动态规划算法实例的一些实现

/*This is the template of *.cpp files */
#include<iostream>
#include<vector>
using namespace std;

int cut_rod(int *p,int n ){//暴力法求最优切割
   if(n == 0)
       return 0;
   int q = -1;
   for(int i = 1;i<=n;++i){
       q = q>p[i] + cut_rod(p,n-i)?q:p[i] + cut_rod(p,n-i);
   }
   return q;
}

int end_cut_rod(int *p,int n){//自底向上动态规划算法求最优切割方法的价值以及切割方案
   int *r = new int[n+1];
   int *s = new int[n+1];
   for(int m = 0;m<=n;++m){
       r[m] = 0;
       s[m] = 0;
   }
   for(int i = 1;i <= n;++i){
       for(int j = 0;j < i;++j){
           int temp = r[j] + p[i-j];
           if(r[i] < temp){
               r[i] = temp;
               s[i] = i - j;
           }
       }
   }
   int k = n;
   while(k > 0){
       cout<<s[k]<<endl;
       k = k - s[k];
   }
   return r[n];
}

int fei(int n){//斐波那契数列之动态规划算法
   int *a = new int[n+1];
   if(n >= 1)
       a[1] = 1;
   if(n >= 2)
       a[2] = 1;
   if(n > 2){
       for(int j = 3;j <= n;++j){
           a[j] = a[j-1] +a[j-2];
       }
   }
   int k = a[n];
   delete[] a;
   return k;
}

void printb(int *a,int n,int x,int y){//打印虚拟二位数组，对指定值加括号
   for(int i = 1;i<n;i++){
       for(int j = 1;j<n;++j){
           if(i == x&&j == y){
               cout<<"("<<a[(n-1)*(i-1)+j-1]<<")"<<" ";
           }else{
               cout<<a[(n-1)*(i-1)+j-1]<<" ";
           }
       }
       cout<<endl;
   }
}

void printa(int *a,int n){//普通打印虚拟二维数组函数
   for(int i = 1;i<n;i++){
       for(int j = 1;j<n;++j){
           cout<<a[(n-1)*(i-1)+j-1]<<"   ";
       }
       cout<<endl;
   }
}

int *matrix_chain_order(int *p,int n){//矩阵链相乘动态规划加括号算法
   int *a = new int[(n-1)*(n-1)];
   int *b = new int[(n-1)*(n-1)];
   for(int i = 1;i<n;++i){
       a[(n-1)*(i-1)+i-1] = 0;
   }
   for(int i = 1;i<n;++i){
       for(int j =1;j<n-i+1;j++){
           a[(n-1)*(j-1)+j+i-1] = 100000;
           for(int k = j;k< j+i;++k){
               int temp = p[j-1]*p[k+1-1]*p[j+i-1+1] + a[(n-1)*(j-1)+k-1] + a[(n-1)*(k+1-1)+j+i-1];
               if(temp < a[(n-1)*(j-1)+j+i-1]){
                   a[(n-1)*(j-1)+j+i-1] = temp;
                   b[(n-1)*(j-1)+j+i-1] = k;
               }
           }
       }
   }
   printa(a,n);
   cout<<endl<<endl;
   printa(b,n);
   return b;
}

void print_optimal_parens(int *s,int i,int j,int n){//矩阵链加括号函数
   if(i == j){
       cout<<"A"<<i;
   }else{
       cout<<"(";
           print_optimal_parens(s,i,s[(n-1)*(i-1)+j-1],n);
           print_optimal_parens(s,s[(n-1)*(i-1)+j-1]+1,j,n);
       cout<<")";
   }
}
int main(){
   int p[15] = {0,2,3,6,8,10,11,18,19,25,34,56,57,58,65};
   cout<<cut_rod(p,14)<<endl<<endl;//暴力切割实例
   int test[] = {30,35,15,5,10,20,25};
   matrix_chain_order(test,7);//矩阵链生成子问题图
   cout<<endl;
   cout<<"实现矩阵链加括号:"<<endl;
   print_optimal_parens(matrix_chain_order(test,7),1,6,7);//实现矩阵链加括号
   cout<<endl;
   cout<<"实现动态规划算法切割:"<<endl;
   cout<<end_cut_rod(p,14)<<"斐波那契数列之动态规划算法求第30个数的值"<<endl;//实现动态规划算法切割
   cout<<fei(30);//斐波那契数列之动态规划算法求第30个数的值
   return 0;
}

来源：https://www.cnblogs.com/candycloud/p/3341510.html

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动态规划算法