P2060 [HNOI2006]马步距离

P2060 [HNOI2006]马步距离

数据到百万级别，明显爆搜不行，剪枝也没法剪。先打表。发现小数据内步数比较受位置关系影响，但数据一大就不影响了。大概搜了一个20*20的表把赋值语句打出来。判断时贪心，看两点间位置差，根据x差或者y差的大小比较来采取两种不同跳法，直到在小范围内再直接借助打的表加以输出。注意起点和目标的位置的及时调整（依据对称性，见line49），方便跳动。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#define dbg(x) cerr<<#x<<" = "<<x<<endl
#define ddbg(x,y) cerr<<#x<<" = "<<x<<"   "<<#y<<" = "<<y<<endl
using namespace std;
typedef long long ll;
template<typename T>inline char MIN(T&A,T B){return A>B?A=B,1:0;}
template<typename T>inline char MAX(T&A,T B){return A<B?A=B,1:0;}
template<typename T>inline T _min(T A,T B){return A<B?A:B;}
template<typename T>inline T _max(T A,T B){return A>B?A:B;}
template<typename T>inline T read(T&x){
    x=0;int f=0;char c;while(!isdigit(c=getchar()))if(c=='-')f=1;
    while(isdigit(c))x=x*10+(c&15),c=getchar();return f?x=-x:x;
}
const int N=21;
int step[N][N]={{0,3,2,3,2,3,4,5,4,5,6,7,6,7,8,9,8,9,10,11,10},
                {3,2,1,2,3,4,3,4,5,6,5,6,7,8,7,8,9,10,9,10,11},
                {2,1,4,3,2,3,4,5,4,5,6,7,6,7,8,9,8,9,10,11,10},
                {3,2,3,2,3,4,3,4,5,6,5,6,7,8,7,8,9,10,9,10,11},
                {2,3,2,3,4,3,4,5,4,5,6,7,6,7,8,9,8,9,10,11,10},
                {3,4,3,4,3,4,5,4,5,6,5,6,7,8,7,8,9,10,9,10,11},
                {4,3,4,3,4,5,4,5,6,5,6,7,6,7,8,9,8,9,10,11,10},
                {5,4,5,4,5,4,5,6,5,6,7,6,7,8,7,8,9,10,9,10,11},
                {4,5,4,5,4,5,6,5,6,7,6,7,8,7,8,9,8,9,10,11,10},
                {5,6,5,6,5,6,5,6,7,6,7,8,7,8,9,8,9,10,9,10,11},
                {6,5,6,5,6,5,6,7,6,7,8,7,8,9,8,9,10,9,10,11,10},
                {7,6,7,6,7,6,7,6,7,8,7,8,9,8,9,10,9,10,11,10,11},
                {6,7,6,7,6,7,6,7,8,7,8,9,8,9,10,9,10,11,10,11,12},
                {7,8,7,8,7,8,7,8,7,8,9,8,9,10,9,10,11,10,11,12,11},
                {8,7,8,7,8,7,8,7,8,9,8,9,10,9,10,11,10,11,12,11,12},
                {9,8,9,8,9,8,9,8,9,8,9,10,9,10,11,10,11,12,11,12,13},
                {8,9,8,9,8,9,8,9,8,9,10,9,10,11,10,11,12,11,12,13,12},
                {9,10,9,10,9,10,9,10,9,10,9,10,11,10,11,12,11,12,13,12,13},
                {10,9,10,9,10,9,10,9,10,9,10,11,10,11,12,11,12,13,12,13,14},
                {11,10,11,10,11,10,11,10,11,10,11,10,11,12,11,12,13,12,13,14,13},
                {10,11,10,11,10,11,10,11,10,11,10,11,12,11,12,13,12,13,14,13,14}};
inline void swap(int&x,int&y){x^=y^=x^=y;}

int main(){//freopen("test.in","r",stdin);freopen("test.out","w",stdout);
    int sx,sy,tx,ty,ans=0;
    read(sx),read(sy),read(tx),read(ty);
    if(sx>tx)swap(sx,tx);if(sy>ty)swap(sy,ty);
    while(tx-sx>=N||ty-sy>=N){//ddbg(sx,sy);
        if(ty-sy<tx-sx)sx+=2,++sy;
        else ++sx,sy+=2;++ans;
        if(sx>tx)swap(sx,tx);if(sy>ty)swap(sy,ty);
    }
    return printf("%d",ans+step[tx-sx][ty-sy]),0;
}