1、n项多项式求和
s=1/1x2/1…1/(2n-1)x(2n/(2n-1))
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#define N 5
int main() {
int n;
float term=1,sum=0.0;//初始化term和s的值
for(n=1;term>1e-6;n++){ //精度控制在le-6
term=(1.0/(2*n-1))*(2*n/(2*n-1));
sum+=term;
}
printf("%f",sum);
return 0;
}
2、nn魔方矩阵实现每行、每列、每一对角线上的元素之和相等 (将1~nn每一个元素放到合适位置)
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#define N 15
int main() {
int a[N][N]= {0};
int k;
printf("请输入魔方矩阵k=");
scanf("%d",&k);
while(1) {
if(k%2==0) {
printf("魔方阶数只能为奇数,请重新输入\n");
scanf("%d",&k);
} else {
break;
}
}
int i,j,m,n;//m、n用于暂时存放上一次i、j
i=0,j=k/2;
a[i][j]=1;//初始位置为第一行、中间列
for(int x=2; x<=k*k; x++) {
m=i,n=j;
i--,j++;//向45°右上方移动也就是行减1,列加1
if(i<0)i=k-1;//如果已经在第一行,那么下一次移动到最后一行
if(j>=k)j=0; //如果已经在第n列,下一次移动到第一列
if(a[i][j]!=0) {
//如果该位置已经有元素占领,则存放在下个位置
i=m+1;
j=n;
}
a[i][j]=x;
}
for(int i=0; i<k; i++) {
for(int j=0; j<k; j++) {
printf("%d ",a[i][j]);
}
printf("\n");
}
return 0;
}
3、 求前20项和 2/1+3/2+5/3…13/8+21/13
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#define N 15
int main() {
int i,n=20;
float a=2,b=1,s=0,t;//a是分子,b是分母
for(int i=0;i<n;i++){
s+=(a/b);
t=a;
a+=b;//分子为前一项分子和分母之和
b=t; //分母为前一项分子
}
printf("%f",s);//32.660263
return 0;
}
4、第一项为2 第二项为3
序列最后两项乘积<10,则最后项为两项乘积
如果最后两项乘积>10,则拆分十位和个位,分别位新的两项
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#define N 15
int main() {
int n,cnt,i=2;
int a[100];
a[0]=2,a[1]=3;
while(cnt!=100) {
int t=a[i-1]*a[i-2];
if(t<10) {
a[i++]=t;
cnt+=1;
} else {
a[i++]=t/10;
a[i++]=t%10;
cnt+=2;
}
}
for(int i=0;i<100;i++){
printf("%d ",a[i]);
}
return 0;
}
5、调和级数 1/1+1/2+1/3+…+1/n 的前n项和,要求用分数
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#define N 15
int gcb(int x,int y) {
return y==0?x:gcb(y,x%y);
}
int main() {
int n,u=1,v=1;//n为级数项数、u为分子、v为分母
scanf("%d",&n);
for(int i=2; i<=n; i++) {
//通分求和
u=u*i+1*v;
v*=i;
int g=gcb(u,v);//用最大公约数,约分
u/=g;
v/=g;
printf("%d/%d ",u,v);
}
return 0;
}
6、求出sinx的近似值 sinx用级数展开
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#define N 15
int func(int n) {
int k=1;
for(int i=1; i<=n; i++) {
k=k*i;
}
return k;
}
int main() {
int x,n,sign=1;
double term,s=0;
scanf("%d",&x);
term=x;
for(n=1; term>5e-6; n+=2) { //每一项为奇数项
term=pow(x,n)/func(n);
s=s+sign*term;
sign=-sign;
}
printf("sin%d的近似值为: %.8lf",x,s);
return 0;
}
求级数 1/1-1/2+1/3+…+1/n
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#define N 15
int main() {
int n,sign=1;//设置负号变量
scanf("%d",&n);
float s=0;
for(int i=1;i<=n;i++){
s+=(float)sign/i;
sign=-sign;
}
printf("%f",s);
return 0;
}
7、输出分母小于或者等于n的最简真分数(不能约分),并且从小到大排序输出
n=5 1/5 1/4 1/3 2/5 1/2 3/5 2/3 3/4 4/5
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#define maxn 999
struct struct_result {
int numerator;//分子
int denominator;//分母
float result;//分数
bool operator <(const struct_result x) {
return result<=x.result;
}
} list[maxn];
