dynamic programming －－knapsack problem 背包问题（c++实现）

/* * KnapsackProblem.cpp * * Created on: Jul 11, 2010 * Author: kevin */ #include <iostream> #include "My_matrix.h" #include <stddef.h> using namespace std; struct Triple //used for storing the single item unit { int no; //item NO. double value; //item value int weight; //item weight };//end of struct Triple void init_table(My_matrix<double>& t, int nRow, int nCol); void print_table(My_matrix<double>& t, int nRow, int nCol); void fill_table(My_matrix<double>& t, int* w,double* v,int n,int cap); void get_results(My_matrix<double>& t,int* w,double* v); void print_results(const Triple* results, int rslt_cnt); extern void my_assert(bool val, char* err_info); //solving the knapsack problem by dynamic programming technique //@param //w - weight //v - values //n - n values with corresponding weights //cap - capacity of the knapsack void knapsackSolve(int* w,double* v,int n,int cap) { Triple* results = NULL; int rslt_cnt = 0; My_matrix<double> table(n+1,cap+1); //the row number is n+1 because the Knapsack Problem // dynamic programming table requires n+1 rows; // so is the column number init_table(table,n+1,cap+1); fill_table(table,w,v,n,cap); print_table(table,n+1,cap+1); get_results(table,w,v); // cout<<"result count: "<<rslt_cnt<<endl; //cout<<"results[0]: "<<results[0].no<<endl; //print_results(results,rslt_cnt); }//end of knapsackSolve void init_table(My_matrix<double>& t, int nRow, int nCol) { for(int i=0;i<nRow;i++) for(int j=0;j<nCol; j++) { if(j==0||i==0) t.setElement(i,j, 0); else t.setElement(i,j, -1); } }//end of init_table void fill_table(My_matrix<double>& t, int* w,double* v,int n,int cap) { my_assert(t.getColCnt() == cap+1, "Cannot fill the table: The column number of the table is invalid."); my_assert(t.getRowCnt() == n+1, "Cannot fill the table: The row number of the table is invalid."); my_assert(n > 0 && cap > 0 && w != NULL && v != NULL, "Invalid parameter in function: void fill_table(...)"); //filling the table using dynamic programming recurrence: //V[i,j] = max{V[i-1,j],v[i-1] + V[i-1,j-w[i-1]]}; if j-w[i-1] >= 0 //V[i,j] = V[i-1,j]; if j-w[i-1] < 0 for(int i = 1; i < n+1; ++i) { for(int j = 1; j < cap+1; ++j) { if(j-w[i-1] >= 0) { double e1 = t.elementAt(i-1,j); double e2 = t.elementAt(i-1,j-w[i-1]) + v[i-1]; double max = (e1 > e2)? e1 : e2; t.setElement(i,j,max); } else { t.setElement(i,j,t.elementAt(i-1,j)); // V[i,j] = V[i-1,j] } } } }//end of fill_table(...) void print_table(My_matrix<double>& t, int nRow, int nCol) { cout<<"Printing dynamic Table: "<<nRow<<" rows, "<<nCol<<" Columns"<<endl; for(int i=0;i<nRow;i++) { for(int j=0;j<nCol;j++) { cout<<(t.elementAt(i,j))<<" "; } cout<<endl; } cout<<endl; }// end of void print_table(...) void get_results(My_matrix<double>& t, int* w,double* v) { Triple* temp = new Triple[t.getRowCnt()]; int rslt_cnt = 0; int i = t.getRowCnt() - 1; //row flag int j = t.getColCnt() - 1; //column flag while(i > 0 && j > 0) { if(t.elementAt(i,j) != t.elementAt(i-1,j)) { //add the ith item to the results temp[rslt_cnt].no = i; temp[rslt_cnt].value = v[i-1]; temp[rslt_cnt].weight= w[i-1]; ++rslt_cnt; j = j-w[i-1]; } --i; } print_results(temp,rslt_cnt); if(temp != NULL) { delete [] temp; } return ; }//end of void get_results(...) void print_results(const Triple* results, int rslt_cnt) { cout<<"No. Value Weight"<<endl; for(int i =0; i<rslt_cnt; ++i) { //cout<<"Inside the loop: i="<<i<<endl; cout<<results[i].no<<" " <<results[i].value<<" "<<results[i].weight <<endl; } }//end of void print_results(...); void test_dp() { int n = 4; int cap = 5; int w[]={2,1,3,2}; double v[]={12,10,20,15}; // My_matrix<double> table(n+1,cap+1); // init_table(table,n+1,cap+1); // fill_table(table,w,v,n,cap); // print_table(table,n+1,cap+1); knapsackSolve(w,v,n,cap); }//end of void test_dp()

