【NOIP2001】【Luogu1049】装箱问题

problem

solution

codes

//数据太水，搜索就好
#include<iostream>
#include<algorithm>
using namespace std;
int n, m, a[110];
int search(int i, int r){
    if(i == n)return r;
    if(r < a[i])return search(i+1, r);
    return min(search(i+1,r), search(i+1,r-a[i]));
}
int main(){
    cin>>m>>n;
    for(int i = 0; i < n; i++)cin>>a[i];
    cout<<search(0,m);
    return 0;
}

//f[i][j],表示在选第i个物品时, 大小为j的体积能否取到
#include<iostream>
using namespace std;
const int maxn = 20010;
int n, m, a[35], f[35][maxn];
int main(){
    cin>>m>>n;
    for(int i = 1; i <= n; i++)cin>>a[i];
    f[0][0] = 1;
    for(int i = 1; i <= n; i++)
        for(int j = 0; j <= m; j++)
            if(f[i-1][j]){
                f[i][j] = f[i-1][j];
                if(j+a[i]<=m)f[i][j+a[i]] = 1;
            }
    for(int i = m; i >= 0; i--)
        if(f[n][i]){ cout<<m-i<<"\n"; return 0;}
    return 0;
}

//f[i]表示大小为i的体积能否取到
#include<iostream>
using namespace std;
const int maxn = 20010;
int n, m, a[maxn], f[maxn];
int main(){
    cin>>m>>n;
    for(int i = 1; i <= n; i++)cin>>a[i];
    f[0] = 1;
    for(int i = 1; i <= n; i++)
        for(int j = m; j >= 0; j--)
            if(f[j] && j+a[i]<=m)
                f[j+a[i]] = 1;
    for(int i = m; i >= 0; i--)
        if(f[i]){ cout<<m-i<<"\n"; return 0;}
    return 0;
}

//01背包, f[i]表示体积为i时得到的最大价值
#include<iostream>
using namespace std;
const int maxn = 20010;
int n, m, w[35], v[35], f[maxn];
int main(){
    cin>>m>>n;
    for(int i = 1; i <= n; i++){
        cin>>w[i];  v[i] = w[i];
    }
    for(int i = 1; i <= n; i++)
        for(int j = m; j >= w[i]; j--)
            f[j] = max(f[j],f[j-w[i]]+v[i]);
    cout<<m-f[m]<<"\n";
    return 0;
}