HDU 1069 Monkey and Banana(最大的单调递减序列啊 dp)
题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=1069
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.
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.
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
Case 1: maximum height = 40
Case 2: maximum height = 21
Case 3: maximum height = 28
Case 4: maximum height = 342
题意:
把给定的长方体(不限)叠加在一起,叠加的条件是。上面一个长方体的长和宽都比以下长方体的长
和宽短;求这些长方体能叠加的最高的高度.(当中(3,2。1)能够摆放成(3,1,2)、(2,1,3)等).
3 个不同的底面和高度。我们能够把每块积木看成三个不同的积木,
*
n个不同的积木,对这3
* n个积木的长依照从大到小排序;
代码例如以下:
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
using namespace std;
struct node
{
int l, w, h;
} a[1047];
bool cmp(node a, node b)
{
if(a.l == b.l)
{
return a.w > b.w;
}
return a.l > b.l;
}
int MAX(int a, int b)
{
if(a > b)
return a;
return b;
}
int dp[1047];//dp[i]:以第i块积木为顶的最大高度
int main()
{
int n;
int cas = 0;
while(scanf("%d",&n) && n)
{
//int L, W, H;
int tt[3];
int k = 0;
for(int i = 0; i < n; i++)
{
scanf("%d%d%d",&tt[0],&tt[1],&tt[2]);
sort(tt,tt+3);
a[k].l = tt[0];
a[k].w = tt[1];
a[k].h = tt[2];
k++;
a[k].l = tt[1];
a[k].w = tt[2];
a[k].h = tt[0];
k++;
a[k].l = tt[0];
a[k].w = tt[2];
a[k].h = tt[1];
k++;
}
sort(a,a+k,cmp);
int maxx = 0;
for(int i = 0; i < k; i++)
{
dp[i] = a[i].h;
for(int j = i-1; j >= 0; j--)
{
if(a[j].l>a[i].l && a[j].w>a[i].w)
{
dp[i] = MAX(dp[i], dp[j]+a[i].h);
}
}
if(dp[i] > maxx)
{
maxx = dp[i];
}
}
printf("Case %d: maximum height = %d\n",++cas,maxx);
}
return 0;
}
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