【bzoj4806~bzoj4809】 象棋四连发 DP-高精度-匈牙利算法-dfs

都是经典题了吧。。我好无聊。。

4806

4806-1801是双倍经验。。DP方程看代码吧。。

/* http://www.cnblogs.com/karl07/ */
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
using namespace std;

#define ll long long 
//#define P 9999973 //bzoj1801
#define P 999983 //bzoj4806
#define C(x) ((x)*(x-1)/2)
int n,m;
ll f[105][105][105];

int main(){
    scanf("%d%d",&n,&m);
    f[0][0][0]=1;
    for (int i=1;i<=n;i++){
        for (int j=0;j<=m;j++){
            for (int k=0;k<=m-j;k++){
                f[i][j][k]+=f[i-1][j][k];
                if (j>=1)          f[i][j][k]+=f[i-1][j-1][k]*(m-j-k+1);
                if (k>=1 && j<=m-1)f[i][j][k]+=f[i-1][j+1][k-1]*(j+1);
                if (j>=2)          f[i][j][k]+=f[i-1][j-2][k]*C(m-j-k+2);
                if (k>=2 && j<=m-2)f[i][j][k]+=f[i-1][j+2][k-2]*C(j+2);
                if (j>=1 && k>=1)  f[i][j][k]+=f[i-1][j][k-1]*j*(m-j-k+1);
                f[i][j][k]%=P;
            }
        }
    }
    ll ans=0;
    for (int i=0;i<=m;i++){
        for (int j=0;j<=m-i;j++){
            ans+=f[n][i][j];
            ans%=P;
        }
    }
    printf("%lld
",ans);
    return 0;
}

4807

就是 max(m,n) C min (m,n) 

/* http://www.cnblogs.com/karl07/ */
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
using namespace std;
struct INT {
    int b,a[60];
    INT (){b=0; for (int i=0;i<=50;i++) a[i]=0;}
};
int A,B,c,n,m;
int P[1000005],p[1000005],cnt[1000005],ip[1000005];
INT Int(int x){
    INT a;
    for (a.b=0 ; x ; a.a[++a.b]=x%10,x/=10);
    return a;
}

INT operator * (const INT &x,const INT &y){
    INT a;
    a.b=min(50,x.b+y.b-1);
    for (int i=1;i<=x.b;i++) for (int j=1;j<=y.b;j++) if (i+j-1<=50) a.a[i+j-1]+=x.a[i]*y.a[j]; 
    for (int i=1;i<=a.b;a.b+=(i==a.b && a.a[i+1] && i+1<=50),i++)  a.a[i+1]+=a.a[i]/10,a.a[i]%=10;
    for (;a.a[a.b]==0 && a.b!=1; a.b--);
    return a;
}

void print_INT(INT x){
    for (int i=min(x.b,50);i>=1;i--) printf("%d",x.a[i]); 
    puts("");
}

void Prime(int n){
    for (int i=2;i<=n;i++){
        if (!P[i]){
            p[++c]=i,ip[i]=c;
            for (int j=i+i;j<=n;j+=i) P[j]=1;
        }
    }
}

void pt(int x) {
    printf("%d
",x);
}

void fac(int x,int y){
    for (int i=1;i<=c && P[x];i++) while (!(x%p[i])) x/=p[i],cnt[i]+=y;
    cnt[ip[x]]+=y;
}

INT ans=Int(1);
int main(){
    scanf("%d%d",&A,&B);
    n=max(A,B),m=max(max(A,B)-min(A,B),min(A,B));
    Prime(n);
    for (int i=m+1;i<=n;i++) fac(i,1);
    for (int i=2;i<=n-m;i++) fac(i,-1);
    for (int i=1;i<=c;i++) while (cnt[i]--) ans=ans*Int(p[i]);
    print_INT(ans);
    return 0;
}

4808

黑白染色然后匈牙利

/* http://www.cnblogs.com/karl07/ */
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
using namespace std;

struct edge{
    int next,to;
}e[1000005];
int ade,n,m,cnt,T,c;
int x[]={1,2,-1,-2,-1,2,1,-2};
int y[]={2,1,-2,-1,2,-1,-2,1};
int mp[205][205],id[205][205],first[1000005],vis[1000005],match[1000005];

void addedge(int x,int y){
    e[++ade].next=first[x];
    e[ade].to=y;
    first[x]=ade;
}

bool check(int x,int y){
    return (x>=1 && x<=n && y>=1 && y<=m && !mp[x][y]);
}

#define s e[x].to
bool hungary(int p){
    for (int x=first[p];x;x=e[x].next){
        if (vis[s]!=T){
            vis[s]=T;
            if (!match[s] || hungary(match[s])) {match[s]=p; return 1;}
        }
    }
    return 0;
}
#undef s

int main(){
    scanf("%d%d",&n,&m);
    for (int i=1;i<=n;i++){
        for (int j=1;j<=m;j++){
            scanf("%d",&mp[i][j]);
            cnt+=(!mp[i][j]);
            id[i][j]=++c;
        }
    }
    for (int i=1;i<=n;i++)
        for (int j=1;j<=m;j++)
            if (((i+j)&1) && !mp[i][j])for (int k=0;k<8;k++) if (check(i+x[k],j+y[k])) addedge(id[i][j],id[i+x[k]][j+y[k]]);
    for (int i=1;i<=n;i++){
        for (int j=1;j<=m;j++){
            if (!mp[i][j] && ((i+j)&1)){
                T=id[i][j];
                cnt-=hungary(T);
            }
        }
    }
    printf("%d
",cnt);
    return 0;
}

4809

直接dfs

/* http://www.cnblogs.com/karl07/ */
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
using namespace std;

int n,ans;
int ban[20][20],y[20],a[40],b[40];

void dfs(int i){
    if (i>n) {ans++; return;} 
    for(int j=1;j<=n;j++) if (!(ban[i][j] || y[j] || a[i+j-1] || b[n-i+j] )){
        y[j]=a[i+j-1]=b[n-i+j]=1;
        dfs(i+1);
        y[j]=a[i+j-1]=b[n-i+j]=0;        
    }
}

int main(){
    scanf("%d",&n);
    for (int i=1;i<=n;i++) for (int j=1;j<=n;j++) scanf("%d",&ban[i][j]);
    dfs(1);
    printf("%d
",ans);
    return 0;
}