算法导论 第15章 动态规划 习题C++实现

chapter15_exercise.h

#ifndef CHAPTER15_EXERCISE_H#define CHAPTER15_EXERCISE_H//the excercise of chapter 15#include<vector>#include<iostream>#include<algorithm>#include<math.h>const int POS_INFI=1000;const int NEG_INFI=-1000;/*class matrix<type>*///自定义的matrix模板类//使用std::vector<type>做容器template<class type>class matrix{public:matrix();matrix(int i, int j);matrix(const matrix& rhs);//matrix& operator=(const matrix& rhs);//friend matrix<type>& operator+(const matrix<type>& lhs, const matrix<type>& rhs);//friend Matirx<type>& operator-(const matrix<type>& lhs, const Matirx<type>& rhs);const type& operator()(const int i, const int j) const;type& operator()(const int i, const int j);const int row()const{ return size1; }const int col()const{ return size2; }private:std::vector<type> mx;int size1;int size2;};template<class type>matrix<type>::matrix(int size1_rhs, int size2_rhs) :size1(size1_rhs),size2(size2_rhs){mx.resize(size1_rhs*size2_rhs);}template<class type>const type& matrix<type>::operator()(int i, int j) const{return mx[i*size2 + j];}template<class type>type& matrix<type>::operator()(int i, int j){return mx[i*size2 + j];}//no member funtiontemplate<class type>std::ostream& operator<<(std::ostream& os, const matrix<type>& m){for (int i = 0; i < m.row(); i++){for (int j = 0; j < m.col(); j++)os << m(i, j) << "\t";os << std::endl;}return os;}template<class type>matrix<type>& operator+(const matrix<type>& lhs, const matrix<type>& rhs){matrix<type> mx_rtn(lhs);for (int i = 0; i < lhs.size1(); i++)for (int j = 0; j < lhs.size2(); j++)mx_rtn(i, j) = lhs(i, j) + rhs(i, j);return mx_rtn;}template<class type>matrix<type>& operator-(const matrix<type>& lhs, const matrix<type>& rhs){matrix<type> mx_rtn(lhs);for (int i = 0; i < lhs.size1(); i++)for (int j = 0; j < lhs.size2(); j++)mx_rtn(i, j) = lhs(i, j) - rhs(i, j);return mx_rtn;}/*class matrix<type>*///15-2void palindrome(const std::vector<char>& x, matrix<int>& c, matrix<int>& b){int n = x.size() - 1;for (int i = 1; i <= n; i++)c(i, i) = 1;for (int l = 2; l <=n;l++)for (int i = 1; i <= n - l + 1; i++){int j = i + l - 1;if (x[i] == x[j]){c(i, j) = c(i + 1, j - 1) + 2;b(i, j) = 1;}else if (c(i + 1, j) < c(i, j - 1)){c(i, j) = c(i, j - 1);b(i, j) = 2;}else{c(i, j) = c(i + 1, j);b(i, j) = 3;}}}void print_palindrome(const matrix<int>& b, const std::vector<char>& x, int i, int j){if (i == j){std::cout << x[i];return;}if (b(i, j) == 1){std::cout << x[i];print_palindrome(b, x, i + 1, j - 1);std::cout << x[i];}else if (b(i, j) == 2)print_palindrome(b, x, i, j - 1);else if (b(i, j) == 3)print_palindrome(b, x, i + 1, j);elsestd::cerr << "printing error" << std::endl;}//15-3double euc_dis(const std::vector<double>& px,const std::vector<double>& py,int m,int n){return