int length;
int gcb(int x,int y) {
return y==0?x:gcb(y,x%y);
}
//快排
int partiton(struct_result list[],int low,int high) {
struct_result pivot=list[low];
while(low<high&&list[high].result>=pivot.result)high--;
list[low]=list[high];
while(low<high&&list[low].result<=pivot.result)low++;
list[high]=list[low];
list[low]=pivot;
return low;
}
void quick_sort(struct_result list[],int low,int high) {
if(low<high) {
int pivotPos=partiton(list,low,high);
quick_sort(list,low,pivotPos-1);
quick_sort(list,pivotPos+1,high);
}
}
int main() {
int n;
scanf("%d",&n);
for(int i=1; i<=n; i++) { //枚举分子和分母
for(int j=i+1; j<=n; j++) {
if(gcb(i,j)==1) {
//如果为最简真分数则添加进入数组
list[length].numerator=i;
list[length].denominator=j;
list[length++].result=(float)i/j;
}
}
}
quick_sort(list,0,length-1);
for(int i=0; i<length; i++) {
printf("%d/%d ",list[i].numerator,list[i].denominator);
if(i+1%10==0)printf("\n");//每十个换行
}
return 0;
}
8、对100个点相互组合组成的线段求出距离最小的长度
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#define maxn 999
struct point{
int x,y;
}point[maxn];
int dis(struct point a,struct point b){
return (a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y);
}
int main() {
for(int i=0;i<100;i++){
scanf("%d%d",&point[i].x,&point[i].y);
}
int mind=0x7f7f7f7f;
for(int i=0;i<100;i++)
for(int j=i+1;j<100;j++){
if(dis(point[i],point[j])<mind){
mind=dis(point[i],point[j]);
}
}
printf("maxdis=",sqrt(mind));
return 0;
}
9、给出100个点,任意三个点组成三角形,求这些三角形的最大面积是多少
给出三个点,可以用向量来做,利用叉积=|a|x|b|xsina 等于平行四边面积为对于三角型面积二倍来求出三角形
也可以利用海伦公式,求出周长为2p 利用海伦公式s=根号下px(p-x)x(p-y)x(p-z)
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#define maxn 999
typedef struct Point{
double x,y;
}Point;
Point decPoint(Point p1,Point p2){ //将坐标转换为向量
Point ret;
ret.x=p1.x-p2.x;
ret.y=p1.y-p2.y;
return ret;
}
double multiPoint(Point p1,Point p2){//叉乘=x2y1-x1y2
return p1.x*p2.y-p1.y*p2.x;
}
double areaByThreePoint(Point A,Point B,Point C){ //三角形面积
return fabs(multiPoint(decPoint(A,B),decPoint(B,C)));
}
int main() {
int i,j,k;
double maxarea;
Point pts[110];
for(int i=0;i<100;i++){
scanf("%lf%lf",&pts[i].x,&pts[i].y);
}
maxarea=areaByThreePoint(pts[0],pts[1],pts[2]);
for(i=0;i<100;i++){
for(j=i+1;j<100;j++){
for(k=j+1;k<100;k++){
double t=areaByThreePoint(pts[i],pts[j],pts[k]);
if(maxarea<t)maxarea=t;
}
}
}
printf("面积最大为:%.2lf",maxarea/2.0);
return 0;
}
10、给出100个圆的圆心坐标和半径,判断哪些圆相切,将相切的圆用一个链表相连接,链表中存放圆的编号
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#define maxn 999
typedef struct node{
int m,n;
struct node* next;
}Node;
typedef struct circle{
int x,y;
double r;
}Circle;
bool isQie(circle a,circle b){
double dis=(a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y);//圆心直接距离的平方
if(pow(a.r+b.r,2)==dis)return true;
return false;
}
int main() {
Node* head,p;
Circle cir[110];
for(int i=0;i<100;i++){
scanf("%d%d%f",cir[i].x,cir[i].y,cir[i].r);
