A题直接枚举即可,枚举日期,暴力匹配
#include<iostream>
#include<algorithm>
#include<vector>
using namespace std;
string p="",s="";
int ans = 0, n;
string mon[]={"01","02","03","04","05","06","07","08","09","10","11","12"};
string day[]={"01","02","03","04","05","06","07","08","09","10",
"11","12","13","14","15","16","17","18","19","20",
"21","22","23","24","25","26","27","28","29","30","31"};
int md[]={31,28,31,30,31,30,31,31,30,31,30,31};
bool check(string t,string s){
int j=0;
for(int i=0;i<t.size();++i){
if(j==s.size()) return true;
if(t[i]==s[j]) j++;
}
return j==s.size();
}
void solve(){
while(cin >> s){
p += s;
}
// cout << p << endl;
n=p.size();
string t = "2023";
for(int i=0;i<12;++i){
for(int j=0;j<md[i];++j){
string N = t + mon[i] + day[j];
if(check(p, N)) {
ans ++;
}
}
}
cout<<ans<<endl;
}
int main(){
solve();
return 0;
}
答案:
可以看出香浓信息熵有单调性(在0不超过1这个前提下)
因此直接二分即可,顺便输出一下结果对应的函数值
#include<bits/stdc++.h>
using namespace std;
#define int long long
double p(int x,int y){ //x 0 y 1
double P0 = 1.0*x/(x+y);
double P1 = 1.0*y/(x+y);
return -1.0*x*x/(x+y)*log2(P0)-1.0*y*y/(x+y)*log2(P1);
}
void solve(){
int n = 23333333;
int l=1, r=(n-1)/2;
double PP = 11625907.5798;
while(l<r){
int mid = (l+r)>>1;
double t = p(mid, n-mid);
if(t<PP) l=mid+1;
else r=mid;
}
cout << l << endl;
l=11027421;
printf("%.5lf", p(l, n-l));
}
signed main(){
solve();
return 0;
}
貌似可以直接O(1)算,但是我选择直接二分
二分的正确性在保证有解的前提下成立
#include<iostream>
#include<vector>
using namespace std;
//V:normal -> 1:X
void solve(){
int n;
cin >> n;
long long x,y,X=1e9,Y=0;
vector<pair<int,int>> vec;
for(int i=0;i<n;++i){
cin >> x >> y;
vec.push_back({x,y});
}
auto check=[&](long long x)->bool{
for(auto u:vec){
if(u.first/x < u.second) return false;
}
return true;
};
long long l=1,r=1e9;
while(l<r){
long long mid=(l+r+1)>>1;
if(check(mid)) l=mid; // x/mid >= y
else r=mid-1;
}
Y=l;
auto find=[&](long long x)->bool{
for(auto u:vec){
if(u.first/x > u.second) return false;
}
return true;
};
l=1,r=1e9;
while(l<r){
long long mid=(l+r)>>1;
if(find(mid)) r=mid;
else l=mid+1;
}
X=l;
cout<<X<<" " << Y<<endl;
}
int main(){
solve();
return 0;
}
顺便跑了几组对拍:
N ≤ \le ≤ 10 直接搜,不要想什么贪心
#include<iostream>
#include<vector>
#include<array>
using namespace std;
bool vis[20];
int n;
bool dfs(int num,int now, vector<array<int,3>>& vec){
if(num==n){
return true;
}
int flag = 0;
for(int i=0;i<n;++i){
if(!vis[i]){
if(now>vec[i][0]+vec[i][1]) return false;
vis[i] = true;
flag |= dfs(num+1, now+vec[i][2], vec);
vis[i]=false;
}
}
return flag;
}
void solve(){
cin >> n;
for(int i=1;i<=n;++i) vis[i] = 0;
vector<array<int,3>> vec;
for(int i=0;i<n;++i){
int x,y,z;
cin >> x >> y >> z;
vec.push_back({x,y,z});
}
bool res = dfs(0, 0, vec);
cout<<(res?"YES":"NO")<<"\n";
}
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
int _=1; cin >>_;
while(_--) solve();
return 0;
}
/*
2
3
0 100 10
10 10 10
0 2 20
3
0 10 20
10 10 20
20 10 20
*/
删最少数使得他是接龙序列,即求原序列的最大接龙子序列,然后用n减去。
最大接龙子序列求法:DP
但是我们发现转移类型一共只有9种1~9
结尾的数字
因此我们可以开一个数组f[i]表示前i个数字,以第i个结尾的最大接龙子序列。
再开一个数组bac[1~9]
表示 以1~9
结尾的最大接龙子序列
每次用第i个数组开头的字母对应的数组更新f[i],然后再用f[i]反过来更新bac即可
细节看代码
#include<iostream>
#include<vector>
#include<array>
#include<string>
using namespace std;
int n;
void solve(){
cin >> n;
vector<string> vec;
for(int i=0;i<n;++i){
string t;
cin >> t;
vec.push_back(t);
}
vector<int> bac(10); //1,2,3....
