题目列表

试题 A: 门牌制作
试题 B: 寻找 2020
试题 C: 蛇形填数
试题 D: 七段码
试题 E: 排序
试题 F: 成绩分析
试题 G: 单词分析
试题 H: 数字三角形
试题 I: 子串分值和
试题 J: 装饰珠
试题 B: 寻找 2020 附件

试题 A: 门牌制作

本题总分： 5 分

问题：
小蓝要为一条街的住户制作门牌号。
这条街一共有 2020 位住户，门牌号从 1 到 2020 编号。
小蓝制作门牌的方法是先制作 0 到 9 这几个数字字符，最后根据需要将字
符粘贴到门牌上，例如门牌 1017 需要依次粘贴字符 1、 0、 1、 7，即需要 1 个
字符 0， 2 个字符 1， 1 个字符 7。
请问要制作所有的 1 到 2020 号门牌，总共需要多少个字符 2？

思路： 暴力

答案： 624

public class Main
{public static void main(String[] args){int ans=0;for(int i=1;i<=2020;i++){ans += judge(i);}System.out.print(ans);}//判断这个数字里有几个 2public static int judge(int a){int temp = 0;while(a!=0){int t = a%10;if(t==2){temp++;}a/=10;}return temp;}
}

试题 B: 寻找 2020

本题总分：5 分

附件在本篇末尾

问题：

小蓝有一个数字矩阵，里面只包含数字 0 和 2。小蓝很喜欢 2020，他想找到这个数字矩阵中有多少个 2020 。
小蓝只关注三种构成 2020 的方式：

同一行里面连续四个字符从左到右构成 2020。
同一列里面连续四个字符从上到下构成 2020。
在一条从左上到右下的斜线上连续四个字符，从左上到右下构成 2020。
例如，对于下面的矩阵：

一共有 5 个 2020。其中 1 个是在同一行里的，1 个是在同一列里的，3 个是斜线上的。
小蓝的矩阵比上面的矩阵要大，由于太大了，他只好将这个矩阵放在了一个文件里面，在试题目录下有一个文件 2020.txt，里面给出了小蓝的矩阵。
请帮助小蓝确定在他的矩阵中有多少个 2020。

思路： 暴力

答案： 16120

import java.io.*;public class HelloWorld
{public static void main(String[] args) throws IOException{BufferedReader in = new BufferedReader(new InputStreamReader(new FileInputStream("D:/demo/1.txt")));char[][] map = new char[300][];for (int i = 0; i < 300; i++){map[i] = in.readLine().toCharArray();}int ans=0;for(int y=0;y<300;y++){for(int x=0;x<300;x++){//横排if(x<=296){if(map[y][x]=='2'&&map[y][x+1]=='0'&&map[y][x+2]=='2'&&map[y][x+3]=='0'){ans++;}}//竖排if(y<=296){if(map[y][x]=='2'&&map[y+1][x]=='0'&&map[y+2][x]=='2'&&map[y+3][x]=='0'){ans++;}}//斜排if(y<=296&&x<=296){if(map[y][x]=='2'&&map[y+1][x+1]=='0'&&map[y+2][x+2]=='2'&&map[y+3][x+3]=='0'){ans++;}}}}System.out.print(ans);}
}

试题 C: 蛇形填数

本题总分： 10 分

问题：
如下图所示，小明用从 1 开始的正整数“蛇形”填充无限大的矩阵。

容易看出矩阵第二行第二列中的数是 5。请你计算矩阵中第 20 行第 20 列的数是多少？

思路： 由题意可看出，求第x行第x列数的规律为：值 = (x-1)*2的累加 + x

则这一题中20行20列的值为：1+2+3+…+(19*2-1)+(19*2) + 20 = 761

答案： 761

public class Main
{public static void main(String[] args){int ans=0;for(int i=1;i<=38;i++){ans += i;}ans+=20;System.out.print(ans);}
}