 

/* * my_assert.cpp * * Created on: Jul 11, 2010 * Author: kevin */ #include <stdlib.h> #include <iostream> using namespace std; // if val == false, err_info will be printed, and the program exits. void my_assert(bool val, char* err_info) { if(!val) { cout<<err_info<<endl; exit(0); } }

 

/* * My_matrix.h * * Created on: Jul 11, 2010 * Author: kevin */ #ifndef MY_MATRIX_H_ #define MY_MATRIX_H_ template <class T> class My_matrix { private: T ** arr; int nRow; int nCol; public: //My_matrix(); ~My_matrix(void); My_matrix(int nRow, int nCol); //My_matrix(const My_matrix<T>& m); T& elementAt(int row, int col); void setElement(int row, int col, const T& val); int getRowCnt(void)const; int getColCnt(void)const; }; #endif /* MY_MATRIX_H_ */ /* * My_matrix.cpp * * Created on: Jul 11, 2010 * Author: kevin */ #include <iostream> #include <stdlib.h> #include "My_matrix.h" using namespace std; extern void my_assert(bool val, char* err_info); template<class T> My_matrix<T>::My_matrix(int nRow, int nCol) { my_assert(nRow > 0, "Invalid Row number in constructing My_matrix"); my_assert(nCol > 0, "Invalid Column number in constructing My_matrix"); arr = new T*[nRow]; for(int i=0;i<nRow;i++) { arr[i] = new T[nCol]; } //initialize all the elements with NULL for(int i=0;i<nRow;i++) for(int j=0;j<nCol;j++) arr[i][j] = NULL; this->nCol = nCol; this->nRow = nRow; } template<class T> My_matrix<T>::~My_matrix(void) { if(arr != NULL) { for(int i=0;i<nRow;i++) { if(arr[i] != NULL) delete[] arr[i]; } } delete []arr; } template<class T> T& My_matrix<T>::elementAt(int row, int col) { my_assert(row >= 0 && row < nRow, "Invalid Row number in My_matrix<T>::elementAt(int,int)"); my_assert(col >= 0 && col < nCol, "Invalid Column number in My_matrix<T>::elementAt(int,int)"); return arr[row][col]; } template<class T> void My_matrix<T>::setElement(int row, int col, const T& val) { my_assert(row >= 0 && row < nRow, "Invalid Row number in My_matrix<T>::setElement(int,int,T)"); my_assert(col >= 0 && col < nCol, "Invalid Column number in My_matrix<T>::setElement(int,int,T)"); arr[row][col] = val; } template<class T> int My_matrix<T>::getRowCnt(void)const { return nRow; } template<class T> int My_matrix<T>::getColCnt(void)const { return nCol; } //template<class T> //void print_my_matrix(const My_matrix<T>& m) //{ // int r = m.getRowCnt(); // int c = m.getColCnt(); // // for(int i=0;i<r;i++) // { // for(int j=0;j<c;j++) // cout<<m.elementAt(i,j)<<" "; // // cout<<endl; // } //} void test_my_matrix() { int r = 8; int c = 4; My_matrix<double> m(r,c); cout<<"Row cnt: "<<m.getRowCnt()<<endl; cout<<"Col cnt: "<<m.getColCnt()<<endl; for(int i=0;i<r;i++) for(int j=0;j<c;j++) m.setElement(i,j,(double)(i+j)); //print_my_matrix(m); for(int i=0;i<r;i++) { for(int j=0;j<c;j++) cout<<m.elementAt(i,j)<<" "; cout<<endl; } }

 

//============================================================================ // Name : Dynamic.cpp // Author : kevin // Version : // Copyright : Kevinland // Description : Hello World in C++, Ansi-style //============================================================================ #include <iostream> #include "Array.h" using namespace std; extern void test_dp(); extern void test_Array(); extern void test_my_matrix(); //extern void test_2D_Array(); int main() { //cout << "!!!Hello World!!!" << endl; // prints !!!Hello World!!! //test_Array(); test_dp(); //test_my_matrix(); return 0; }