vector<int> f(n+1, 0);
int ans = 0 ;
for(int i=0;i<n;++i){
f[i]=max(1, bac[vec[i][0]-'0']+1);
ans=max(ans, f[i]);
bac[vec[i].back()-'0'] =
max(bac[vec[i].back()-'0'], f[i]);
}
cout << n-ans << endl;
}
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
int _=1;
// cin >>_;
while(_--) solve();
return 0;
}
先用边缘的海水进行bfs求出"真的海水",然后再对所有岛屿进行BFS,此时BFS的时候非真的海水可以直接识别为陆地然后入队。
两遍BFS得到答案。
#include<iostream>
#include<vector>
#include<array>
#include<string>
#include<queue>
#define x first
#define y second
using namespace std;
int n,m;
char G[60][60];
int vis[60][60], g[60][60], water[60][60];
int d[][2]={1,0,0,1,-1,0,0,-1};
int mov[][2]={{1,0},{-1,0},{0,1},{0,-1},{1,-1},
{1,1},{-1,-1},{-1,1}};
void solve(){
cin >> n >> m;
for(int i=1;i<=n;++i){
for(int j=1;j<=m;++j){
vis[i][j] = g[i][j] = water[i][j] = 0;
}
}
for(int i=1;i<=n;++i){
cin >> (G[i]+1);
for(int j=1;j<=m;++j){
g[i][j] = G[i][j]-'0';
}
}
queue<pair<int,int>> q;
for(int i=1;i<=n;++i){
if(g[i][1] == 0){
water[i][1] = true;
q.push({i, 1});
}
if(g[i][m] == 0){
water[i][m] = true;
q.push({i, m});
}
}
for(int i=1;i<=m;++i){
if(g[1][i] == 0){
if(!water[1][i]){
water[1][i] = true;
q.push({1, i});
}
}
if(g[n][i] == 0){
if(!water[n][i]){
water[n][i] = true;
q.push({n, i});
}
}
}
while(q.size()){
auto u=q.front(); q.pop();
int x=u.x,y=u.y;
for(int i=0;i<8;++i){
int xx=x+mov[i][0], yy=y+mov[i][1];
if(xx>=1&&xx<=n&&yy>=1&&yy<=m&&!water[xx][yy]&&!g[xx][yy]){
q.push({xx, yy});
water[xx][yy] = true;
}
}
}
while(q.size()) q.pop();
int idx = 0;
for(int i=1;i<=n;++i){
for(int j=1;j<=m;++j){
if(!water[i][j]&&g[i][j]&&!vis[i][j]){
q.push({i, j});
vis[i][j]=++idx;
while(q.size()){
auto u=q.front(); q.pop();
int x=u.x,y=u.y;
for(int i=0;i<4;++i){
int xx=x+d[i][0], yy=y+d[i][1];
if(xx>=1&&xx<=n&&yy>=1&&yy<=m
&&!vis[xx][yy]&&!water[xx][yy]){
vis[xx][yy]=idx;
q.push({xx,yy});
}
}
}
}
}
}
cout << idx << endl;
}
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
int _=1;
cin >>_;
while(_--) solve();
return 0;
}
/*
2
5 5
01111
11001
10101
10001
11111
5 6
111111
100001
010101
100001
111111
*/
二分/双指针都行
先按照位置处理出来两个数组
然后枚举开头的位置,二分出结尾在另一个数组的合法位置,直接累加答案
#include<iostream>
#include<vector>
#include<array>
#include<string>
#include<queue>
#define x first
#define y second
using namespace std;
int k;
char st,ed;
string p;
void solve(){
cin >> k;
cin >> p >> st >> ed;
vector<int> ps,pe;