试题 D: 七段码

本题总分：10 分

问题：
小蓝要用七段码数码管来表示一种特殊的文字。

上图给出了七段码数码管的一个图示，数码管中一共有 7 段可以发光的二极管，分别标记为 a, b, c, d, e, f, g。
小蓝要选择一部分二极管（至少要有一个）发光来表达字符。在设计字符的表达时，要求所有发光的二极管是连成一片的。

例如：b 发光，其他二极管不发光可以用来表达一种字符。
例如：c 发光，其他二极管不发光可以用来表达一种字符。这种方案与上
一行的方案可以用来表示不同的字符，尽管看上去比较相似。

例如：a, b, c, d, e 发光，f, g 不发光可以用来表达一种字符。
例如：b, f 发光，其他二极管不发光则不能用来表达一种字符，因为发光的二极管没有连成一片。
请问，小蓝可以用七段码数码管表达多少种不同的字符？

思路： dfs出所有情况，然后用并查集判断是否属于同一子集

答案： 80

import java.util.ArrayList;
import java.util.Collection;public class test
{static int ans = 0;static int[] jl = new int[10];static int[][] map = new int[10][10];static int[] father = new int[10];public static void main(String[] args){//储存关系 a~g对应1~7map[1][2] = map[2][1] = 1;//a bmap[1][6] = map[6][1] = 1;//a fmap[2][7] = map[7][2] = 1;//b gmap[2][3] = map[3][2] = 1;//b cmap[3][4] = map[4][3] = 1;//c d map[3][7] = map[7][3] = 1;//c gmap[4][5] = map[5][4] = 1;//d emap[5][6] = map[6][5] = 1;//e fmap[5][7] = map[7][5] = 1;//e g map[6][7] = map[7][6] = 1;//f g//dfs遍历所有情况dfs(0);//System.out.print(ans);}public static void dfs(int n){//当7个灯都有状态时 进行判定if(n==7){//把亮着的灯统计下来ArrayList<Integer> a = new ArrayList<>();for(int i=1;i<=7;i++){if(jl[i]==1){a.add(new Integer(i));}}//判断if(a.size()!=0){if(judge(a)==1){ans++;}}a.clear();return;}//否则dfs灯情况jl[n+1] = 1;dfs(n+1);jl[n+1] = 0;dfs(n+1);}public static int judge(ArrayList<Integer> a){//System.out.println(++js);//并查集父集重置for(int i=0;i<10;i++){father[i] = i;}//并集for(int i=0;i<a.size();i++){for(int ii=0;ii<a.size();ii++){//如果两边相连的话 进行并集操作if(map[a.get(i).intValue()][a.get(ii).intValue()]==1){int fx = find(a.get(i).intValue());int fy = find(a.get(ii).intValue());   if(fx!=fy){father[fx] = fy;}} }}//查看是否都属于一个集合int temp = find(a.get(0).intValue());for(int i=1;i<a.size();i++){if(find(a.get(i).intValue())!=temp){return 0;}}return 1;}//查集public static int find(int x){return father[x]==x ? x : (father[x] = find(father[x]));}}

试题 E: 排序

本题总分： 15 分

思路： 不能有相同字符的话就从a开始倒着加，因为14+13+12+11+10+9+8+7+6+5+4+3+2+1+0 = 105，所以一共有15个字母。然后让总排序次数减五次，因为字典序要求最小，则让第六位向前挪5次即可。

