刷题(二)+基础复习

P8778 [蓝桥杯 2022 省 A] 数的拆分

真的不是黄题的难度。。。。刚开始以为就是个质因子分解的题

import java.io.*;
import java.util.*;
import java.util.concurrent.ScheduledExecutorService;

public class Main {
    static Scanner cin=new Scanner(System.in);
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
    static int N=4010;static long INF=Long.MAX_VALUE/2;static long mod=1000000007;
    static long prime[]=new long[N];static int cnt=0;
    static boolean vis[]=new boolean[N];
    public static void init()
    {
        for(int i=2;i<=4000;i++){
            if(!vis[i]){
                prime[++cnt]=i;
                for(int j=i;j<=4000;j+=i){
                    vis[j]=true;
                }
            }
        }
    }
    public static boolean check(long x)
    {
        long k=(long)Math.pow(x,1.0/2);
        if(k*k==x||(k+1)*(k+1)==x)
            return true;
        k=(long)Math.pow(x,1.0/3);
        if(k*k*k==x||(k+1)*(k+1)*(k+1)==x||(k+2)*(k+2)*(k+2)==x)
            return true;
        return false;
    }
    public static void main(String[] args) throws IOException
    {
        init();
        int t=cin.nextInt();
        while(t-->0)
        {
            long x=cin.nextLong();
            if(check(x)){
                out.println("yes");
                continue;
            }
            int flag=1;
            for(int i=1;i<=cnt;i++){
                if(x%prime[i]==0) {
                    int g = 0;
                    while (x % prime[i] == 0) {
                        g++;
                        x /= prime[i];
                    }
                    if (g == 1) {
                        flag = 0;
                        break;
                    }
                }
            }
            if(flag>0 && check(x))
                out.println("yes");
            else
                out.println("no");
        }
        out.close();
    }
}

P8804 [蓝桥杯 2022 国 B] 故障

会卡精度，两个浮点数相等的条件设置到10的-9次方或者更低。

import java.io.*;
import java.util.*;

public class Main {
    static Scanner cin=new Scanner(System.in);
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
    static int N=4010;static long INF=Long.MAX_VALUE/2;static long mod=1000000007;
    static int n,m,k,b[]=new int[105];
    static double a[][]=new double[105][105],p[]=new double[105],ans[]=new double[105];

    public static void main(String[] args) throws IOException
    {
        n=cin.nextInt();m=cin.nextInt();
        for(int i=1;i<=n;i++) p[i]=cin.nextDouble()*0.01;
        for(int i=1;i<=n;i++)
            for(int j=1;j<=m;j++) a[i][j]=cin.nextDouble()*0.01;
        k=cin.nextInt();
        for(int i=1;i<=k;i++){
            int x=cin.nextInt();b[x]=1;
        }
        for(int i=1;i<=n;i++){
            ans[i]=p[i];
            for(int j=1;j<=m;j++){
                if(b[j]>0) ans[i]*=a[i][j];
                else ans[i]*=(1-a[i][j]);
            }
        }
        double sum=0;
        for(int i=1;i<=n;i++) sum+=ans[i];
        List<double[]> e=new ArrayList<>();
        for(int i=1;i<=n;i++)
            e.add(new double[]{(double) i,ans[i]/sum});
        Collections.sort(e, new Comparator<double[]>() {
            @Override
            public int compare(double[] o1, double[] o2) {
                if(Math.abs(o1[1]-o2[1])<1e-9)
                    return (int) (o1[0]-o2[0]);
                if(o1[1]>o2[1]) return -1;
                else return 1;
            }
        });
        for(double[] k:e){
            System.out.println((int)k[0]+" "+String.format("%.2f",k[1]*100).toString());
        }
        out.close();
    }
}