sqrt((px[m]-px[n])*(px[m]-px[n])+(py[m]-py[n])*(py[m]-py[n]));}void euclidean_tsp(const std::vector<double>& px,const std::vector<double>& py,matrix<double>& b,matrix<int>& r){int n=px.size()-1;b(1,2)=euc_dis(px,py,1,2);for(int j=3;j<=n;j++){for(int i=1;i<=j-2;i++){b(i,j)=b(i,j-1)+euc_dis(px,py,j-1,j);r(i,j)=j-1;}b(j-1,j)=POS_INFI;for(int k=1;k<=j-2;k++){double q=b(k,j-1)+euc_dis(px,py,k,j);if(q<b(j-1,j)){b(j-1,j)=q;r(j-1,j)=k;}}}b(n,n)=b(n-1,n)+euc_dis(px,py,n-1,n);}void print_path(const matrix<int>&r,int i,int j){if(i<j){int k=r(i,j);if(k!=i)std::cout<<k<<std::endl;if(k>1)print_path(r,i,k);}else{int k=r(j,i);if(k>1){print_path(r,k,j);std::cout<<k<<std::endl;}}}void print_tour(const matrix<int>& r,int n){std::cout<<n<<std::endl;std::cout<<n-1<<std::endl;int k=r(n-1,n);print_path(r,k,n-1);std::cout<<k<<std::endl;}//15-4 print neatlyvoid print_neatly(const std::vector<int>& l,int n,int m,matrix<int>& extras,matrix<int>& lc,std::vector<int>& c,std::vector<int>& p){for(int i=1;i<=n;i++){extras(i,i)=m-l[i];for(int j=i+1;j<=n;j++)extras(i,j)=extras(i,j-1)-l[j]-1;}for(int i=1;i<=n;i++)for(int j=i;j<=n;j++){if(extras(i,j)<0)lc(i,j)=POS_INFI;else if(j==n&&extras(i,j)>=0)lc(i,j)=0;else lc(i,j)=(extras(i,j))^3;}c[0]=0;for(int j=1;j<=n;j++){c[j]=POS_INFI;for(int i=1;i<=j;i++)if(c[i-1]+lc(i,j)<c[j]){c[j]=c[i-1]+lc(i,j);p[j]=i;}}}int give_lines(std::vector<int>& p,int j){int i=p[j];int k=1;if(i!=1)k=give_lines(p,i-1)+1;std::cout<<"line:"<<k<<"\tcontains\t"<<i<<"\t-->\t"<<j<<std::endl;return k;}//15-5 edit distancevoid op_sequence(matrix<int>& op,int kill,int i,int j){int ii,int jj;if(i==0&&j==0)return;if(op(i,j)==0||op(i,j)==1){ii=i-1;jj=j-1;}else if(op(i,j)==4){ii=i-2;jj=j-2;}else if(op(i,j)==2){ii=i-1;jj=j;}else if(op(i,j)==3){ii=i;jj=j-1;}else{ii=kill;jj=j;}op_sequence(op,kill,i,j);std::cout<<op(i,j)<<std::endl;}void edit_distance(std::vector<int>& x,std::vector<int>& y,std::vector<int>& cost,int m,int n,int kill,matrix<int>& c,matrix<int>& op){for(int i=0;i<=m;i++){c(i,0)=i*cost[2];op(i,0)=2;}for(int j=0;j<=n;j++){c(0,j)=j*cost[3];op(0,j)=3;}for(int i=1;i<=m;i++)for(int j=1;j<=n;j++){c(i,j)=POS_INFI;if(x[i]==y[j]){c(i,j)=c(i-1,j-1)+cost[0];op(i,j)=0;}if(x[i]!=y[j]&&c(i-1,j-1)+cost[1]<c(i,j)){c(i,j)=c(i-1,j-1)+cost[1];op(i,j)=1;}if(i>=2&&j>=2&&x[i]==y[j-1]&&x[i-1]==y[j]&&c(i-1,j-2)+cost[4]<c(i,j)){c(i,j)=c(i-2,j-2)+cost[4];op(i,j)=4;}if(c(i-1,j)+cost[2]<c(i,j)){c(i,j)=c(i-1,j)+cost[2];op(i,j)=2;}if(c(i,j-1)+cost[3]<c(i,j)){c(i,j)=c(i,j-1)+cost[3];op(i,j)=3;}}for(int i=0;i<=m-1;i++)if(c(i,n)+cost[5]<c(m,n)){c(m,n)=c(i,n)+cost[5];op(m,n)=5;kill=i;}}//15-8 break string void print_break(std::vector<int>& l,matrix<int>& b,int i,int j){if(j-i>=2){int k=b(i,j);std::cout<<" break at:"<<k;print_break(l,b,i,k);print_break(l,b,k,j);}}void