答案即为：9 14 13 12 11 10 8 7 6 5 4 3 2 1 0

答案： jonmlkihgfedcba

以下题目均能通过AcWing和蓝桥杯题库的数据测试

试题 F: 成绩分析

试题 F: 成绩分析本题总分： 15 分
时间限制: 1.0s 内存限制: 512.0MB

问题：
小蓝给学生们组织了一场考试，卷面总分为 100 分，每个学生的得分都是一个 0 到 100 的整数。
请计算这次考试的最高分、最低分和平均分。

输入：
输入的第一行包含一个整数 n，表示考试人数。接下来 n 行，每行包含一个 0 至 100 的整数，表示一个学生的得分。

输出：
输出三行。第一行包含一个整数，表示最高分。第二行包含一个整数，表示最低分。
第三行包含一个实数，四舍五入保留正好两位小数，表示平均分。

样例输入：

样例输出：

99
10
71.29

评测用例规模与约定：
对于 50% 的评测用例， 1 ≤ n ≤ 100。
对于所有评测用例， 1 ≤ n ≤ 10000。

思路： 送分题，挨个统计即可

AC代码： OJ链接

import java.util.Scanner;public class Main
{public static void main(String[] args){Scanner sc = new Scanner(System.in);int n = sc.nextInt();int max = 0;int min = 101;double he = 0;for(int i=0;i<n;i++){int t = sc.nextInt();if(t>max){max = t;}if(t<min){min = t;}he += t;}double ans = (double)(int)((he/n+0.005)*100)/100;System.out.println(max);System.out.println(min);System.out.println(ans);}
}

试题 G: 单词分析

时间限制: 1.0s 内存限制: 512.0MB
本题总分：20 分

问题：
小蓝正在学习一门神奇的语言，这门语言中的单词都是由小写英文字母组成，有些单词很长，远远超过正常英文单词的长度。小蓝学了很长时间也记不住一些单词，他准备不再完全记忆这些单词，而是根据单词中哪个字母出现得最多来分辨单词。
现在，请你帮助小蓝，给了一个单词后，帮助他找到出现最多的字母和这个字母出现的次数。

输入：
输入一行包含一个单词，单词只由小写英文字母组成。

问题：
输出两行，第一行包含一个英文字母，表示单词中出现得最多的字母是哪个。如果有多个字母出现的次数相等，输出字典序最小的那个。
第二行包含一个整数，表示出现得最多的那个字母在单词中出现的次数。

样例输入：

lanqiao

样例输出：

a
2

样例输入：

longlonglongistoolong

样例输出：

o
6

评测用例规模与约定：
对于所有的评测用例，输入的单词长度不超过 1000。

思路： 暴力统计即可

代码： OJ链接

import java.util.Scanner;public class Main
{public static void main(String[] args){Scanner sc = new Scanner(System.in);String s = sc.nextLine();int[] ans = new int[30];for(int now=0;now<s.length();now++){ans[(int)(s.charAt(now)-'a')+1]++;}int end = 1;for(int now=1;now<=26;now++){if(ans[end]<ans[now]){end = now;}}System.out.println((char)('a'+end-1));System.out.println(ans[end]);}
}

试题 H: 数字三角形

时间限制: 1.0s 内存限制: 512.0MB
本题总分：20 分

问题：
上图给出了一个数字三角形。从三角形的顶部到底部有很多条不同的路径。
对于每条路径，把路径上面的数加起来可以得到一个和，你的任务就是找到最大的和。
路径上的每一步只能从一个数走到下一层和它最近的左边的那个数或者右边的那个数。此外，向左下走的次数与向右下走的次数相差不能超过 1。

输入：
输入的第一行包含一个整数 N (1 < N ≤ 100)，表示三角形的行数。下面的N 行给出数字三角形。数字三角形上的数都是 0 至 100 之间的整数。

输出：
输出一个整数，表示答案。

样例输入：

样例输出：

思路： B组这题是简化过的，数据量少了，也多了条件，所以直接dfs暴力就好。当左右差减一大于剩下行数时，说明走到末尾时必定相差超过1，可以进行剪枝。

AC代码：
OJ链接1 链接里是本题版本，用DFS写
OJ链接2 链接里是未简化的版本，用DP写

import java.util.Scanner;public class Main
{static int ans = 0;static int num = 0;static int[][] map = new int[510][510];public static void main(String[] args){Scanner sc = new Scanner(System.in);num = sc.nextInt();for(int i=1;i<=num;i++){for(int ii=1;ii<=i;ii++){map[i][ii]=sc.nextInt();}}dfs(1,1,0+map[1][1],0);System.out.print(ans);}public static void dfs(int y,int x,int he,int cha)//y x 和  左右差{if(x<=0||x>y)//剪枝 越界{return;}if(Math.abs(cha)-1>(num-y))//剪枝 左右差大于剩下行数 {return;}if(y==num)//到达最底层{if(he>ans&&Math.abs(cha)<=1){ans = he;}return;}dfs(y+1,x,he+map[y+1][x],cha-1);//左下dfs(y+1,x+1,he+map[y+1][x+1],cha+1);//右下}
}

