2019年海淀区青少年程序设计挑战活动小学组复赛试题详细答案

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1 约数

#include <iostream>
#include <cmath>
using namespace std;

int main()
{
    int n;
    cin >> n;
    int root = sqrt(n);
    for(int i = 2; i <= root; i++)
    {
        if(0 == n % i)
        {
            cout << n / i;
            return 0;
        }
    }

    cout << 1;
    return 0;
}

2 阶乘

#include<iostream>
using namespace std;

// zero count from tail of n!
int zeroCnt1(int n)
{
    int cnt = 0;
    while(n)
    {
        n /= 5;
        cnt += n;
    }

    return cnt;
}

// zero count from tail of n!! when n is even
int zeroCnt2(int n)
{
    n /= 10;
    int cnt = n;
    while(n)
    {
        n /= 5;
        cnt += n;
    }

    return cnt;
}

int main()
{
    int n;
    cin >> n;
    cout << zeroCnt1(n) << ' ';

    if(n % 2)
    {
        cout << 0;
    }
    else
    {
        cout << zeroCnt2(n) << endl;
    }

    return 0;
}

3 序列

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

int main()
{
    int n;
    cin >> n;
    vector<int> vec;
    for(int i = 0; i < n; i++)
    {
        int x;
        cin >> x;
        vec.push_back(x);
        reverse(vec.begin(), vec.end());
    }

    for(int i = 0; i < n; i++)
    {
        cout << vec[i] << ' ';
    }

    return 0;
}

4 糖果

#include <iostream>
#include <memory.h>
using namespace std;

int main()
{
    int cnt[256];
    memset(cnt, 0, sizeof(cnt));
    int start = 0;
    int maxLen = 0;
    int len = 0;

    string s;
    cin >> s;
    for(unsigned i = 0; i < s.size(); i++)
    {
        cnt[s[i]]++;
        if(2 == cnt[s[i]])
        {
            start++;
            cnt[s[i]] = 1;
        }

        len = i - start + 1;
        if(len > maxLen)
        {
            maxLen = len;
        }
    }

    cout << maxLen;
    return 0;
}

5 迷宫

#include <iostream>
#include <cstdio>
using namespace std;

char maze[10][10];

int main()
{
    freopen("maze.in", "r", stdin);

    int n, m;
    cin >> n >> m;
    int row, col;
    for(row = 1; row <= n; row++)
    {
        for(col = 1; col <= m; col++)
        {
            cin >> maze[row][col];
            if('S' == maze[row][col])
            {
                maze[row][col] = '1';
            }
        }
    }

    int cnt = 0;
    bool flag = true;
    while(flag)
    {
        flag = false;
        for(int row = 1; row <= n; row++)
        {
            for(int col = 1; col <= m; col++)
            {
                if(maze[row][col] == '1')
                {
                    if(maze[row+1][col]=='*')
                    {
                        cnt++;
                        maze[row+1][col]='1';
                        flag = true;
                    }
                    if(maze[row-1][col]=='*')
                    {
                        cnt++;
                        maze[row-1][col]='1';
                        flag = true;
                    }
                    if(maze[row][col+1]=='*')
                    {
                        cnt++;
                        maze[row][col+1]='1';
                    }
                    if(maze[row][col-1]=='*')
                    {
                        cnt++;
                        maze[row][col-1]='1';
                        flag = true;
                    }


                    if(maze[row+1][col]=='.')
                    {
                        maze[row+1][col]='1';
                        flag = true;
                    }
                    if(maze[row-1][col]=='.')
                    {
                        maze[row-1][col]='1';
                        flag = true;
                    }
                    if(maze[row][col+1]=='.')
                    {
                        maze[row][col+1]='1';
                        flag = true;
                    }
                    if(maze[row][col-1]=='.')
                    {
                        maze[row][col-1]='1';
                        flag = true;
                    }
                }//if
            }//for
        }//for
    }//while

    cout << cnt << endl;

    return 0;
}

6 盒子

#include <iostream>
#include <algorithm>
using namespace std;

int main()
{
    int n;
    cin >> n;
    int a[n];
    for(int i = 0; i < n; i++)
    {
        cin >> a[i];
    }

    sort(a, a + n, greater<int>());

    int cnt = 0;
    int sum = 0;
    for(int i = 0; i < n; i++)
    {
        cnt++;
        sum += (a[i] + 1); // 1 means the box itself
        if(sum >= n)
        {
            cout << cnt;
            return 0;
        }
    }

    return 0;
}

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