第十四届蓝桥杯编程题部分代码题解

C. 冶炼金属

最大值就是取 $a/b$ 的最小值，最小值就是二分找到满足 $mid\ast (b_i+1)\ge a_i$ 的最小值

#include<bits/stdc++.h>
#define int long long
#define x first
#define y second
using namespace std;

void solve()
{
    int n;
    cin >> n;
    vector<pair<int, int>> a(n);
    for (int i = 0; i < n; i++) cin >> a[i].x >> a[i].y;
    int l = 0, r = 1e9;
    auto check = [&](int mid)
    {
        for (int i = 0; i < n; i++)
            if (mid * (a[i].y + 1) <= a[i].x) return false;
        return true;
    };
    while (l < r)
    {
        int mid = l + r >> 1;
        if (check(mid)) r = mid;
        else l = mid + 1;
    }
    cout << l << ' ';
    int minn = 1e9;
    for (int i = 0; i < n; i++)
        minn = min(minn, a[i].x / a[i].y);
    cout << minn << '\n';
}

signed main()
{
    // freopen("Sample.in", "r", stdin);
    ios::sync_with_stdio(false);
    cin.tie(0);
    int T = 1;
    // cin >> T;
    while (T--) solve();
    // cout << "Time:" << (double)clock() / 1000 << '\n';
    return 0;
}

D. 飞机降落

全排列枚举所有降落方案，然后判断即可

#include<bits/stdc++.h>
#define int long long
#define x first
#define y second
using namespace std;

void solve()
{
    int n;
    cin >> n;
    vector<int> t(n + 10), d(n + 10), l(n + 10);
    for (int i = 0; i < n; i++) cin >> t[i] >> d[i] >> l[i];
    vector<int> p(n);
    for (int i = 0; i < n; i++) p[i] = i;
    do {
        int tt = 0;
        bool flag = true;
        for (int i = 0; i < n; i++)
        {
            int x = p[i];
            if (tt > t[x] + d[x])
            {
                flag = false;
                break;
            }
            tt = max(tt, t[x]);
            tt += l[x];
        }
        if (flag) 
        {
            cout << "YES" << '\n';
            return;
        }
    } while (next_permutation(p.begin(), p.end()));
    cout << "NO" << '\n';
}

signed main()
{
    // freopen("Sample.in", "r", stdin);
    ios::sync_with_stdio(false);
    cin.tie(0);
    int T = 1;
    cin >> T;
    while (T--) solve();
    // cout << "Time:" << (double)clock() / 1000 << '\n';
    return 0;
}

E. 接龙数列

状态定义：$f[i,j]$ 为前 $i$ 个数，以 $j$ 结尾的最长合法子序列，答案就是 $n-max$

#include<bits/stdc++.h>
#define int long long
#define x first
#define y second
using namespace std;

void solve()
{
    int n;
    cin >> n;
    map<int, int> mp;
    vector<int> a(n);
    vector<pair<int, int>> b(n);
    for (int i = 0; i < n; i++) cin >> a[i];
    for (int i = 0; i < n; i++)
    {
        b[i].y = a[i] % 10;
        int x = a[i];
        while (x >= 10) x /= 10;
        b[i].x = x;
    }
    int ans = 0;
    for (int i = 0; i < n; i++)
    {
        int x = mp[b[i].x];
        mp[b[i].y] = max(mp[b[i].y], x + 1);
        ans = max(ans, mp[b[i].y]);
    }
    cout << n - ans << '\n';
}

signed main()
{
    // freopen("Sample.in", "r", stdin);
    ios::sync_with_stdio(false);
    cin.tie(0);
    int T = 1;
    // cin >> T;
    while (T--) solve();
    // cout << "Time:" << (double)clock() / 1000 << '\n';
    return 0;
}

F. 岛屿个数

嵌套搜索，先搜索海水的部分，遇到岛屿就把岛屿的所有连通块搜索并标记

#include<bits/stdc++.h>
#define int long long
#define x first
#define y second
using namespace std;