试题 I: 子串分值和

时间限制: 1.0s 内存限制: 512.0MB
本题总分：25 分

问题：
对于一个字符串 S，我们定义 S 的分值 f(S) 为 S 中出现的不同的字符个数。

例如 f(“aba”)=2，f(“abc”)=3,f(“aaa”)=1。

现在给定一个字符串 S[0…n−1]（长度为 n），请你计算对于所有 S 的非空子串 Si…j，f(S[i…j]) 的和是多少。

输入：
输入一行包含一个由小写字母组成的字符串 S。

输出：
输出一个整数表示答案。

样例输入：

ababc

样例输出：

样例说明：

子串 f值
a     1
ab    2
aba   2
abab  2
ababc 3b    1ba   2bab  2babc 3a   1ab  2abc 3b  1bc 2c 1

评测用例规模与约定：
对于 20% 的评测用例，1≤n≤10；
对于 40% 的评测用例，1≤n≤100；
对于 50% 的评测用例，1≤n≤1000；
对于 60% 的评测用例，1≤n≤10000；
对于所有评测用例，1≤n≤100000。

思路： 总体思路和C组的那道题有点类似，不过这个更绕一点，没那个直接。

思路就是每一个字符的权值为：(上一次出现的与当前出现的位置间隔+1) * (末尾与当前位置差值+1)
如果是第一次出现，前间隔值就为当前位置-1

例如： ababc 末尾长度为5a的当前位置为1，前间隔值为0，权值为 (0+1) * (5-1+1) = 5
b的当前位置为2，前间隔值为1，权值为 (1+1) * (5-2+1) = 8
a的当前位置为3，前间隔值为1，权值为 (1+1) * (5-3+1) = 6
b的当前位置为4，前间隔值为1，权值为 (1+1) * (5-4+1) = 4
c的当前位置为5，前间隔值为4，权值为 (4+1) * (5-5+1) = 5累加：5+8+6+4+5 = 28

代码： OJ链接

import java.util.Scanner;public class Main
{public static void main(String[] args){Scanner sc = new Scanner(System.in);String s = sc.nextLine();//前数组int[] piror = new int[s.length()+10];//答案值long ans = 0;//中间值数组 用来储存每个字母的前后值位置int[] temp = new int[26];//初始化for(int i=0;i<s.length()+10;i++){piror[i] = 0;}//找每个位置字符的上一位for(int i=1;i<=s.length();i++){int t = s.charAt(i-1)-'a';//计算出数组位置piror[i] = i-temp[t];//计算出与上一位相同字母位置的差值temp[t] = i;}//计算答案 前差值*后值等于当前字符的权值 累加即可for(int i=1;i<=s.length();i++){ans += (long)(piror[i]) * (long)(s.length()-i+1);}System.out.println(ans);}
}

试题 J: 装饰珠

本题总分： 25 分
时间限制: 1.0s 内存限制: 512.0MB

样例输入：

1 1
2 1 2
1 1
2 2 2
1 1
1 3
3
1 5 1 2 3 5 8
2 4 2 4 8 15
3 2 5 10

样例输出：

样例说明：

按照如下方式镶嵌珠子得到最大价值 18，括号内表示镶嵌的装饰珠的种类编号：

1: (1)
2: (1) (2)
3: (1)
4: (2) (2)
5: (1)
6: (2)

思路：

AC代码： OJ链接

试题 B: 寻找 2020 附件

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2020 蓝桥杯 Java实现 10月B组省赛

题目列表

试题 A: 门牌制作

试题 B: 寻找 2020

试题 C: 蛇形填数

试题 D: 七段码

试题 E: 排序

试题 F: 成绩分析

试题 G: 单词分析

试题 H: 数字三角形

试题 I: 子串分值和

试题 J: 装饰珠

试题 B: 寻找 2020 附件

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