【题解】[牛客OI周赛3-提高组]B.1408 线性DP

题目链接

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
const int N=2e3+10;
int n,dp[N][N],w[N],b[N],c1[N][N],c2[N][N];
int main()
{
	//freopen("in.txt","r",stdin);
	cin>>n;
	for(int i=1,x;i<=2*n;i++)
	{
		char ch;
		cin>>ch>>x;
		if(ch=='W')w[x]=i;
		else b[x]=i;
	}
	for(int i=1;i<=n;i++)
	    for(int j=i+1;j<=n;j++)
	    {
	    	c1[i][n]+=(w[j]<w[i]);
	    	c2[i][n]+=(b[j]<b[i]);
		}
	for(int i=1;i<=n;i++)
	    for(int j=n-1;j>=0;j--)
	    {
	    	c1[i][j]=c1[i][j+1]+(b[j+1]<w[i]);
	    	c2[i][j]=c2[i][j+1]+(w[j+1]<b[i]);
		}
	memset(dp,0x3f,sizeof(dp));dp[0][0]=0;
	for(int i=0;i<=n;i++)
	    for(int j=0;j<=n;j++)
	    {
	    	if(i==0&&j==0)continue;
	    	if(i>0)dp[i][j]=min(dp[i][j],dp[i-1][j]+c1[i][j]);
	    	if(j>0)dp[i][j]=min(dp[i][j],dp[i][j-1]+c2[j][i]);
		}
	printf("%d\n",dp[n][n]);
	return 0;
}

总结

线性DP好题