break_string(int m,std::vector<int>& l,matrix<int>& c,matrix<int>& b){for(int i=1;i<=m-1;i++)c(i,i)=c(i,i+1)=0;c(m,m)=0;for(int len=3;len<=m;len++)for(int i=1;i<=m-len+1;i++){int j=i+len-1;c(i,j)=POS_INFI;for(int k=i+1;k<j-1;k++)if(c(i,k)+c(k,j)<c(i,j)){c(i,j)=c(i,k)+c(k,j);b(i,j)=k;}c(i,j)+=l[j]-l[i];}std::cout<<"the minimum cost is :"<<c(1,m)<<std::endl;print_break(l,b,1,m);}//15-11 inventory planningvoid inventory_planning(int n,int m,int c,int D,std::vector<int>& d,matrix<int>& cost,matrix<int>& make,int h (int)){for(int s=0;s<=D;s++){int f=std::max(d[n]-s,0);cost(n,s)=std::max(f-m,0)+h(s+f-d[n]);make(n,s)=f;}int u=d[n];for(int k=n-1;k>=1;k--){u+=d[k];for(int s=0;s<=D;s++){cost(k,s)=POS_INFI;for(int f=std::max(d[k]-s,0);f<=u-s;f++){int val=cost(k+1,s+f-d[k])+c*std::max(f-m,0)+h(s+f-d[k]);if(val<cost(k,s)){cost(k,s)=val;make(k,s)=f;}}}}std::cout<<cost(1,0)<<std::endl;int s=0;for(int k=1;k<=n;k++){std::cout<<" month "<<k<<" make"<<make(k,s)<<std::endl;s+=s+make(k,s)-d[k];}}//15-12 base ball playersvoid free_agent_vorp(const matrix<int>& cost,const matrix<int>& vorp,int budget,int P,matrix<int>& v,matrix<int>& who){int N=cost.row();for(int x=0;x<=budget;x++){v(N,x)=NEG_INFI;who(N,x)=0;for(int k=1;k<=P;k++)if(cost(N,k)<=x&&vorp(N,k)>=v(N,x)){v(N,x)=vorp(N,k);who(N,x)=k;}}for(int i=N-1;i>=1;i--)for(int x=0;x<=budget;x++){v(i,x)=v(i+1,x);who(i,x)=0;for(int k=1;k<=P;k++)if(cost(i,k)<=x&&v(i+1,x-cost(i,k))+vorp(i,k)>v(i,x)){v(i,x)=v(i+1,x-cost(i,k))+vorp(i,k);who(i,x)=k;}}std::cout<<"the maximum vorp is:"<<v(1,budget)<<std::endl;int amt=budget;for(int i=1;i<=N;i++){int k=who(i,amt);if(k!=0){std::cout<<"sign player "<<k<<std::endl;amt-=cost(i,k);}}std::cout<<"total money spend:"<<budget-amt<<std::endl;}#endif

chapter15_exercise_test.cpp

#include"chapter15_exercise.h"void main(){//char carray[] = { 's','c', 'h', 'a', 'r', 'a', 'c', 't', 'e', 'r' };//std::vector<char> x(carray, carray + sizeof(carray) / sizeof(char));//int n = x.size() - 1;//matrix<int> c(n + 1, n + 1);//matrix<int> b(n + 1, n + 1);//palindrome(x, c, b);//std::cout << c << std::endl;//std::cout << b << std::endl;//print_palindrome(b, x, 1, n);//double pxarray[]={0,1,2,3,4,5,6,7};//double pyarray[]={0,7,1,4,5,2,6,3};//std::vector<double> px(pxarray,//pxarray+sizeof(pxarray)/sizeof(double));//std::vector<double> py(pyarray,//pyarray+sizeof(pyarray)/sizeof(double));//int n=px.size()-1;//matrix<double> b(n+1,n+1);//matrix<int> r(n,n+1);//euclidean_tsp(px,py,b,r);//std::cout<<r<<std::endl;//print_tour(r,n);const int n=100;const int m=20;std::vector<int> l(n+1,0);for(int i=0;i<=n;i++)l[i]=rand()%3+2;matrix<int> extras(n+1,n+1);matrix<int> lc(n+1,n+1);std::vector<int> c(n+1,0);std::vector<int> p(n+1,0);print_neatly(l,n,m,extras,lc,c,p);give_lines(p,n);}