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HDU1069 Monkey and Banana —— 普通DP or LIS

时间:2017-10-02 17:49:42      阅读:244      评论:0      收藏:0      [点我收藏+]

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题目链接:http://acm.split.hdu.edu.cn/showproblem.php?pid=1069

 

Monkey and Banana

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 16589    Accepted Submission(s): 8834


Problem Description
A group of researchers are designing an experiment to test the IQ of a monkey. They will hang a banana at the roof of a building, and at the mean time, provide the monkey with some blocks. If the monkey is clever enough, it shall be able to reach the banana by placing one block on the top another to build a tower and climb up to get its favorite food.

The researchers have n types of blocks, and an unlimited supply of blocks of each type. Each type-i block was a rectangular solid with linear dimensions (xi, yi, zi). A block could be reoriented so that any two of its three dimensions determined the dimensions of the base and the other dimension was the height. 

They want to make sure that the tallest tower possible by stacking blocks can reach the roof. The problem is that, in building a tower, one block could only be placed on top of another block as long as the two base dimensions of the upper block were both strictly smaller than the corresponding base dimensions of the lower block because there has to be some space for the monkey to step on. This meant, for example, that blocks oriented to have equal-sized bases couldn‘t be stacked. 

Your job is to write a program that determines the height of the tallest tower the monkey can build with a given set of blocks.
 

 

Input
The input file will contain one or more test cases. The first line of each test case contains an integer n,
representing the number of different blocks in the following data set. The maximum value for n is 30.
Each of the next n lines contains three integers representing the values xi, yi and zi.
Input is terminated by a value of zero (0) for n.
 

 

Output
For each test case, print one line containing the case number (they are numbered sequentially starting from 1) and the height of the tallest possible tower in the format "Case case: maximum height = height".
 

 

Sample Input
1 10 20 30 2 6 8 10 5 5 5 7 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 5 31 41 59 26 53 58 97 93 23 84 62 64 33 83 27 0
 

 

Sample Output
Case 1: maximum height = 40 Case 2: maximum height = 21 Case 3: maximum height = 28 Case 4: maximum height = 342
 

 

Source
 
 
 
题解:
 
 
普通DP:
技术分享
 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 const int MAXN = 100;
 4 
 5 int block[MAXN][3];
 6 int dp[MAXN][MAXN];
 7 
 8 int main()
 9 {
10     int n, kase = 0;
11     while(scanf("%d",&n) && n)
12     {
13         int N = 0;
14         for(int i = 1; i<=n; i++)
15         {
16             int a, b, h;
17             scanf("%d%d%d", &a, &b, &h);
18             block[++N][0] = min(b,h), block[N][1] = max(b,h), block[N][2] = a;
19             block[++N][0] = min(a,h), block[N][1] = max(a,h), block[N][2] = b;
20             block[++N][0] = min(a,b), block[N][1] = max(a,b), block[N][2] = h;
21         }
22 
23         int ans = -2000000;
24         memset(dp, 0, sizeof(dp));
25         for(int i = 1; i<=N; i++)   //初始化第一个
26             dp[1][i] = block[i][2], ans = max(dp[1][i], ans);
27 
28         for(int i = 2; i<=N; i++)   //第i个
29         for(int j = 1; j<=N; j++)   //第i个放编号为j的块
30         for(int k = 1; k<=N; k++)   //j能否放在k上
31              if(block[j][0]<block[k][0] && block[j][1]<block[k][1])
32                 dp[i][j] = max(dp[i][j], dp[i-1][k]+block[j][2]), ans = max(dp[i][j], ans);
33 
34         printf("Case %d: maximum height = %d\n", ++kase, ans);
35     }
36     return 0;
37  }
View Code

LIS:

技术分享
 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 const int MAXN = 100;
 4 
 5 struct node
 6 {
 7     int a, b, h;
 8     bool operator<(const node x){
 9         return a>x.a;
10     }
11 }block[MAXN];
12 int dp[MAXN];
13 
14 int main()
15 {
16     int n, kase = 0;
17     while(scanf("%d",&n) && n)
18     {
19         int N = 0;
20         for(int i = 1; i<=n; i++)
21         {
22             int a, b, h;
23             scanf("%d%d%d", &a, &b, &h);
24             block[++N].a = min(b,h), block[N].b = max(b,h), block[N].h = a;
25             block[++N].a = min(a,h), block[N].b = max(a,h), block[N].h = b;
26             block[++N].a = min(a,b), block[N].b = max(a,b), block[N].h = h;
27         }
28         sort(block+1, block+1+N);
29         int ans = -2000000;
30         for(int i = 1; i<=N; i++)    //初始化第一个
31             dp[i] = block[i].h, ans = max(ans, dp[i]);
32 
33         for(int i = 1; i<=N; i++)
34             for(int j = 1; j<i; j++)
35                 if(block[i].a<block[j].a && block[i].b<block[j].b)
36                     dp[i] = max(dp[i], dp[j]+block[i].h), ans = max(ans, dp[i]);
37 
38         printf("Case %d: maximum height = %d\n", ++kase, ans);
39     }
40     return 0;
41  }
View Code

 

 
 

HDU1069 Monkey and Banana —— 普通DP or LIS

标签:bottom   ace   scanf   eterm   equal   log   opened   search   not   

原文地址:http://www.cnblogs.com/DOLFAMINGO/p/7620396.html

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