}
for(int i=0;i<100;i++){
for(int j=i+1;j<100;j++){
if(isQie(cir[i],cir[j])){
p=(Node*)malloc(sizeof(Node));//头插法
p->m=i;
p->n=j;
p->next=head;
head=p;
}
}
}
return 0;
}
11、求解二元一次方程 ax^2+bx+c=0
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#define maxn 999
int main() {
double a,b,c,disc,x1,x2;
scanf("%lf%lf%lf",&a,&b,&c);
if(fabs(a)<1e-6)printf("不是二元一次方程");//a=0
else{
disc=b*b-4*a*c;//判断几个实根
if(fabs(disc)<=1e-6)printf("%f",-b/(2*a));//只有一个根
else if(fabs(disc)>1e-6){
x1=(-b+sqrt(disc))/(2*a);
x2=(-b-sqrt(disc))/(2*a);
printf("两个解分别为%lf,%lf",x1,x2);
}else{
printf("无解");//disc<0
}
}
return 0;
}
12、利用二分法找到 2x^3- 4x^3+3x-6=0 位于-10~10直接的一个跟 x=3
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#define eps 1e-6
double f(double x){
return 2*x*x*x-4*x*x+3*x-6;
}
int main() {
double m=-10,n=10;
double i,s,k;
if(f(m)*f(n)<0){
while(fabs(m-n)>eps){//两个端点不相同
i=(m+n)/2;
s=f(i);
if(fabs(s)<eps)break;
else if(f(i)*f(m)<0)n=i;
else if(f(i)*f(n)<0)m=i;
}
}
printf("%lf%lf",m,n);
k=(m+n)/2;
printf("%lf",k);
return 0;
}
13、利用牛顿迭代法求12题根,x1=1.5
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#define eps 1e-6
float fun(float x){
return 2*x*x*x-4*x*x+3*x-6;
}
float fun1(float x){
return 6*x*x-8*x+3;
}
int main() {
float x1=1.5,x2=x1-fun(x1)/fun1(x1); //根据斜率公式表示新的与x轴交点x2
while(fabs(x1-x2)>1e-8){
x1=x2;
x2=x1-fun(x1)/fun1(x1);
}
printf("%f",x2);
return 0;
}
14、判断某点是否在三角形内部
利用叉乘,判断D点是否在AB BC CA 的左侧, 分别CA 与AD做叉乘,AB 与BD做叉乘,BC与CD做叉乘,判断符号是否相同
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#define eps 1e-6
typedef struct Point{
double x,y;
}Point;
Point decPoint(Point p1,Point p2){ //定义向量
Point ret;
ret.x=p1.x-p2.x;
ret.y=p1.y-p2.y;
return ret;
}
double multiPoint(Point ver1,Point ver2){ //叉乘
return (ver1.x*ver2.y-ver1.y*ver2.x);
}
int sign(double x){ //判断符号
if(fabs(x)<eps)return 0;//等于0
else if(x>0)return 1;
return 0;
}
int main() {
Point points[4];// A B C D
for(int i=0;i<4;i++){
scanf("%lf%lf",&points[i].x,&points[i].y);
}
int sgn[3];//存放三个叉乘后向量的符号
//叉乘向量 CA 和 AD
Point CA=decPoint(points[0],points[2]);
Point AD=decPoint(points[3],points[0]);
double verA=multiPoint(CA,AD);
sgn[0]=sign(verA);
printf("%lf\n",verA);
//叉乘 AB BD
Point AB=decPoint(points[1],points[0]);
Point BD=decPoint(points[3],points[1]);
double verB=multiPoint(AB,BD);
sgn[1]=sign(verB);
printf("%lf\n",verB);
//叉乘 BC CD
Point BC=decPoint(points[2],points[1]);
Point CD=decPoint(points[3],points[2]);
double verC=multiPoint(BC,CD);
sgn[2]=sign(verC);
printf("%lf\n",verC);
if(sgn[0]==0||sgn[1]==0||sgn[2]==0)printf("Point D is on the triangle!"); //在边上或者延长线上
else if(sgn[0]==sgn[1]&&sgn[1]==sgn[2]) printf("Point D is in the triangle!");
else printf("Point D is out of the triangle!");
return 0;
}
15、递归编写函数,求出数组中所有数的和
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#define eps 1e-6
