HDU - 5534 Partial Tree（每种都装的完全背包）

Partial Tree

In mathematics, and more specifically in graph theory, a tree is an undirected graph in which any two nodes are connected by exactly one path. In other words, any connected graph without simple cycles is a tree.

You find a partial tree on the way home. This tree has d is the degree of this node. What's the maximum coolness of the completed tree?

InputThe first line contains an integer n>100.OutputFor each test case, please output the maximum coolness of the completed tree in one line.Sample Input

Sample Output

5
19




因为每种装的范围为【1，+无穷】，然而分组背包的三次方会T，所以要想办法将其转化为完全背包模型。
因为每个点都至少有一度，所以我们预先放入n个一度，本来要放的2×n-2度现在只剩n-2度。
每当再次放入一个x度时，他的贡献为x-1度，在放入的同时减掉之前预先放好的一度。这样便保证了每个点至少有一度。

#include<bits/stdc++.h>
#define MAX 2018
#define INF 0x3f3f3f3f
using namespace std;
typedef long long ll;

int a[MAX];
ll dp[MAX];

int main()
{
    int t,n,m,i,j,k;
    scanf("%d",&t);
    while(t--){
        scanf("%d",&n);
        for(i=1;i<n;i++){
            scanf("%d",&a[i]);
        }
        memset(dp,-INF,sizeof(dp));
        dp[0]=0;
        for(i=2;i<n;i++){
            for(j=i-1;j<=n-2;j++){
                dp[j]=max(dp[j],dp[j-(i-1)]+a[i]-a[1]);
            }
        }
        printf("%I64d\n",dp[n-2]+n*a[1]);
    }
    return 0;
}