经典算法示例概要

经典算法示例//问题描述：有n个运动员进行比赛，但要求每个运动员与其他人进行一场比赛。

//每个运动员一天只能进行一场，且整个赛程在n-1天内结束程序（一）：#include<iostream.h>#include<iomanip.h>#include<math.h>#define N 1000int n;int A[N+1][N+1];void arrange(int n){ int i,j,n2;if(n==2) { A[1][0]=1;A[1][1]=2;A[2][0]=2;A[2][1]=1;} else { n2= n/2;arrange(n2);for (i=n2+1; i<=n;i++)for(j=0;j<=n2-1;j++) A[i][j]=A[i-n2][j]+n2;for (i=1; i<=n2;i++)for(j=n2;j<=n-1;j++)A[i][j]= A[i+n2][j-n2];for (i=n2+1; i<=n;i++)for(j=n2;j<=n-1;j++) A[i][j]=A[i-n2][j-n2];}}void print(){int i,j;for(i=1;i<=n;i++){cout<<endl;for(j=0;j<n;j++) cout<<setw(6)<<A[i][j];cout<<endl;}}void main(){cout<<"运动员个数n=";cin>>n;arrange(n);print();cout<<endl;}程序（二）：#include<iostream.h>#include<iomanip.h>#include<math.h>#define N 1000int n;int A[N+1][N+1];void arrange(int n){int i,j,k1,k2,m;A[1][0]=1;A[1][1]=2;A[2][0]=2;A[2][1]=1;k2=2;for (m=1;m<=ceil(log(n)/log(2))-1;m++ ){ k1=k2;k2=k2*2;for (i=k1+1;i<=k2;i++)for (j=0;j<=k1-1;j++) A[i][j]=A[i-k1][j]+k1;for (i=1;i<=k1;i++)for (j=k1;j<=k2-1;j++) A[i][j]=A[i+k1][j-k1];for (i=k1+1;i<= k2;i++)for( j=k1;j<=k2-1;j++) A[i][j]=A[i-k1][j-k1]; } }void print(){int i,j;for(i=1;i<=n;i++){cout<<endl;for(j=0;j<n;j++) cout<<setw(6)<<A[i][j];cout<<endl;}}void main(){cout<<"n=";cin>>n;arrange(n);print();cout<<endl;}//汗塔塔程序设计：程序（一）：#include<iostream.h>typedef struct snode{ int n;char a,b,c,cp;struct snode *next;} snode,*slink;void push(slink &s,int n,char a,char b,char c,int cp){ slink s1;s1=new snode;s1->n=n;s1->a=a;s1->b=b;s1->c=c;s1->cp=cp;s1->next=s;s=s1;}void pop(slink &s,int &n,char &a,char &b,char &c,int &cp){ slink s1;if(s){n=s->n;a=s->a;b=s->b;c=s->c;cp=s->cp;s1=s;s=s->next ;delete s1;}}int c=0;void move(char x,int n,char z){cout<<"第"<<++c<<"步: Move disk "<<n<<" from "<<x<<" to "<<z<<endl;}void hanoi(int n,char x,char y,char z){ int cp;slink s=NULL;char t;n10:;if (n==1) {move(x,1,z);goto n13;}else {push(s,n,x,y,z,11);n=n-1;t=y;y=z;z=t;goto n10;//hanoi(n-1,x,z,y);n11:;move(x,n,z);push(s,n,x,y,z,13);n=n-1;t=x;x=y;y=t;goto n10;//hanoi(n-1,y,x,z);}n13:;if (s) {pop(s,n,x,y,z,cp);if (cp==11) goto n11;if (cp==13) goto n13;}}void main(){hanoi(3,'A','B','C');}程序（二）：//递归编程#include<iostream.h>int c=0;void move(char x,int n,char z){cout<<"第"<<++c<<"步: Move disk "<<n<<" from "<<x<<" to "<<z<<endl;}void hanoi(int n,char x,char y,char z){ if (n==1) move(x,1,z);else {hanoi(n-1,x,z,y);move(x,n,z);hanoi(n-1,y,x,z);}}void main(){hanoi(3,'A','B','C');}//背包程序设计：程序（一）：#include<iostream.h>//#define