第14届蓝桥杯国赛题解

T1. 八进制回文数

#include 
typedef long long LL;
using namespace std;
int a[30];
//转八进制
LL f(LL m) {
    LL sum = 0, n = 0;
    while(m) {
        a[++ n] = m % 8;
        m /= 8;
    }
    for(int i = n; i >= 1; i --) sum = sum * 10 + a[i];
    return sum;
}
//数字反转
LL r(LL m)
{
    LL sum = 0;
    while(m) { 
        sum = sum * 10 + m % 10;
        m /= 10;
    }
    return sum;
}
int main()
{
    int n;
    cin >> n;
     //枚举平方根
    for(int i = 1; i <= n / i; i ++)
    {
        LL m = f(i * i);
        if(m == r(m)) 
            cout << i * i << " ";
    }
}

T2. 主要成分

#include 
#include 
#include 
using namespace std;
const int N = 1e6 + 10;
int a[N];
int main()
{
    int n;
    scanf("%d", &n);
    unordered_map<int, int> h;
    for(int i = 0; i < n; i ++)
    {
        scanf("%d", &a[i]);
        if(h.count(a[i])) h[a[i]] ++;
        else h[a[i]] = 1;
    }
    for(int i = 0; i < n; i ++) {
        if(h[a[i]] >= n / 2) {
            cout << a[i];
            return 0;
        }
    }
    cout << "No";
    return 0;
}

T3. 简单算数题

#include 
#include 
#include 
using namespace std;
stack<int> stk, op;
void eval() {
    int b = stk.top(); stk.pop();
    int a = stk.top(); stk.pop();
    char p = op.top(); op.pop();
    if(p == '+') stk.push(a + b);
    else if(p == '-') stk.push(a - b);
    else if(p == '*') stk.push(a * b);
    else if(p == '/') stk.push(a / b);
}
int main()
{
    string s;
    getline(cin, s);
    //运算符优先级
    unordered_map<char, int> pr {{'+', 1}, {'-', 1}, {'*', 2}, {'/', 2}};
    for(int i = 0; i < s.size(); i ++) {
        if(s[i] == ' ') continue;
        else if(isdigit(s[i]))
        {
            int j = i, x = 0;
            while(isdigit(s[j])) x = x * 10 + s[j ++] - '0';
            stk.push(x);
            i = j - 1;
        }
        else 
        {
        	//计算栈中优先级大于等于当前运算符
            while(!op.empty() && pr[op.top()] >= pr[s[i]]) eval();
            op.push(s[i]);   
        }
    }
    while(!op.empty()) eval();
    cout << stk.top();
    return 0;
}

T4. 数独填数

#include 
using namespace std;
char g[100][100];
//sum[x]表示x字符的出现总数，row[i][x]表示第i行中x字符有没有出现过
//col[i][x]表示第i列中x字符有没有出现过
//f[i][x]表示第i个大格子中x字符有没有出现过
int sum[150], row[10][150], col[10][150], f[10][150]; 
int check(int i, int j, char x) {
    if(sum[x] > 8) return 0;
    if(row[i][x]) return 0;
    if(col[j][x]) return 0;
    // i / 3 * 3 + j / 3; 大格子
    if(f[i / 3 * 3 + j / 3][x]) return 0;
    return 1;
}
void dfs(int n) {
    if(n > 80) 
    {
        for(int i = 0; i < 9; i ++)
        {
            for(int j = 0; j < 9; j ++)
                cout << g[i][j];
            cout << endl;
        }
        exit(0);
    }
    int i = n / 9, j = n % 9; //i行j列
    //已经填过数了
    if(g[i][j] != '.') 
    {
        dfs(n + 1);
        return ;
    }
    //枚举该位置可以填的数
    for(int x = '1'; x <= '9'; x ++)
    {
        if(!check(i, j, x)) continue;
        g[i][j] = x;
        sum[x] ++;
        row[i][x] = 1;
        col[j][x] = 1;
        f[i / 3 * 3 + j / 3][x] = 1;
        dfs(n + 1);
        g[i][j] = '.';
        sum[x] --;
        row[i][x] = 0;
        col[j][x] = 0;
        f[i / 3 * 3 + j / 3][x] = 0;
    }
    
}
int main()
{
    char x;
    for(int i = 0; i < 9; i ++)
    {
        for(int j = 0; j < 9; j ++)
        {
            cin >> x;
            g[i][j] = x;
            sum[x] ++;
            row[i][x] = 1;
            col[j][x] = 1;
            f[i / 3 * 3 + j / 3][x] = 1;
        }
    }
    dfs(0);
    return 0;
}