Dire Wolf——HDU5115（区间DP）

Posted 2022-04-29 dwvictor

题意

就是有一对狼，每个狼有初始的攻击力，并且还能给左右两边的狼提供攻击力加成，当冒险家杀死一头狼的时候他也会受到这个狼目前攻击力的伤害

实例解析

3
3 5 7
8 2 0

有三头狼，刚开始第二头狼给他左右两边的狼各加2攻击力，由于第一头狼左边没有狼，所以只给第二头狼加，第三头狼还那样，一系列操作后攻击力为（5，13，9），从左往右杀死狼

1、受到5点攻击，且第二头狼的攻击力加成消失（5，9）

2、受到5点攻击，且第三头狼攻击加成消失（7）

3最后结果5+5+7=17

 

题解

 

dp[i][j]=min(dp[i][j], dp[i][k-1]+dp[k+1][j]+a[k]+b[i-1]+b[j+1])

dp[i][i]=a[i]+b[i-1]+b[j+1];

这个dp[i][j]中的i、j就代表在原给出的序列中杀死第i到j头狼的最小伤害

其中这个k(i<=k<=j)就是枚举那一头狼是最后杀死的

 

这个dp[i][i]就提供了dp[i][j]的结果，所以要确定求dp[i][j]的时候dp[k][k](i<=k<=j)已经求出来了（典型的由部分推整体）

 

C++代码

 

#include<bits/stdc++.h>
using namespace std;
int a[300],b[300];
int dp[300][300];
const int inf = 999999999;
int main()
    int t;
    cin >> t;int cas = 0;
    while(t--)
        memset(a,0,sizeof a);
        memset(b,0,sizeof b);
        memset(dp,0,sizeof dp);
        int n;
        
        cin >> n;
        for(int i = 1;i <= n ; i++) cin >> a[i];
        for(int i = 1;i <= n;  i++) cin >> b[i];
        for(int i = n;i >= 1; --i )
            for(int j = i;j <= n ; ++j)
                if(i == j)
                
                dp[i][j] = a[i] + b[i-1] + b[i+1];
                continue;
            
                dp[i][j] = inf;
                for(int k = i;k <= j; ++k)
                           //             cout << dp[i][j] << endl; 

                    dp[i][j] = min(dp[i][j],dp[i][k - 1] + dp[k + 1][j] + a[k] + b[i-1] + b[j + 1]);
                
            
        
        printf("Case #%d: %d\n",++cas,dp[1][n]);
    
 

 

题面

Dire Wolf

Time Limit: 5000/5000 MS (Java/Others)    Memory Limit: 512000/512000 K (Java/Others)
Total Submission(s): 4487    Accepted Submission(s): 2665

Problem Description

Dire wolves, also known as Dark wolves, are extraordinarily large and powerful wolves. Many, if not all, Dire Wolves appear to originate from Draenor.
Dire wolves look like normal wolves, but these creatures are of nearly twice the size. These powerful beasts, 8 - 9 feet long and weighing 600 - 800 pounds, are the most well-known orc mounts. As tall as a man, these great wolves have long tusked jaws that look like they could snap an iron bar. They have burning red eyes. Dire wolves are mottled gray or black in color. Dire wolves thrive in the northern regions of Kalimdor and in Mulgore.
Dire wolves are efficient pack hunters that kill anything they catch. They prefer to attack in packs, surrounding and flanking a foe when they can.
— Wowpedia, Your wiki guide to the World of Warcra

Matt, an adventurer from the Eastern Kingdoms, meets a pack of dire wolves. There are N wolves standing in a row (numbered with 1 to N from left to right). Matt has to defeat all of them to survive.

Once Matt defeats a dire wolf, he will take some damage which is equal to the wolf’s current attack. As gregarious beasts, each dire wolf i can increase its adjacent wolves’ attack by b_i. Thus, each dire wolf i’s current attack consists of two parts, its basic attack ai and the extra attack provided by the current adjacent wolves. The increase of attack is temporary. Once a wolf is defeated, its adjacent wolves will no longer get extra attack from it. However, these two wolves (if exist) will become adjacent to each other now.

For example, suppose there are 3 dire wolves standing in a row, whose basic attacks ai are (3, 5, 7), respectively. The extra attacks b_i they can provide are (8, 2, 0). Thus, the current attacks of them are (5, 13, 9). If Matt defeats the second wolf first, he will get 13 points of damage and the alive wolves’ current attacks become (3, 15).

As an alert and resourceful adventurer, Matt can decide the order of the dire wolves he defeats. Therefore, he wants to know the least damage he has to take to defeat all the wolves.

 

 

Input

The first line contains only one integer T , which indicates the number of test cases. For each test case, the first line contains only one integer N (2 ≤ N ≤ 200).

The second line contains N integers a_i (0 ≤ a_i ≤ 100000), denoting the basic attack of each dire wolf.

The third line contains N integers b_i (0 ≤ b_i ≤ 50000), denoting the extra attack each dire wolf can provide.

 

 

Output

For each test case, output a single line “Case #x: y”, where x is the case number (starting from 1), y is the least damage Matt needs to take.

 

 

Sample Input

2 3 3 5 7 8 2 0 10 1 3 5 7 9 2 4 6 8 10 9 4 1 2 1 2 1 4 5 1

 

 

Sample Output

Case #1: 17 Case #2: 74

Hint

In the ?rst sample, Matt defeats the dire wolves from left to right. He takes 5 + 5 + 7 = 17 points of damage which is the least damage he has to take.

 

 

Source

2014ACM/ICPC亚洲区北京站-重现赛（感谢北师和上交）