Making the Grade [kuangbin带你飞]刷题记录

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Making the Grade

题目链接
请添加图片描述

核心思想 :

暴力枚举版的dp
我们可以发现一个结论 : 只要a[i]需要改变 , 那么它一定会等于它前面那个最终确定值或者后面那个最终确定值即就是这个 :只要a[i]需要改变那么b[i]==b[i-1]或者a[i-1]或者b[i+1]或者a[i+1]
推到这里了我们就可以直接dp枚举出答案了

AC代码

#include<iostream>
#include<queue>
#include<string>
#include<string.h>
#include<algorithm>
#include<cstdio>
#include<map>
#include<set>
#include<stack>
#include<vector>
#include<cmath>
using namespace std;
typedef long long ll;
#define repi(x,y,z) for(int x = y; x<=z;++x)
#define deci(x,y,z) for(int x = y; x>=z;--x)
#define repl(x,y,z) for(ll x = y; x<=z;++x)
#define decl(x,y,z) for(ll x = y; x>=z;--x)
#define gcd(a, b) __gcd(a, b)
#define lcm(a, b) (a * b / gcd(a, b))
#define INF 0x3f3f3f3f
#define ms(a,b) memset( a, b , sizeof (a) )
#define txt intxt()
#define CAS int cas;cin>>cas;while(cas--)
#define py  puts("YES")
#define pn  puts("NO")
#define pcn  putchar('\n')
inline void intxt( ){#ifndef ONLINE_JUDGEfreopen("in.txt","r",stdin);#endif
}
inline int read( ){int f = 1,x = 0;char ch = getchar();while (ch < '0' || ch > '9')   {if (ch == '-') f = -1; ch = getchar();}while (ch >= '0' && ch <= '9') {x = x * 10 + ch - '0'; ch = getchar();}x *= f;return x;
}
const int maxn=2e3+5;int n;
ll a[maxn];
ll b[maxn];
ll dp[maxn][maxn];ll abb( ll aa ){//这里是手写的求绝对值if(aa>=0)return aa;return -aa;
}int main(){txt;n=read();repi(i,1,n){a[i]=read();b[i]=a[i];}sort( b+1,b+1+n );repi(i,1,n){repi(j,1,n){dp[i][j] = 1e18;}}ll ans=1e18;repi(i,1,n){repi(j,1,n){dp[i][j]=min( dp[i][j],dp[i-1][j]+abb( a[i]-b[j] ) );}repi(j,2,n){dp[i][j]=min( dp[i][j],dp[i][j-1] );//只要满足b[j]>b[j-1],就可以把dp[i][j]替换成dp[i][j-1]}}repi(i,1,n){ans=min(ans,dp[n][i]);}cout<<ans<<endl;return 0;
}