POJ 2392 Space Elevator (多重揹包+優化)

Space Elevator

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 7378		Accepted: 3464

Description

The cows are going to space! They plan to achieve orbit by building a sort of space elevator: a giant tower of blocks. They have K (1 <= K <= 400) different types of blocks with which to build the tower. Each block of type i has height h_i (1 <= h_i <= 100) and is available in quantity c_i (1 <= c_i <= 10). Due to possible damage caused by cosmic rays, no part of a block of type i can exceed a maximum altitude a_i (1 <= a_i <= 40000).

Help the cows build the tallest space elevator possible by stacking blocks on top of each other according to the rules.

Input

* Line 1: A single integer, K

* Lines 2..K+1: Each line contains three space-separated integers: h_i, a_i, and c_i. Line i+1 describes block type i.

Output

* Line 1: A single integer H, the maximum height of a tower that can be built

Sample Input

3
7 40 3
5 23 8
2 52 6

Sample Output

48

Hint

OUTPUT DETAILS:

From the bottom: 3 blocks of type 2, below 3 of type 1, below 6 of type 3. Stacking 4 blocks of type 2 and 3 of type 1 is not legal, since the top of the last type 1 block would exceed height 40.

Source

USACO 2005 March Gold


題意：

有一頭牛想要建一座石塔，他有很多不同類型的石塊。
每類石塊有三個屬性：1. (h): 石塊的高度；2. (a): 石塊能達到的最大高度；3. (c): 石塊的數量

思路：

採用多重揹包。
注意點：在做揹包前需要對石塊能到達的最大高度（a）進行排序，防止石塔到了一定高度後，剩下的一些石塊所能達到的最大高度小於這個高度，那剩下的這些石塊也就不能往上放了。排序時按升序排序，先放能達到最大高度小的石塊。
優化：直接標記能到達的最高點。

/*************************************************************************
	> File Name: C.cpp
	> Author: BSlin
	> Mail:  
	> Created Time: 2013年10月01日 星期二 19時18分57秒
 ************************************************************************/

#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <iterator>
#include <vector>
#include <map>
#include <set>
#include <stack>
#include <queue>
#define MP make_pair
#define INF (1<<30)
#define PI acos(-1.0)
#define esp 1e-8
const int dx[4]={0,0,0,0};
using namespace std;
#define read freopen("in.txt","r",stdin)
#define write freopen("out.txt","w",stdout)
#if defined (_WIN32) || defined (__WIN32) || defined (WIN32) || defined (__WIN32__)
#define LL __int64
#define LLS "%" "I" "6" "4" "d"
#else
#define LL long long
#define LLS "%" "l" "l" "d"
#endif


struct node {
    int h,a,c;
    bool operator < (const node b) const {
        return a < b.a;
    }
}data[410];

int dp[40010];

int main(int argc, char** argv) {
    //read;
    int n,ans;
    while(scanf("%d",&n) != EOF) {
        memset(dp,0,sizeof(dp));
        ans = 0;
        for(int i=0; i<n; i++) {
            scanf("%d%d%d",&data[i].h,&data[i].a,&data[i].c);
            data[i].c = min(data[i].c,data[i].a/data[i].h);
        }
        sort(data,data+n);
        for(int i=0; i<n; i++) {
            for(int j=0; j<data[i].c; j++) {
                for(int k=data[i].a; k>=data[i].h; k--) {  //不會覆蓋到以後的值
                    dp[k] = max(dp[k],dp[k-data[i].h] + data[i].h);
                    if(ans < dp[k]) ans = dp[k];
                }
            }
        }
        printf("%d\n",ans);
    }
    return 0;
}

優化後

/*************************************************************************
	> File Name: CC.cpp
	> Author: BSlin
	> Mail:  
	> Created Time: 2013年10月01日 星期二 21時25分11秒
 ************************************************************************/

#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <iterator>
#include <vector>
#include <map>
#include <set>
#include <stack>
#include <queue>
#define MP make_pair
#define INF (1<<30)
#define PI acos(-1.0)
#define esp 1e-8
const int dx[4]={0,0,0,0};
using namespace std;
#define read freopen("in.txt","r",stdin)
#define write freopen("out.txt","w",stdout)
#if defined (_WIN32) || defined (__WIN32) || defined (WIN32) || defined (__WIN32__)
#define LL __int64
#define LLS "%" "I" "6" "4" "d"
#else
#define LL long long
#define LLS "%" "l" "l" "d"
#endif



struct node {
    int h,a,c;
    bool operator < (const node b) const {
        return a < b.a;
    }
}data[410];

bool dp[40010];
int cnt[40010];

int main(int argc, char** argv) {
    //read;
    int n,ans;
    while(scanf("%d",&n) != EOF) {
        memset(dp,0,sizeof(dp));
        for(int i=0; i<n; i++) {
            scanf("%d%d%d",&data[i].h,&data[i].a,&data[i].c);
        }
        sort(data,data + n);
        dp[0] = 1;
        ans = 0;
        for(int i=0; i<n; i++) {
            memset(cnt,0,sizeof(cnt));
            for(int j=data[i].h; j<=data[i].a; j++) {
                if(!dp[j] && dp[j-data[i].h] && cnt[j-data[i].h] + 1 <= data[i].c) {
                    dp[j] = true;
                    cnt[j] = cnt[j-data[i].h] + 1;
                    if(ans < j) ans = j;
                }
            }
        }
        printf("%d\n",ans);
    }
    return 0;
}