[DP] [模板] 01背包

1.标准模板

以横轴坐标为体积

以纵轴坐标为当前物品至首物品

则 dp[i][j] 即为 OPT(体积j, 物品1 - i)

//#pragma GCC optimize(2)
#include <cstdio>
#include <iostream>
#include <cstdlib>
#include <cmath>
#include <cctype>
#include <string>
#include <cstring>
#include <algorithm>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <ctime>
#include <vector>
#include <fstream>
#include <list>
#include <iomanip>
#include <numeric>
using namespace std;
typedef long long ll;

const int MAXN = 1e6 + 10;

struct good
{
    int val, size;
}arr[MAXN];

int sval, len;

int dp[110][11000] = {0};

int main()
{
    ios::sync_with_stdio(false);

    cin.tie(0);     cout.tie(0);

    cin>>sval>>len;

    for(int i = 1; i <= len; i++)
    {
        cin>>arr[i].size>>arr[i].val;
    }

    for(int i = 1; i <= len; i++)
    {
        for(int j = 1; j <= sval; j++)
        {
            if(j < arr[i].size)
                dp[i][j] = dp[i - 1][j];
            else
                dp[i][j] = max(dp[i - 1][j], dp[i - 1][j - arr[i].size] + arr[i].val);
        }
    }

    cout<<dp[len][sval]<<endl;

    return 0;
}

2.空间压缩

#include<iostream>
using namespace std;

int dp[11000]={0}, volume[1000], value[1000];

int main()
{
    int len, sumvolume;
    
	cin>>len>>sumvolume;
    
    for(int i = 1; i <= len; i++)
		cin>>volume[i]>>value[i];
    
	for(int i = 1; i <= len; i++)
    {
    	for(int j = sumvolume; j >= volume[i]; j--)
    	{
        	dp[j] = max(dp[j], dp[j - volume[i]] + value[i]);
        }

	}
    	
    cout<<dp[sumvolume]<<endl;
    
    return 0;
}

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