P8783 [蓝桥杯 2022 省 B] 统计子矩阵

80分做法，矩阵前缀和+四重循环

import java.io.*;
import java.util.*;

public class Main {
    static Scanner cin=new Scanner(System.in);
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
    static int N=4010;static long INF=Long.MAX_VALUE/2;static long mod=1000000007;
    static int n,m,val,a[][]=new int[505][505],sum[][]=new int[505][505];

    public static void main(String[] args) throws IOException
    {
        n=cin.nextInt();m=cin.nextInt();val=cin.nextInt();
        for(int i=1;i<=n;i++)
            for(int j=1;j<=m;j++) {
                a[i][j]=cin.nextInt();
                sum[i][j]=sum[i-1][j]+sum[i][j-1]-sum[i-1][j-1]+a[i][j];
            }
        int ans=0,tmp=0;
        for(int i=1;i<=n;i++)
        {
            for(int j=1;j<=m;j++)
            {
                for(int k=0;k<i;k++)
                {
                    for(int g=0;g<j;g++)
                    {
                        tmp=sum[i][j]-sum[i][g]-sum[k][j]+sum[k][g];
                        if(tmp<=val) ans++;
                    }
                }
            }
        }
        System.out.println(ans);
        out.close();
    }
}

双指针优化一重循环，ac

import java.io.*;
import java.util.*;

public class Main {
    static Scanner cin=new Scanner(System.in);
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
    static int N=4010;static long INF=Long.MAX_VALUE/2;static long mod=1000000007;
    static int n,m,val,a[][]=new int[505][505],sum[][]=new int[505][505];
    public static int sum(int x1,int y1,int x2,int y2)
    {
        return sum[x2][y2]-sum[x1-1][y2]-sum[x2][y1-1]+sum[x1-1][y1-1];
    }
    public static void main(String[] args) throws IOException
    {
        n=cin.nextInt();m=cin.nextInt();val=cin.nextInt();
        for(int i=1;i<=n;i++)
            for(int j=1;j<=m;j++) {
                a[i][j]=cin.nextInt();
                sum[i][j]=sum[i-1][j]+sum[i][j-1]-sum[i-1][j-1]+a[i][j];
            }
        long ans=0;
        int up=0,down=0,l=0,r=0;
        for(up=1;up<=n;up++)
        {
            for(down=up;down<=n;down++)
            {
                for(r=1,l=1;r<=m;r++)
                {
                    while(l<=r&&sum(up,l,down,r)>val) l++;
                    if(l<=r) ans+=r-l+1;
                }
            }
        }
        System.out.println(ans);
        out.close();
    }
}

P8808 [蓝桥杯 2022 国 C] 斐波那契数组

暴力枚举数组前两项。数组长度最大不超过30（1，1，2，3，5，8……）。
而长度受到起始2项的限制。

import java.io.*;
import java.util.*;

public class Main {
    static Scanner cin=new Scanner(System.in);
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
    static int N=100010;static long INF=Long.MAX_VALUE/2;static long mod=1000000007;
    static int n,a[]=new int[N],f[]=new int[N];
    public static void main(String[] args) throws IOException
    {
        n=cin.nextInt();
        int mx=0;
        for(int i=1;i<=n;i++) {
            a[i]=cin.nextInt();
            mx=Math.max(mx,(int)Math.log(a[i]));
        }
        int ans=1000000;
        for(int i=1;i<=mx*30;i++)
        {
            int cnt=0;
            f[1]=f[2]=i;
            if(f[1]!=a[1]) cnt++;
            if(f[2]!=a[2]) cnt++;
            for(int j=3;j<=n;j++)
            {
                f[j]=f[j-1]+f[j-2];
                if(f[j]!=a[j]) {
                    cnt++;
                    if(cnt>=ans) break;
                }
            }
            ans=Math.min(ans,cnt);
        }
        out.println(ans);
        out.close();
    }
}

经典DFS

import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {
    static Scanner cin=new Scanner(System.in);
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
    static int N=200010;static long INF=Long.MAX_VALUE/2;static long mod=1000000007;
    public static int n,a[]=new int[N];
    public static boolean vis[]=new boolean[N];
    public static void dfs(int u)
    {
        if(u==n)
        {
            for(int i=0;i<n;i++)
                out.print(a[i]+" ");
            out.println();
            return;
        }
        for(int i=1;i<=n;i++)
        {
            if(!vis[i]){
                a[u]=i;
                vis[i]=true;
                dfs(u+1);
                vis[i]=false;
            }
        }
    }
    public static void main(String[] args) throws IOException
    {
        n=cin.nextInt();
        dfs(0);
        out.close();
    }
}

