[POJ 3666] Making the Grade

Posted 2020-12-04 evenbao

[题目链接]

         http://poj.org/problem?id=3666

[算法]

       离散化 + dp

[代码] 

          

#include <algorithm>  
#include <bitset>  
#include <cctype>  
#include <cerrno>  
#include <clocale>  
#include <cmath>  
#include <complex>  
#include <cstdio>  
#include <cstdlib>  
#include <cstring>  
#include <ctime>  
#include <deque>  
#include <exception>  
#include <fstream>  
#include <functional>  
#include <limits>  
#include <list>  
#include <map>  
#include <iomanip>  
#include <ios>  
#include <iosfwd>  
#include <iostream>  
#include <istream>  
#include <ostream>  
#include <queue>  
#include <set>  
#include <sstream>  
#include <stdexcept>  
#include <streambuf>  
#include <string>  
#include <utility>  
#include <vector>  
#include <cwchar>  
#include <cwctype>  
#include <stack>  
#include <limits.h> 
using namespace std;
#define MAXN 2010
typedef long long ll;
const ll INF = 1e15;

int i,n,len;
ll a[MAXN],tmp[MAXN];
ll ans;
ll dp[MAXN][MAXN];

ll myabs(ll x)
{
    return x < 0 ? -x : x;
}
inline ll dp1()
{
    int i,j;
    ll mn = INF,ret = INF;
    for (i = 1; i <= n; i++)
    {
        for (j = 1; j <= len; j++)
        {
            dp[i][j] = INF;
        }
    }
    for (i = 1; i <= len; i++) dp[1][i] = myabs(a[1] - tmp[i]);
    for (i = 2; i <= n; i++)
    {
        mn = INF;
        for (j = 1; j <= len; j++)
        {
            mn = min(mn,dp[i-1][j]);
            dp[i][j] = mn + myabs(a[i] - tmp[j]);
        }    
    }
    for (i = 1; i <= len; i++) ret = min(ret,dp[n][i]);
    return ret;
}
inline ll dp2()
{
    int i,j;
    ll mn = INF,ret = INF;
    for (i = 1; i <= n; i++)
    {
        for (j = 1; j <= len; j++)
        {
            dp[i][j] = INF;
        }
    }    
    for (i = 1; i <= len; i++) dp[1][i] = myabs(a[1] - tmp[i]);
    for (i = 2; i <= n; i++)
    {
        mn = INF;
        for (j = len; j >= 1; j--)
        {
            mn = min(mn,dp[i-1][j]);
            dp[i][j] = mn + myabs(a[i] - tmp[j]);
        }
    }
    for (i = 1; i <= len; i++) ret = min(ret,dp[n][i]);
    return ret;
}

int main()
{
    
    scanf("%d",&n);
    for (i = 1; i <= n; i++) 
    {
        scanf("%lld",&a[i]);
        tmp[i] = a[i];
    }
    sort(tmp+1,tmp+n+1);
    len = unique(tmp+1,tmp+n+1) - tmp - 1;
    ans = min(dp1(),dp2());
    printf("%lld
",ans);

    return 0;
}