for(int i=0;i<p.size();++i){
if(p[i]==st) ps.push_back(i);
if(p[i]==ed) pe.push_back(i);
}
long long ans = 0;
for(int i=0;i<ps.size();++i){
int x = ps[i];
int X = x + k - 1;
int l=0,r=pe.size()-1;
while(l<r){
int mid=(l+r)>>1;
if(pe[mid] >= X) r=mid;
else l=mid+1;
}
if(pe[l] >= X){
ans += pe.size() - l;
}
}
cout<<ans<<endl;
}
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
int _=1;
// cin >>_;
while(_--) solve();
return 0;
}
双链表维护每个数左边和右边分别是什么数
set维护每个位置的值和要删的最小值
本题考察STL的用法
#include<iostream>
#include<vector>
#include<algorithm>
#include<array>
#include<string>
#include<queue>
#include<set>
#define x first
#define y second
using namespace std;
int n,k;
void solve(){
cin >> n >> k;
vector<int> a(n+1),pre(n+1),nxt(n+1);
set<pair<int,int>> ds;
for(int i=1;i<=n;++i){
pre[i] = i-1;
nxt[i] = i+1;
}
for(int i=1;i<=n;++i){
cin >> a[i];
ds.insert({a[i], i});
}
for(int t=1;t<=k;++t){
auto pos=ds.begin();
int x=pos->first, y=pos->second;
int l = pre[y], r = nxt[y];
ds.erase(pos);
pre[nxt[y]]=pre[y];
nxt[pre[y]]=nxt[y];
pre[y]=-1, nxt[y]=-1;
if(l>0){
ds.erase(ds.find({a[l], l}));
a[l] += x;
ds.insert({a[l], l});
}
if(r<=n){
ds.erase(ds.find({a[r], r}));
a[r] += x;
ds.insert({a[r], r});
}
}
vector<pair<int,int>> temp;
for(auto u:ds){
temp.push_back({u.y, u.x});
}
sort(temp.begin(), temp.end());
for(auto u:temp){
cout << u.y << " ";
}cout<<"\n";
}
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
int _=1;
// cin >>_;
while(_--) solve();
return 0;
}
LCA, 没啥好说的文章来源:https://www.toymoban.com/news/detail-408979.html
#include<iostream>
#include<vector>
#include<array>
#include<string>
#include<queue>
#define x first
#define y second
using namespace std;
#define debug(x) cout<<#x<<": "<<x<<endl
#define N 100010
vector<pair<int,int>> edge[N];
int n,m,k;
int dep[N],fa[20][N];
int rout[N];
queue<int> q;
void bfs(){
for(int i=1;i<=n;++i) dep[i]=-1;
dep[1]=0;
q.push(1);
while(q.size()){
auto u=q.front(); q.pop();
for(auto v:edge[u]){
int ver = v.x, w=v.y;
if(dep[ver]==-1){
dep[ver] = dep[u] + w;
q.push(ver);
fa[0][ver] = u;
for(int i=1;i<=19;++i){
fa[i][ver] = fa[i-1][fa[i-1][ver]];
}
}
}
}
}
int lca(int x,int y){
if(dep[x] < dep[y]) swap(x, y);
for(int i=19;i>=0;--i){
if(dep[fa[i][x]] >= dep[y])
x = fa[i][x];
}
if(x==y) return x;
for(int i=19;i>=0;--i){
if(fa[i][x]!=fa[i][y])
x=fa[i][x], y=fa[i][y];
}
return fa[0][x];
}
