Monkey and Banana HDU - 1069------DP
2017-08-07 09:48
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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
题意:给你n种长宽高规格的箱子,每种箱子有无限个,三个维度,任选其中的两个最底面,按照上方的箱子的‘长宽’小于下方箱子‘长宽’的原则垒箱子,求可以垒的最大高度。
每种规格的箱子就有了三种摆法,用结构体存起各种情况,排序后,dp一遍就可以啦。
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#define inf 0x7fffff
using namespace std;
struct node
{
int l;
int w;
int s;
int h;
} a[12000];
int n,dp[12000];
int cmp (node a,node b)
{
return a.s>b.s;
}
int main ()
{
int x,y,z,ax;
int tt=1;
while(scanf("%d",&n),n)
{
ax=0;
for(int i=0; i<n; i++)
{
scanf("%d %d %d",&x,&y,&z);
a[ax].l=max(x,y); //储存每种箱子的三种摆法,并切硬性规定l>w(长度 大于宽度,以后 好比较)
a[ax].w=min(x,y);
a[ax].s=x*y;
a[ax++].h=z;
//
a[ax].l=max(z,y);
a[ax].w=min(z,y);
a[ax].s=z*y;
a[ax++].h=x;
//
a[ax].l=max(x,z);
a[ax].w=min(x,z);
a[ax].s=x*z;
a[ax++].h=y;
}
sort(a,a+ax,cmp);
dp[0]=a[0].h;
int Max=dp[0];
for(int i=1; i<ax; i++)
{
dp[i]=a[i].h;
for(int j=0;j<i;j++)
{
if(a[i].s<a[j].s && a[i].l<a[j].l && a[i].w<a[j].w )//简单的dp过程
{
dp[i]=max(dp[j]+a[i].h,dp[i]);
}
}
Max=max(dp[i],Max);
}
printf("Case %d: maximum height = %d\n",tt++,Max);
}
return 0;
}
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
题意:给你n种长宽高规格的箱子,每种箱子有无限个,三个维度,任选其中的两个最底面,按照上方的箱子的‘长宽’小于下方箱子‘长宽’的原则垒箱子,求可以垒的最大高度。
每种规格的箱子就有了三种摆法,用结构体存起各种情况,排序后,dp一遍就可以啦。
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#define inf 0x7fffff
using namespace std;
struct node
{
int l;
int w;
int s;
int h;
} a[12000];
int n,dp[12000];
int cmp (node a,node b)
{
return a.s>b.s;
}
int main ()
{
int x,y,z,ax;
int tt=1;
while(scanf("%d",&n),n)
{
ax=0;
for(int i=0; i<n; i++)
{
scanf("%d %d %d",&x,&y,&z);
a[ax].l=max(x,y); //储存每种箱子的三种摆法,并切硬性规定l>w(长度 大于宽度,以后 好比较)
a[ax].w=min(x,y);
a[ax].s=x*y;
a[ax++].h=z;
//
a[ax].l=max(z,y);
a[ax].w=min(z,y);
a[ax].s=z*y;
a[ax++].h=x;
//
a[ax].l=max(x,z);
a[ax].w=min(x,z);
a[ax].s=x*z;
a[ax++].h=y;
}
sort(a,a+ax,cmp);
dp[0]=a[0].h;
int Max=dp[0];
for(int i=1; i<ax; i++)
{
dp[i]=a[i].h;
for(int j=0;j<i;j++)
{
if(a[i].s<a[j].s && a[i].l<a[j].l && a[i].w<a[j].w )//简单的dp过程
{
dp[i]=max(dp[j]+a[i].h,dp[i]);
}
}
Max=max(dp[i],Max);
}
printf("Case %d: maximum height = %d\n",tt++,Max);
}
return 0;
}
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