int sum(int n,int a[]){
if(n==1)return a[0];
return sum(n-1,a)+a[n-1];
}
int main() {
int a[10]={1,2,3,4,5,6,7,8,9,10};
printf("%d",sum(10,a));
return 0;
}
16、利用递归求出一个整数个个位数之和
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#define eps 1e-6
int sum(int n){
if(n<10)return n;
return n%10+sum(n/10);
}
int main() {
int n=1031;
printf("%d",sum(n));
return 0;
}
17、一根木条在五分之二处截断, 将剩余木条也在五分至二处截断,知道所有木条长度均小于5,求出一个折成多少木条
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#define eps 1e-6
int f(double n){
if(n<=5)return 1;
return f(2*n/5)+f(3*n/5);
}
int main() {
printf("%d",f(6));
return 0;
}
18、读入文件中学生成绩,将学生成绩用一个链表有高分到低分排列起来,一边读入,一边排序
#include<stdio.h>
#include<stdlib.h> //malloc
typedef struct Grade{
int num;
char name[20];
int disscore;
int repscore;
int testscore;
int totscore;
struct Grade* next;
}GradeNode,*GradeList;
int main() {
FILE* fpin=fopen("2018Exp.txt","r");//打开文件
GradeList head;
head->next=NULL;
GradeNode* gNode;
while(!feof(fpin)){ //如果文件不为空
gNode=(GradeNode*)malloc(sizeof(GradeNode));
fscanf(fpin,"%d",&gNode->num);
fscanf(fpin,"%s",&gNode->name);
fscanf(fpin,"%d",&gNode->disscore);
fscanf(fpin,"%d",&gNode->repscore);
fscanf(fpin,"%d",&gNode->testscore);
gNode->totscore=(int)(0.2*gNode->disscore+0.2*gNode->repscore+0.6*gNode->testscore);
GradeNode* p=head->next;//p为当前节点
GradeNode* q=head;//q为p的前一个节点
while(p&&p->totscore>gNode->totscore){//找到gNode所在合适的位置
p=p->next;
q=q->next;
}
q->next=gNode;
gNode->next=p;
}
fclose(fpin);//关闭文件
return 0;
}
19、从键盘接收学生个数、学生数据返回一个学生链表,学号由小到大排名,将链表写入文件
#include<stdio.h>
#include<stdlib.h> //malloc
typedef struct Student{
int stuNum;
int score;
char sex;
char name[20];
struct Student* next;
}Student,*StuList;
StuList head=NULL;//设置头节点
StuList CreateList(int n){
Student* stu;
while(n){
stu=(Student*)malloc(sizeof(Student));
scanf("%d%d",&stu->stuNum,&stu->score);
scanf("%c",&stu->sex);
scanf("%s",&stu->name);
Student *p=head->next;
Student *q=head;
while(p&&p->stuNum<stu->stuNum){
p=p->next;
q=q->next;
}
q->next=stu;
stu->next=p;
n--;
}
return head;
}
bool WriteFile(StuList stuList){
FILE* fpin;
if((fpin=fopen("output.txt","w"))==NULL){
printf("FILE Open Error!");
return false;
}
while(stuList){
fprintf(fpin,"%d ",stuList->stuNum);
fprintf(fpin,"%d ",stuList->score);
fprintf(fpin,"%c ",stuList->sex);
fprintf(fpin,"%s\n ",stuList->name);
stuList=stuList->next;
}
fclose(fpin);
return true;
}
int main() {
int n;
printf("请输入学生个数: ");
scanf("%d",&n);
head=CreateList(n);
WriteFile(head);
return 0;
}
20、将小写字母转换为大写字母,并且写入文件中
#include<stdio.h>
#include<stdlib.h> //malloc
int main() {
FILE *fpin;
char str[100];
printf("请输入字符串: \n");
gets(str);
int i=0;
while(str[i]!='\0'){
if(str[i]>='a'&&str[i]<='z'){
str[i]=str[i]-'a'+'A';
}
i++;
}
if((fpin=fopen("test.txt","w"))==NULL){
printf("无法打开文件\n");
} else{
fputs(str,fpin);
fclose(fpin);
}
return 0;
