2020第十一届蓝桥杯第二场省赛C++A组【A-H】

A. 门牌制作

答案

624

代码

#include <bits/stdc++.h>
using namespace std;
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int cnt = 0;
    for (int i = 1; i <= 2020; i++) {
        int x = i;
        while (x) {
            if (x % 10 == 2) ++cnt;
            x /= 10;
        }
    }
    cout << cnt << "\n";
    return 0;
}

B. 既约分数

答案

2481215

代码

#include <bits/stdc++.h>
using namespace std;
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int cnt = 0;
    for (int i = 1; i <= 2020; i++) {
        for (int j = 1; j <= 2020; j++) {
            if (__gcd(i, j) == 1) 
                ++cnt;
        }
    }
    cout << cnt << "\n";
    return 0;
}

C. 蛇形填数

答案

761

代码

#include <bits/stdc++.h>
using namespace std;
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int x = 1, y = 1;
    int a[100][100] = {};
    int num = 1;
    for (int i = 1; x <= 50; i++) {
        for (int j = 0; j < i; j++) {
            a[x][y] = num++;
            if (j != i - 1) {
                if (i & 1) --x, ++y;
                else ++x, --y;
            }
        }
        if (i & 1) ++y;
        else ++x;
    }
    cout << a[20][20] << "\n";
    return 0;
}

D. 七段码

答案

80

代码

#include <bits/stdc++.h>
using namespace std;

bool light[7];
vector<vector<int> > G(7);
int ans;

bool judge(vector<int> &v1) {
    vector<int> v2;
    queue<int> que;
    bool vis[7] = {};
    que.push(v1[0]);
    vis[v1[0]] = true;
    while (!que.empty()) {
        int u = que.front();
        que.pop();
        v2.push_back(u);
        for (int i = 0; i < G[u].size(); i++) {
            int v = G[u][i];
            if (find(v1.begin(), v1.end(), v) != v1.end() && !vis[v]) {
                que.push(v);
                vis[v] = true;
            }
        }
    }
    sort(v1.begin(), v1.end());
    sort(v2.begin(), v2.end());
    return v2 == v1;
}

void dfs(int dep) {
    if (dep == 7) {
        vector<int> v;
        for (int i = 0; i < 7; i++) if (light[i]) v.push_back(i);
        if (v.size() && judge(v)) ++ans;    
        return;
    }
    light[dep] = true;
    dfs(dep + 1);
    light[dep] = false;
    dfs(dep + 1);
}

void build_graph() {
    G[0].push_back(1), G[0].push_back(5);
    G[1].push_back(0), G[1].push_back(2), G[1].push_back(6);
    G[2].push_back(1), G[2].push_back(3), G[2].push_back(6);
    G[3].push_back(2), G[3].push_back(4);
    G[4].push_back(3), G[4].push_back(5), G[4].push_back(6);
    G[5].push_back(0), G[5].push_back(4), G[5].push_back(6);
    G[6].push_back(1), G[6].push_back(2), G[6].push_back(4), G[6].push_back(5);
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    build_graph();
    dfs(0);
    cout << ans << "\n";
    return 0;
}

E. 平面分割

答案

1391

代码

#include <bits/stdc++.h>
using namespace std;
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int line[25] = {};
    line[1] = 2;
    for (int i = 2; i <= 20; i++) {
        line[i] = line[i - 1] + i;
    }
    int ans = line[20];
    for (int i = 1; i <= 20; i++) {
        ans += 40 + 2 * (i - 1);
    }
    cout << ans << "\n";
    return 0;
}

F. 成绩分析

代码

#include <bits/stdc++.h>
using namespace std;
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int n;
    scanf("%d", &n);
    int mx = -1, mi = 101, sum = 0;
    for (int i = 0; i < n; i++) {
        int x;
        scanf("%d", &x);
        mx = max(mx, x);
        mi = min(mi, x);
        sum += x;
    }
    printf("%d\n", mx);
    printf("%d\n", mi);
    printf("%.2f\n", 1.0 * sum / n);
    return 0;
}

G. 回文日期

代码

#include <bits/stdc++.h>
using namespace std;
const int month[2][13] = {
    { 0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 },
    { 0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 }
};
string my_to_string(int n) {
    string s;
    do {
        s += '0' + n % 10;
        n /= 10;
    } while (n);
    reverse(s.begin(), s.end());
    return s;
}
int my_stoi(const string &s) {
    int res = 0;
    for (int i = 0; i < int(s.size()); i++) {
        res = res * 10 + s[i] - '0';
    }
    return res;
}
bool is(int year) {
    return (year % 4 == 0 && year % 100 != 0) || (year % 400 == 0);
}
bool legal(const string &s) {
    int y = my_stoi(s.substr(0, 4));
    int m = my_stoi(s.substr(4, 2));
    int d = my_stoi(s.substr(6, 2));
    if (m < 1 || m > 12) return false;
    if (d < 1 || d > month[is(y)][m]) return false;
    return true;
}
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    vector<int> v1, v2;
    for (int i = 1000; i <= 9999; i++) {
        string s1(my_to_string(i));
        string s2(s1.rbegin(), s1.rend());
        string s = s1 + s2;
        string t(s.rbegin(), s.rend());
        if (legal(s)) {
            if (s == t) {
                v1.push_back(my_stoi(s));
            }
            if ((s[0] == s[2] && s[2] == s[5] && s[5] == s[7]) && 
                (s[1] == s[3] && s[3] == s[4] && s[4] == s[6]) && 
                (s[0] != s[1])) {
                v2.push_back(my_stoi(s));
            }
        }
    }
    int n;
    cin >> n;
    cout << *upper_bound(v1.begin(), v1.end(), n) << "\n";
    cout << *upper_bound(v2.begin(), v2.end(), n) << "\n";
    return 0;
}

H. 子串分值

代码

#include <bits/stdc++.h>
using namespace std;
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    string s;
    cin >> s;
    int n = s.size();
    vector<vector<int> > pos(26);
    for (int i = 0; i < 26; i++) {
        pos[i].push_back(-1);
    }
    for (int i = 0; i < n; i++) {
        pos[s[i] - 'a'].push_back(i);
    }
    for (int i = 0; i < 26; i++) {
        pos[i].push_back(n);
    }
    long long ans = 0;
    for (int i = 0; i < 26; i++) {
        for (int j = 1; j + 1 < int(pos[i].size()); j++) {
            int l = pos[i][j] - pos[i][j - 1] - 1;
            int r = pos[i][j + 1] - pos[i][j] - 1;
            ans += 1LL * (l + 1) * (r + 1);
        }
    }
    cout << ans << "\n";
    return 0;
}