N 1000void greedy_knapsack(){ float M,cu,temp;int n,i,j,k; float *p,*w,*pw,*x; int *a;cout<<"请输入码头货物种数n：";cin>>n;cout<<"请输入船队总吨位即背包容量M：";cin>>M;p=newfloat[n+1];w=newfloat[n+1];pw=new float[n+1];x=new float[n+1];a=new int[n+1];for(i=1;i<=n;i++){cout<<"请输入码头第"<<i<<"种货物的总重量w 和总运费p：";cin>>w[i]>>p[i];}for(i=1;i<=n;i++){pw[i]=p[i]/w[i];a[i]=i;}for(i=1;i<=n-1;i++){k=i;for(j=i+1;j<=n;j++) if (pw[j]>pw[k]) k=j;temp=pw[i];pw[i]=pw[k];pw[k]=temp;j=a[i];a[i]=a[k];a[k]=j;}for(i=1;i<=n;i++) x[i]=0;cu=M;i=1;while (w[a[i]]<=cu) {x[a[i]]=1;cu=cu-w[a[i]];i=i+1;} x[a[i]]=cu/w[a[i]];cout<<"该船队对这"<<n<<"种货物的本次运量比例向量如下:\n(";for(i=1;i<n;i++) cout<<x[i]<<",";cout<<x[n]<<")"<<endl;}main(){greedy_knapsack();}程序（二）：#include<iostream.h>#define N 1000void greedy_knapsack(){ float p[N],w[N],pw[N],x[N],M,cu,temp;int n,i,j,k,a[N];cout<<"请输入码头货物种数n(<"<<N<<")：";cin>>n;cout<<"请输入船队总吨位即背包容量M：";cin>>M;for(i=1;i<=n;i++){cout<<"请输入码头第"<<i<<"种货物的总重量w 和总运费p：";cin>>w[i]>>p[i];}for(i=1;i<=n;i++){pw[i]=p[i]/w[i];a[i]=i;}for(i=1;i<=n-1;i++){k=i;for(j=i+1;j<=n;j++) if (pw[j]>pw[k]) k=j;temp=pw[i];pw[i]=pw[k];pw[k]=temp;j=a[i];a[i]=a[k];a[k]=j;}for(i=1;i<=n;i++) x[i]=0;cu=M;i=1;while (w[a[i]]<=cu) {x[a[i]]=1;cu=cu-w[a[i]];i=i+1;}x[a[i]]=cu/w[a[i]];cout<<"该船队对这"<<n<<"种货物的本次运量比例向量如下:\n(";for(i=1;i<n;i++) cout<<x[i]<<",";cout<<x[n]<<")"<<endl;}void main(){greedy_knapsack();}动态程序设计：#include<iostream.h>#include<iomanip.h>#define N 100//此处MAX设为2的31次幂减1，是有符号长整数的最大值，即2147483647#define MAX 32768*65536-1int r[N+1];long int D[N+1][N+1];void DM(int n){int i,j,k;long int T;for(i=1;i<=n-1;i++)for(j=1;j<=n-i;j++){D[j][j+i]=MAX;for(k=0;k<=i-1;k++){T=D[j][j+k]+D[j+k+1][j+i]+r[j-1]*r[j+k]*r[j+i];if(T<D[j][j+i]){D[j][j+i]=T;D[j+i][j]=j+k;}}}}void p(int i,int j) {int t;if (i==j) cout<<"(M"<<i<<")";else if (i+1==j) cout<<"(M"<<i<<"M"<<j<<")";else {t=D[j][i];cout<<"(";p(i,t);p(t+1,j);cout<<")";} }void main(){int i,j,n;cout<<"n=";cin>>n;cout<<"Please input r0,r1,r2,...,rn:";for (i=0;i<=n;i++) cin>>r[i];DM(n);p(1,n);cout<<endl;for(i=1;i<=n;i++){cout<<endl;for(j=1;j<=n;j++) cout<<setw(8)<<D[i][j];} }排列程序：程序一：#include<iostream.h>#include<iomanip.h>#define maxn 100int n;char list[maxn+1];void print() {int i;cout<<endl;for(i=1;i<=n;i++) cout<<setw(3)<<list[i];}void permu(int m){int k;char t;if (m==1) print();else { k=m;n9:if (k<1) goto n2;t=list[k];list[k]=list[m];list[m]=t;permu(m-1);t=list[k];list[k]=list[m];list[m]=t;k--;goto n9;n2:;}}void main(){ int