}
21、创建学生链表,将指定年龄的学生删除,将删除后的链表写入文件
#include<stdio.h>
#include<stdlib.h> //malloc
typedef struct Student{
int num;
int age;
char name[20];
struct Student * next;
}Student,*StuList;
StuList head;
StuList CreateList(int n){ //创建带头结点的单链表
Student *p,*r=head;
while(n){ //尾插法
p=(Student*)malloc(sizeof(Student));
scanf("%d%d%s",&p->num,&p->age,&p->name);
r->next=p;
r=p;
n--;
}
r->next=NULL;
return head;
}
void save(StuList list,int age){
FILE *file;
if((file=fopen("output.txt","w"))==NULL)printf("File Open Error!");
Student *p=list->next;
Student *q=list;
while(p){
if(p->age==age){ //删除节点
q=p->next;
free(p);
p=q->next;
}
}
p=head->next;
while(p){
fprintf(file,"%5d\n",p->num);
fprintf(file,"%s\n",p->name);
fprintf(file,"5d\n",p->age);
p=p->next;
}
fclose(file);
}
int main() {
StuList list=CreateList(10);
save(list,20);
return 0;
}
22、从键盘读入学生链表,进行冒泡排序,在从文件读入一个学生链表进行冒泡排序,最后将两个链表归并排序
#include<stdio.h>
#include<stdlib.h>
typedef struct Student{
int num;
char name[10];
int grade;
struct Student* next;
}Student,*StuList;
void BubbleSort(StuList list){ //传入带头节点的链表
bool flag=true;
Student *p,*q,*r;
while(flag){ // q p r 相对关系
q=list;
p=list->next;
r=p->next;
flag=false;
while(r){
if(p->grade>r->grade){
p->next=r->next;//交换节点
r->next=p;
q->next=r;
p=r;//调回相对关系
r=p->next;
flag=true;
}
q=p;
p=r;
r=r->next;
}
}
}
StuList CreateList(int n){
StuList head=(Student*)malloc(sizeof(Student));
head->next=NULL;
Student *p;
while(n){
p=(Student*)malloc(sizeof(Student));
printf("请输入学生学号: ");
scanf("%d",&p->num);
printf("请输入学生姓名: ");
scanf("%s",&p->name);
printf("请输入学生成绩: ");
scanf("%d",&p->grade);
p->next=head->next;
head->next=p;//头插法
n--;
}
return head;
}
//按照学生成绩打印信息
void PrintList(StuList list){
StuList p=list->next;
while(p){
printf("%d-->",p->grade);
p=p->next;
}
printf("\n");
}
StuList ReadList(int n){
FILE *fpin;
if((fpin=fopen("in.txt","r"))==NULL){
printf("File Open Error!");
exit(0);
}
StuList head;
Student *p;
while(n--){
p=(Student*)malloc(sizeof(Student));
fscanf(fpin,"%d%s%d",&(p->num),&(p->name),&(p->grade));
p->next=head; //尾插法
head=p;
}
fclose(fpin);
return head;
}
//递归的Merge
StuList Merge(Student *pHead1,Student *pHead2){
if(pHead1==NULL){
return pHead2;
}
if(pHead2==NULL){
return pHead1;
}
Student* head=(Student*)malloc(sizeof(Student));
if(pHead1->grade<pHead2->grade){
head=pHead1;
head->next=Merge(pHead1->next,pHead2);
}else{
head=pHead2;
head->next=Merge(pHead1,pHead2->next);
}
return head;
}
int main() {
int n;//学生个数
printf("请输入学生个数: ");
scanf("%d",&n);
StuList list1=CreateList(n);
PrintList(list1);
BubbleSort(list1);
printf("请输入学生个数: ");
scanf("%d",&n);
StuList list2=CreateList(n);
PrintList(list2);
BubbleSort(list2);//冒泡排序
printf("Merge两个链表\n");
StuList list=(Student*)malloc(sizeof(Student));
list->next=Merge(list1->next,list2->next);
PrintList(list);
return 0;
}