int dist(int x,int y){
return dep[x]+dep[y]-2*dep[lca(x,y)];
}
void solve(){
cin >> n >> k;
for(int i=1;i<n;++i){
int x,y,z;
cin >> x >> y >> z;
edge[x].push_back({y, z});
edge[y].push_back({x, z});
}
bfs();
vector<int> a(k+1);
for(int i=1;i<=k;++i){
cin >> a[i];
}
int now = a[1];
long long time = 0;
for(int i=1;i<=k;++i){
time += dist(now, a[i]);
now = a[i];
}
cout << time - dist(a[1], a[2]) << " ";
now = a[1];
for(int i=2;i<=k;++i){
int temp = time;
temp -= dist(now, a[i]);
if(i!=k){
temp -= dist(a[i], a[i+1]);
temp += dist(now, a[i+1]);
}
cout << temp << " ";
now = a[i];
}cout << "\n";
}
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
int _=1;
// cin >>_;
while(_--) solve();
return 0;
}
/*
6 4
1 2 1
1 3 1
3 4 2
3 5 2
4 6 3
2 6 5 1
*/
树上差分,也是LCA,最后再DFS一下文章来源地址https://www.toymoban.com/news/detail-408979.html
#include<iostream>
#include<vector>
#include<array>
#include<string>
#include<queue>
#define x first
#define y second
using namespace std;
#define debug(x) cout<<#x<<": "<<x<<endl
#define N 100010
int n,m,k;
vector<int> edge[N];
pair<int,int> p[N];
int w[N],dep[N],fa[20][N];
pair<int,int> edges[N];
void bfs(){
for(int i=1;i<=n;++i) dep[i]=-1;
queue<int> q;
q.push(1);
dep[1]=1;
while(q.size()){
auto u=q.front(); q.pop();
for(auto v:edge[u]){
if(dep[v]==-1){
dep[v]=dep[u]+1;
q.push(v);
fa[0][v] = u;
for(int i=1;i<=19;++i)
fa[i][v]=fa[i-1][fa[i-1][v]];
}
}
}
}
int lca(int x,int y){
if(dep[x]<dep[y]) swap(x, y);
for(int i=19;i>=0;--i){
if(dep[fa[i][x]] >= dep[y])
x=fa[i][x];
}
if(x==y) return x;
for(int i=19;i>=0;--i){
if(fa[i][x]!=fa[i][y])
x=fa[i][x], y=fa[i][y];
}
return fa[0][x];
}
int f[N];
void dfs(int u,int pre){
f[u] = w[u];
for(auto v:edge[u]){
if(v!=pre){
dfs(v, u);
f[u] += f[v];
}
}
}
void solve(){
cin >> n >> m;
for(int i=1;i<n;++i){
int x,y;
cin >> x >> y;
edge[x].push_back(y);
edge[y].push_back(x);
edges[i] = {x, y};
}
bfs();
for(int i=1;i<=m;++i){
cin >> p[i].x >> p[i].y;
w[p[i].x] ++, w[p[i].y] ++;
w[fa[0][lca(p[i].x, p[i].y)]] -= 1;
w[lca(p[i].x, p[i].y)] -= 1;
}
dfs(1, -1);
int ans = -1;
for(int i=1;i<n;++i){
int x=edges[i].x, y=edges[i].y;
if(dep[x]<dep[y]) swap(x, y);
//y-x
if(f[x]==m){
ans=max(ans, i);
}
}
cout<<ans<<endl;
}
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
int _=1;
// cin >>_;
while(_--) solve();
return 0;
}
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