动态规划---01背包问题

有N件物品和一个容量为V的背包。第i件物品的费用是c[i]，价值是w[i]。求解将哪些物品装入背包可使价值总和最大。

 

#include <iostream>
#include <algorithm>
#include <cstring>
#define MaxObjNum 100
#define MaxPackageVolume 100000
using namespace std;
int ObjNum, PackageVolume;
int ObjWeight[MaxObjNum], ObjVal[MaxObjNum];
int BackUp[MaxPackageVolume][MaxObjNum];
int DynamicProgramming(int RemainV, int pos) {
    int ReturnVal;
    if (BackUp[RemainV][pos] != -1)
        ReturnVal = BackUp[RemainV][pos];
    else if (pos == 0) {
        if (RemainV >= ObjWeight[pos])
            ReturnVal = ObjVal[pos];
        else
            ReturnVal = 0;
    }
    else if (RemainV >= ObjWeight[pos])
        ReturnVal = max(DynamicProgramming(RemainV - ObjWeight[pos], pos - 1) + ObjVal[pos], DynamicProgramming
        (RemainV, pos - 1));
    else
        ReturnVal = DynamicProgramming(RemainV, pos - 1);
    BackUp[RemainV][pos] = ReturnVal;
    return ReturnVal;
}
int main() {
    memset(BackUp, -1, sizeof(BackUp));
    cin >> PackageVolume >> ObjNum;
    for (int i = 0; i < ObjNum; ++i) {
        cin >> ObjWeight[i] >> ObjVal[i];
    }
    cout << DynamicProgramming(PackageVolume, ObjNum - 1) << endl;
    return 0;
}