,fu,du)}}}nrerror("Too many iterations in routine dbrent");return0.0;Never get here.}CITED REFERENCES AND FURTHER READING:Acton,F.S.1970,Numerical Methods That Work;1990,corrected edition(Washington:Mathe-matical Association of America),pp.55;454–458.[1]Brent,R.P.1973,Algorithms for Minimization without Derivatives(Englewood Cliffs,NJ:Prentice-Hall),p.78.10.4Downhill Simplex Method inMultidimensionsWith this section we begin consideration of multidimensional minimization, that is,finding the minimum of a function of more than one independent variable. This section stands apart from those which follow,however:All of the algorithms after this section will make explicit use of a one-dimensional minimization algorithm as a part of their computational strategy.This section implements an entirely self-contained strategy,in which one-dimensional minimization does notfigure.The downhill simplex method is due to Nelder and Mead[1].The method requires only function evaluations,not derivatives.It is not very efficient in terms of the number of function evaluations that it requires.Powell’s method(§10.5)is almost surely faster in all likely applications.However,the downhill simplex method may frequently be the best method to use if thefigure of merit is“get something working quickly”for a problem whose computational burden is small.The method has a geometrical naturalness about it which makes it delightful to describe or work through:A simplex is the geometricalfigure consisting,in N dimensions,of N+1 points(or vertices)and all their interconnecting line segments,polygonal faces,etc. In two dimensions,a simplex is a triangle.In three dimensions it is a tetrahedron, not necessarily the regular tetrahedron.(The simplex method of linear programming,Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press. P rograms Copyright (C) 1988-1992 by Numerical Recipes Software. Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copying of machine-readable files (including this one) to any server c omputer, is strictly prohibited. To order Numerical Recipes books, d iskettes, or CDROMs visit website or call 1-800-872-7423 (North America only), o r send email to trade@ (outside North America).。