N皇后问题

法一：

import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {
    static Scanner cin=new Scanner(System.in);
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
    static int N=200010;static long INF=Long.MAX_VALUE/2;static long mod=1000000007;
    public static int n,ans,a[]=new int[N];
    public static char c[][]=new char[55][55];
    public static boolean col[]=new boolean[N],dg[]=new boolean[N],udg[]=new boolean[N];
    public static void dfs(int u)
    {
        if(u==n)
        {
            ans++;
            for(int i=0;i<n;i++) {
                for(int j=0;j<n;j++)
                    out.print(c[i][j]);
                out.println();
            }
            out.println("----------------------");
            return;
        }
        for(int i=0;i<n;i++)
        {
            if(!col[i]&&!dg[i+u]&&!udg[i-u+n]) {
                c[u][i]='Q';
                col[i]=dg[i+u]=udg[i-u+n]=true;
                dfs(u+1);
                c[u][i]='.';
                col[i]=dg[i+u]=udg[i-u+n]=false;
            }
        }
    }
    public static void main(String[] args) throws IOException
    {
        n=cin.nextInt();
        for(int i=0;i<n;i++) for(int j=0;j<n;j++) c[i][j]='.';
        dfs(0);
        out.println(ans);
        out.close();
    }
}

法二：枚举每一个格子

import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {
    static Scanner cin=new Scanner(System.in);
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
    static int N=200010;static long INF=Long.MAX_VALUE/2;static long mod=1000000007;
    public static int n,ans,a[]=new int[N];
    public static char c[][]=new char[55][55];
    public static boolean row[]=new boolean[N],col[]=new boolean[N],dg[]=new boolean[N],udg[]=new boolean[N];
    public static void dfs(int x,int y,int cnt)
    {
        if(y==n) {y=0;x++;}
        if(x==n)
        {
            if(cnt==n){
                for(int i=0;i<n;i++) {
                    for(int j=0;j<n;j++) out.print(c[i][j]);
                    out.println();
                }
                ans++;
                out.println("----------------------");
            }
            return;
        }
        //不放皇后
        dfs(x,y+1,cnt);
        // 放皇后
        if(!row[x]&&!col[y]&&!dg[x+y]&&!udg[x-y+n])
        {
            c[x][y]='Q';
            row[x]=col[y]=dg[x+y]=udg[x-y+n]=true;
            dfs(x,y+1,cnt+1);
            row[x]=col[y]=dg[x+y]=udg[x-y+n]=false;
            c[x][y]='.';
        }
    }
    public static void main(String[] args) throws IOException
    {
        n=cin.nextInt();
        for(int i=0;i<n;i++) for(int j=0;j<n;j++) c[i][j]='.';
        dfs(0,0,0);
        out.println(ans);
        out.close();
    }
}

经典BFS

import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {
    static Scanner cin=new Scanner(System.in);
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
    static int N=1010;static long INF=Long.MAX_VALUE/2;static long mod=1000000007;
    public static int n,m,a[][]=new int[N][N],d[][]=new int[N][N];
    public static int dx[]=new int[]{-1,1,0,0};
    public static int dy[]=new int[]{0,0,-1,1};
    public static int bfs()
    {
        Queue<int[]> q=new LinkedList<>();
        for(int i=0;i<n;i++)
            for(int j=0;j<m;j++) d[i][j]=-1;
        d[0][0]=0;
        q.add(new int[]{0,0});
        while(!q.isEmpty())
        {
            int[] tmp=q.peek();
            q.poll();
            for(int i=0;i<4;i++){
                int x=tmp[0]+dx[i],y=tmp[1]+dy[i];
                if(x>=0&&x<n&&y>=0&&y<m&&a[x][y]==0&&d[x][y]==-1){
                    d[x][y]=d[tmp[0]][tmp[1]]+1;
                    q.add(new int[]{x,y});
                }
            }
        }
        return d[n-1][m-1];
    }
    public static void main(String[] args) throws IOException
    {
        n=cin.nextInt();
        m=cin.nextInt();
        for(int i=0;i<n;i++)
            for(int j=0;j<m;j++)
                a[i][j]=cin.nextInt();
        out.println(bfs());
        out.close();
    }
}
/*
5 5
0 1 0 0 0
0 1 0 1 0
0 0 0 0 0
0 1 1 1 0
0 0 0 1 0
 */