Installing Apps(贪心+01背包)

2024-02-10 16:58
文章标签 贪心 01 背包 apps installing

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5008: Installing Apps

时间限制: 2 Sec   内存限制: 128 MB
提交: 163   解决: 22
[ 提交][ 状态][ 讨论版][命题人: admin]

题目描述

Sandra recently bought her first smart phone. One of her friends suggested a long list of applications (more commonly known as “apps”) that she should install on the phone. Sandra immediately started installing the apps from the list, but after installing a few, the phone did not have enough disk space to install any more apps. 
Sometimes, the app installation failed because there was not even enough space to download the installation package. Other apps could be downloaded just fine, but had insufficient space to store the installed app.
Each app that Sandra installs has a download size d and a storage size s. To download the app, Sandra’s phone must have at least d megabytes of free disk space. After the app has been installed, it then uses s megabytes of disk space on the phone. The download size may be smaller than the storage size (e.g., if the app data is heavily compressed) or larger than the storage size (e.g., if the download contains material that might not get used such as translations to different languages). The installer is very efficient and can transform the downloaded package to an installed app without using any extra disk space. Thus, to install an app, the phone must have at least max(d, s) megabytes of free  disk space.
Sandra quickly realised that she may have run out of space just because she installed apps in the wrong order. Thus, she decided to give the installation another try. She uninstalled all apps, and will now choose an installation order that lets her install the largest number of apps from the list.
Sandra may not install any app more than once.
Help her determine what apps on the list she should install, and in what order.

输入

The input consists of:
• One line with two integers n, c (1 ≤ n ≤ 500, 1 ≤ c ≤ 10 000), the number of available apps and the available disk space of the phone in megabytes.
• n lines, each with two integers d, s (1 ≤ d, s ≤ 10 000), the download size and storage size of an app, in megabytes.

输出

Output one line with the maximum number of apps that can be installed. 

样例输入

2 100
99 1

1 99

样例输出

2

提示

来源

nwerc2017 


题意:有n种手机软件,每一种软件的安装包大小是d,安装后的软件大小是s(删除了安装包),那么若有c的手机内存,最多能安装多少个手机软件。

题解:按照贪心原则,可按安装包和软件大小的差值进行排序,同时在装背包的时候要考虑是否能装进d,即c-j>=d-s

#include<stdio.h>
#include <algorithm>
#include<iostream>
#include<string.h>
#include<vector>
#include<stdlib.h>
#include<math.h>
#include<queue>
#include<deque>
#include<ctype.h>
#include<map>
#include<set>
#include<stack>
#include<string>
#include<algorithm>
#define INF 0x3f3f3f3f
#define gcd(a,b) __gcd(a,b)
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define FAST_IO ios::sync_with_stdio(false)
const double PI = acos(-1.0);
const double eps = 1e-6;
const int MAX=1e5+10;
const int mod=1e9+7;
typedef long long ll;
using namespace std;inline ll lcm(ll a,ll b){return a/gcd(a,b)*b;}
inline ll qpow(ll a,ll b){ll r=1,t=a; while(b){if(b&1)r=(r*t)%mod;b>>=1;t=(t*t)%mod;}return r;}
inline ll inv1(ll b){return qpow(b,mod-2);}
inline ll exgcd(ll a,ll b,ll &x,ll &y){if(!b){x=1;y=0;return a;}ll r=exgcd(b,a%b,y,x);y-=(a/b)*x;return r;}
inline ll read(){ll x=0,f=1;char c=getchar();for(;!isdigit(c);c=getchar()) if(c=='-') f=-1;for(;isdigit(c);c=getchar()) x=x*10+c-'0';return x*f;}
struct node
{int d,s,m;
}e[11000];
int n,c;
int cmp(node a,node b)
{return a.d-a.s>b.d-b.s;
}int dp[30000305];
int main()
{int i,j;scanf("%d%d",&n,&c);for(i=1;i<=n;i++)scanf("%d%d",&e[i].d,&e[i].s);sort(e+1,e+1+n,cmp);int ans=0;for(i=1;i<=n;i++)for(j=c;j>=e[i].s;j--)if(c-j>=e[i].d-e[i].s)dp[j]=max(dp[j],dp[j-e[i].s]+1),ans=max(ans,dp[j]);printf("%d\n",ans);return 0;
}

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