i;cout<<"n=";cin>>n;for(i=1;i<=n;i++) cin>>list[i];//for(i=1;i<=n;i++) cout<<list[i];permu(n);cout<<endl;}程序二：#include<iostream.h>#include<iomanip.h>#define maxn 100typedef struct snode{ int k,m,cp;struct snode *next;} snode,*slink;void push(slink &s,int k,int m,int cp){slinks1;s1=newsnode;s1->k=k;s1->m=m;s1->cp=cp;s1->next=s ;s=s1;}void pop(slink &s,int &k,int &m,int &cp){slinks1;if(s){k=s->k;m=s->m;cp=s->cp;s1=s;s=s->next;delete s1;}} int n;char list[maxn+1];void print(){int i;cout<<endl;for(i=1;i<=n;i++) cout<<setw(3)<<list[i];}void permu(int m){int k,cp;char t;slink s;s=NULL;n10:;if (m<=1) {print();goto n13;}else { k=m;n9:if (k<1) goto n2;t=list[k];list[k]=list[m];list[m]=t;push(s,k,m,11);m=m-1;goto n10;//permu(m-1);n11:;t=list[k];list[k]=list[m];list[m]=t;k--;goto n9;n2:;}n13:; if (s) {pop(s,k,m,cp);goto n11;}}void main(){int i;cout<<"n=";cin>>n;for(i=1;i<=n;i++) cin>>list[i];//for(i=1;i<=n;i++) cout<<list[i];permu(n);cout<<endl;}程序三：#include<iostream.h>#include<iomanip.h>#define maxn 100typedef struct snode{ int k,m;struct snode *next;} snode,*slink;void push(slink &s,int k,int m){slinks1;s1=new snode;s1->k=k;s1->m=m;s1->next=s;s=s1;}void pop(slink &s,int &k,int &m){ slink s1;if (s) {k=s->k;m=s->m;s1=s;s=s->next;delete s1;}}int n;char list[maxn+1];void print() {int i;cout<<endl;for(i=1;i<=n;i++) cout<<setw(3)<<list[i]; }void permu(int m){int k;char t;slink s;s=NULL;n10:;if (m<=1) {print();goto n13;}else { k=m;n9:if (k<1) goto n2;t=list[k];list[k]=list[m];list[m]=t;push(s,k,m);m=m-1;goto n10;//permu(m-1);n11:;t=list[k];list[k]=list[m];list[m]=t;k--;goto n9;n2:;}n13:; if (s) {pop(s,k,m);goto n11;}}Void main(){int i;cout<<"n=";cin>>n;for(i=1;i<=n;i++) cin>>list[i];//for(i=1;i<=n;i++) cout<<list[i];permu(n);cout<<endl;}程序四：#include<iostream.h>#include<iomanip.h>#define maxn 100int n;char list[maxn+1];void print() {int i;cout<<endl;for(i=1;i<=n;i++) cout<<setw(3)<<list[i]; }void permu(int m){int k;char t;if (m==1) print();else for(k=m;k>=1;k--){t=list[k];list[k]=list[m];list[m]=t;permu(m-1);t=list[k];list[k]=list[m];list[m]=t;} }Void main(){int i;cout<<"n=";cin>>n;for(i=1;i<=n;i++) cin>>list[i];//for(i=1;i<=n;i++) cout<<list[i];permu(n);cout<<endl;}Prog1:#define maxn 1000int n,a[maxn];permute(int k) {int p,q;for (p=1;p<=n;p++){for (q=1;q<k;q++) if (p==a[q]) goto next;a[k]=p;if (k<n) permute(k+1);else {printf("\n");for (q=1;q<=n;q++) printf("%3d",a[q]);}next:;}}Void main(){printf("n=?");scanf("%d",&n);permute(1);}组合程序:#define