蓝桥杯百校真题大联赛第5期（二）

A组

回路计数

#include <iostream>
using namespace std;

typedef long long LL;

const int N = 22, M = 1 << N;

LL f[M][N];
bool e[N][N];

int gcd(int a, int b)
{
	return b ? gcd(b, a % b) : a;
}

int main()
{
	for (int i = 1; i <= 21; i ++)
		for (int j = 1; j <= 21; j ++)
			if(gcd(i, j) == 1)
				e[i][j] = true;
				
	f[2][1] = 1;
	for (int i = 2; i <= M - 2; i ++)
		for (int j = 1; j <= 21; j ++)
			if(i >> j & 1)
				for (int k = 1; k <= 21; k ++)
					if(i - (1 << j) >> k & 1 && e[k][j])
						f[i][j] += f[i - (1 << j)][k];
	
	LL ans = 0;
	for (int i = 2; i <= 21; i ++)
		ans += f[M - 2][i];
	
	cout << ans << endl;		
	return 0;								
}

#include <iostream>
#include <algorithm>
using namespace std;
typedef long long LL;

int main()
{
  LL ans = 881012367360;
  cout << ans << endl;
  return 0;
}

砝码称重

#include <iostream>
#include <cstring>
#include <algorithm>

using namespace std;

const int N = 110, M = 200010, B = M / 2;

int n;
int w[N];
bool f[N][M];

int main()
{
    scanf("%d", &n);
    for (int i = 1; i <= n; i ++ ) scanf("%d", &w[i]);
    
    f[0][B] = true;
    for (int i = 1; i <= n; i ++ )
        for (int j = 0; j <= M ; j ++ )
        {
            if (f[i - 1][j])
            {
                if (j - w[i] >= 0) f[i][j - w[i]] = true;
                if (j + w[i] <= M) f[i][j + w[i]] = true;
                f[i][j] = true;
            }
        }
    
    int res = 0;
    for (int j = B + 1; j <= M; j ++ )
        res += f[n][j];
    
    cout << res << endl;
    
    return 0;
}

左孩子右兄弟

#include <iostream>
#include <cstring>
#include <algorithm>
#include <vector>

using namespace std;
const int N = 100010;
vector<int> g[N];
int n;

int dfs(int u)
{
    int ans = 0;
    int cnt = g[u].size();
    for (int i = 0; i < cnt; i ++ )
    {
        ans = max(ans, dfs(g[u][i]));
    }
    return ans + cnt;
}

int main()
{
    cin >> n;
    for (int i = 2; i <= n; i ++ )
    {
        int x;
        scanf("%d", &x);
        g[x].push_back(i);
    }
    
    int ans = dfs(1);
    cout << ans << endl;
    return 0;
}

B组

测试次数

#include <iostream>
using namespace std;
#define Max(a,b) (a>b?a:b)

int main()
{
  int dp[4][1005] = {0};
  for(int i = 0; i <= 1000; i++)
    dp[1][i] = i;
  for(int cnt = 2; cnt <= 3; cnt++)
    for(int ind = 1; ind <= 1000; ind++){
      int val = 10000, max;
      for(int k = 1; k <= ind; k++){
        max = Max(dp[cnt-1][k-1], dp[cnt][ind-k])+1;
        if(val > max)  val = max;
      }
      dp[cnt][ind] = val;
    }

  cout<<dp[3][1000];
  return 0;
}

快速排序

#include<bits/stdc++.h>
using namespace std;
int quick_select(int a[], int l, int r, int k) {
    int p = rand() % (r - l + 1) + l;
    int x = a[p];
    {int t = a[p]; a[p] = a[r]; a[r] = t;}
    int i = l, j = r;
    while(i < j) {
        while(i < j && a[i] < x) i++;
        if(i < j) {
            a[j] = a[i];
            j--;
        }
        while(i < j && a[j] > x) j--;
        if(i < j) {
            a[i] = a[j];
            i++;
        }
    }
    a[i] = x;
    p = i;
    if(i - l + 1 == k) return a[i];
    if(i - l + 1 < k) return quick_select( a, i, r, k ); //填空   //通过观察对比else的quick_select参数可直接写出结果
    else return quick_select(a, l, i - 1, k);
}
    
int main()
{
    int a[100];
    int n;
    cin>>n;
    for(int i=0;i<n;i++)
    cin>>a[i];
    cout<<quick_select(a, 0, n-1, 5);
    return 0;
}

递增三元组

#include <iostream>
#include<algorithm>
using namespace std;
int main()
{
    int a[100005], b[100005], c[100005];
    long long n = 0, ans = 0;
    long long i = 0, s1 = 0, s2 = 0;
    cin >> n;
    for (i = 0; i < n; i++) cin >> a[i];
    for (i = 0; i < n; i++) cin >> b[i];
    for (i = 0; i < n; i++) cin >> c[i];
    sort(a, a + n); sort(b, b + n); sort(c, c + n);

    for (i = 0; i < n; i++)
    {
        //s1 = 0; s2 = 0;
        while (s1 < n && a[s1] < b[i]) s1++;
        while (s2 < n && c[s2] <= b[i]) s2++;
        ans += ((long long)s1 * (n - s2));
    }
    cout << ans << endl;
    return 0;
}

C组

质数

#include <iostream>
using namespace std;
int isprime(int x)
{
  for(int i=2;i*i<=x;i++)
  {
    if(x%i==0)
    return 0;
  }
  return 1;
}
int ans=1;
int main()
{
  for(int i=2;i<20000;i++)
  {
    if(ans==2019&&isprime(i))
    cout<<i;
    if(isprime(i))
    {
      ans++;
    }
  }
  //cout<<"17569";
  return 0;
}

最大降雨量

#include <iostream>
using namespace std;
int isprime(int x)
{
  for(int i=2;i*i<=x;i++)
  {
    if(x%i==0)
    return 0;
  }
  return 1;
}
int ans=1;
int main()
{
  for(int i=2;i<20000;i++)
  {
    if(ans==2019&&isprime(i))
    cout<<i;
    if(isprime(i))
    {
      ans++;
    }
  }
  //cout<<"17569";
  return 0;
}

旋转

#include <iostream>
using namespace std;

int n, m;
int a[1002][1002];

int main()
{
  // 请在此输入您的代码
  cin >> n >> m;
  for(int i = 0; i < n; i++) {
    for(int j = 0; j < m; j++) {
      cin >> a[i][j];
    }
  }
  for(int i = 0; i < m; i++) {
    for(int j = n - 1; j >= 0; j--) {
      cout << a[j][i] << " ";
    }
    cout << endl;
  }
  return 0;
}