void solve()
{
    int n, m;
    cin >> n >> m;
    vector<vector<char>> g(n + 2, vector<char>(m + 2, '0'));
    for (int i = 1; i <= n; i ++)
        for (int j = 1; j <= m; j ++)
            cin >> g[i][j];
    vector<vector<bool>> st(n + 2, vector<bool>(m + 2));
    int ans = 0;
    int dx[] = {-1, 0, 1, 0, -1, -1, 1, 1};
    int dy[] = {0, 1, 0, -1, -1, 1, -1, 1};
    auto dfs = [&](auto &&dfs, int x, int y) -> void
    {
        for (int i = 0; i < 4; i ++)
        {
            int nx = x + dx[i];
            int ny = y + dy[i];
            if (nx < 1 || nx > n || ny < 1 || ny > m || g[nx][ny] == '0') continue;
            if (!st[nx][ny])
            {
                st[nx][ny] = 1;
                dfs(dfs, nx, ny);
            }
        }
    };
    auto dfs1 = [&](auto &&dfs1, int x, int y) -> void
    {
        for (int i = 0; i < 8; i ++)
        {
            int nx = x + dx[i];
            int ny = y + dy[i];
            if (nx < 0 || nx > n + 1 || ny < 0 || ny > m + 1 || st[nx][ny]) continue;
            st[nx][ny] = 1;
            if (g[nx][ny] == '0') dfs1(dfs1, nx, ny);
            else 
            {
                st[nx][ny] = 1;
                ans ++;
                dfs(dfs, nx, ny);
            }
        }
    };
    dfs1(dfs1, 0, 0);
    cout << ans << '\n';
}

signed main()
{
    // freopen("Sample.in", "r", stdin);
    ios::sync_with_stdio(false);
    cin.tie(0);
    int T = 1;
    cin >> T;
    while (T--) solve();
    // cout << "Time:" << (double)clock() / 1000 << '\n';
    return 0;
}

G. 字串简写

处理 $b$ 的前缀和，然后扫一遍即可

#include<bits/stdc++.h>
#define int long long
#define x first
#define y second
using namespace std;

void solve()
{
    int k;
    cin >> k;
    string s;
    char a, b;
    cin >> s >> a >> b;
    int n = s.size();
    s = " " + s;
    vector<int> B(n + 10);
    for (int i = 1; i <= n; i++)
        if (s[i] == b) B[i] ++;
    for (int i = 1; i <= n; i++) B[i] += B[i - 1];
    int ans = 0;
    for (int i = 1; i <= n; i++)
    {
        if (s[i] == a)
        {
            if (i + k - 1 > n) continue;
            ans += B[n] - B[i + k - 2];
        }
    }
    cout << ans << '\n';
}

signed main()
{
    // freopen("Sample.in", "r", stdin);
    ios::sync_with_stdio(false);
    cin.tie(0);
    int T = 1;
    // cin >> T;
    while (T--) solve();
    // cout << "Time:" << (double)clock() / 1000 << '\n';
    return 0;
}

H. 整数删除

首先初始化下每个数的前驱和后继

开一个小根堆，把所有数的大小和位置都放进去

每次循环，拿到数组中最小的数，标记上位置，然后操作它和它的前驱后继

但是可能拿到的数，已经被改变过了，所以我们需要开一个 $map$ ，记录下每个位置被改变过多少次

最后把没有被标记的数输出即可

#include<bits/stdc++.h>
#define int long long
#define x first
#define y second
using namespace std;

void solve()
{
    int n, k;
    cin >> n >> k;
    vector<int> a(n + 10);
    for (int i = 1; i <= n; i++) cin >> a[i];
    vector<pair<int, int>> b(n + 10);
    for (int i = 1; i <= n; i++) b[i] = {i - 1, i + 1};
    priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> heap;
    for (int i = 1; i <= n; i++) heap.push({a[i], i});
    map<int, int> mp;
    vector<bool> st(n + 10);
    for (int i = 0; i < k; i++)
    {
        while (mp[heap.top().y])
        {
            mp[heap.top().y] --;
            heap.pop();
        }
        auto t = heap.top();
        heap.pop();
        st[t.y] = true;
        int l = b[t.y].x, r = b[t.y].y;
        b[l].y = r, b[r].x = l;
        a[l] += t.x, a[r] += t.x;
        mp[l] ++, mp[r] ++;
        if (l) heap.push({a[l], l});
        if (r <= n) heap.push({a[r], r});
    }
    for (int i = 1; i <= n; i++)
        if (!st[i]) cout << a[i] << ' ';
}

signed main()
{
    // freopen("Sample.in", "r", stdin);
    ios::sync_with_stdio(false);
    cin.tie(0);
    int T = 1;
    // cin >> T;
    while (T--) solve();
    // cout << "Time:" << (double)clock() / 1000 << '\n';
    return 0;
}