maxn 1000int n,r,a[maxn];combination(int k){int p,q;for (p=a[k-1]+1;p<=n;p++){a[k]=p;if (k<r) combination(k+1);else {printf("\n");for (q=1;q<=r;q++) printf("%3d",a[q]);}}}main(){ printf("n,r=?");scanf("%d%d",&n,&r);a[0]=0;combination(1);}//皇后问题#define maxn 1000int n,a[maxn];queen(int k) {int p,q;for (p=1;p<=n;p++){for (q=1;q<k;q++){if (p==a[q]) goto next;if (abs(q-k)==abs(a[q]-p)) goto next;}a[k]=p;if (k<n) queen(k+1);else {printf("\n");for (q=1;q<=n;q++) printf("%3d",a[q]);}next:;}}main(){printf("n=?");scanf("%d",&n);queen(1);}Prog41://砝码问题（贪婪算法）#include<iostream.h>#include<iomanip.h>#define maxn 1000#define maxw 10000int n;int p[maxn+1],a[maxn+1],c[maxw+1];void weight(int k){int j,s;a[k]=p[k];do{if (k<n) weight(k+1);else {s=0;for(j=1;j<=n;j++) s=s+a[j];if (s>0)if (c[s]==0){for(j=1;j<=n;j++)cout<<setw(4)<<a[j];cout<<"---"<<s<<endl;c[s]=1;}}a[k]=a[k]-p[k];}while(a[k]>=-p[k]);}Void main(){int i;cout<<"n=";cin>>n;for(i=1;i<=n;i++){cout<<"p["<<i<<"]=";cin>>p[i];} for(i=1;i<=maxw;i++) c[i]=0;weight(1);}prog42://马步问题#include<iostream.h>#include<iomanip.h>#define NN 100int n;int a[]={2,1,-1,-2,-2,-1,1,2};int b[]={1,2,2,1,-1,-2,-2,-1};long int h[NN+1][NN+1],q;int try1(int x,int y){int k,u,v;for(k=0;k<8;k++){u=x+a[k];v=y+b[k];if (u>0&&u<=n&&v>0&&v<=n)if (h[u][v]==0) {h[u][v]=q;if (q<n*n) {q++;if(try1(u,v))return1;else{h[u][v]=0;q--;goto next;} }else return 1; }next:;}return 0;}void print(){int i,j;for(i=1;i<=n;i++){cout<<endl;for(j=1;j<=n;j++) cout<<setw(6)<<h[i][j];cout<<endl;}cout<<endl;}main(){int i,j,x0,y0;cout<<"n=";cin>>n;//cout<<"x0,y0=";cin>>x0>>y0;for (x0=1;x0<=n;x0++)for (y0=1;y0<=n;y0++){for(i=1;i<=n;i++) for(j=1;j<=n;j++) h[i][j]=0;q=1;h[x0][y0]=q++;if (try1(x0,y0)) print();}}Prog43://马步问题#include<iostream.h> #include<iomanip.h>#define NN 100int n;int a[]={2,1,-1,-2,-2,-1,1,2};int b[]={1,2,2,1,-1,-2,-2,-1};long int h[NN+1][NN+1];char temp[5];void print() {int i,j;for(i=1;i<=n;i++){cout<<endl;for(j=1;j<=n;j++) cout<<setw(6)<<h[i][j];cout<<endl;}cout<<endl;}int try1(int i,int x,int y){int k,u,v;for(k=0;k<8;k++){u=x+a[k];v=y+b[k];if (u>0&&u<=n&&v>0&&v<=n)if (h[u][v]==0) {h[u][v]=i;if (i<n*n) if (try1(i+1,u,v)) return 1;else{h[u][v]=0;gotonext;}else return1; }next:;}return 0;}Void main(){int i,j,x0,y0;cout<<"n=";cin>>n;//cout<<"x0,y0=";cin>>x0>>y0;for (x0=1;x0<=n;x0++)for (y0=1;y0<=n;y0++){for(i=1;i<=n;i++) for(j=1;j<=n;j++) h[i][j]=0;h[x0][y0]=1;if (try1(2,x0,y0)) print();}}。