22/11/24

1，单调队列；

(76条消息) 单调队列专题_Dull丶的博客-CSDN博客

2，kmp算法；

先是自己和自己匹配，求出ne数组，然后和另一串匹配，进行求解；

循环里三步：while，if，记录ne数组/挪串匹配；

#pragma GCC optimize(3)
#include<bits/stdc++.h>
#define rep1(i,a,n) for( int i=(a);i<(n);++i)
#define rep2(i,a,n) for( int i=(a);i<=(n);++i)
#define per1(i,n,a) for( int i=(n);i>(a);i--)
#define per2(i,n,a) for( int i=(n);i>=(a);i--)
#define quick_cin() cin.tie(0),cout.tie(0),ios::sync_with_stdio(false)
#define memset(a,i,b) memset((a),(i),sizeof (b))
#define memcpy(a,i,b) memcpy((a),(i),sizeof (b))
#define endl "\n"
#define lowbit(m) ((-m)&(m))
#define dbug(y) cout<<(y)<<"\n"
#define dbug2(a,b) cout<<(a)<<" "<<(b)<<"\n"
#define dbug3(a,b,c) cout<<(a)<<" "<<(b)<<" "<<(c)<<"\n"
#define dbug4(a,b,c,d) cout<<(a)<<" "<<(b)<<" "<<(c)<<" "<<(d)<<"\n"
#define tulun int e[N],ne[N],h[N],w[N],idx
#define T_solve() int T;cin>>T;while(T--)solve()
#define pi 3.14159265358979323846
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int,int> PII;
typedef pair<long long,long long> PLL;
typedef double dob;
const int N=1e6+10,mod=1e6+3,base=131;
char s[N],p[N];
int ne[N];
int n,m;
signed main()
{
    quick_cin();
    cin>>n>>p+1>>m>>s+1;
    for(int i=2,j=0;i<=n;i++)
    {
        while(j&&p[i]!=p[j+1])j=ne[j];
        if(p[i]==p[j+1])j++;
        ne[i]=j;
    }
    for(int i=1,j=0;i<=m;i++)
    {
        while(j&&s[i]!=p[j+1])j=ne[j];
        if(s[i]==p[j+1])j++;
        if(j==n)
        {
            cout<<i-n<<" ";
            j=ne[j];
        }
    }
    return 0;
}

3，trie树，最大异或和；

#pragma GCC optimize(3)
#include<bits/stdc++.h>
#define rep1(i,a,n) for( int i=(a);i<(n);++i)
#define rep2(i,a,n) for( int i=(a);i<=(n);++i)
#define per1(i,n,a) for( int i=(n);i>(a);i--)
#define per2(i,n,a) for( int i=(n);i>=(a);i--)
#define quick_cin() cin.tie(0),cout.tie(0),ios::sync_with_stdio(false)
#define memset(a,i,b) memset((a),(i),sizeof (b))
#define memcpy(a,i,b) memcpy((a),(i),sizeof (b))
#define endl "\n"
#define lowbit(m) ((-m)&(m))
#define dbug(y) cout<<(y)<<"\n"
#define dbug2(a,b) cout<<(a)<<" "<<(b)<<"\n"
#define dbug3(a,b,c) cout<<(a)<<" "<<(b)<<" "<<(c)<<"\n"
#define dbug4(a,b,c,d) cout<<(a)<<" "<<(b)<<" "<<(c)<<" "<<(d)<<"\n"
#define tulun int e[N],ne[N],h[N],w[N],idx
#define T_solve() int T;cin>>T;while(T--)solve()
#define pi 3.14159265358979323846
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int,int> PII;
typedef pair<long long,long long> PLL;
typedef double dob;
const int N=1e6+10,mod=1e6+3,base=131;
int a[N],son[N<<2][2],idx;
int n;
void insert(int x)
{
    int p=0;
    per2(i,30,0)
    {
        int s=x>>i&1;
        if(!son[p][s])son[p][s]=++idx;
        p=son[p][s];
    }
}
int search(int x)
{
    int p=0,res=0;
    per2(i,30,0)
    {
        int s=x>>i&1;
        if(son[p][!s])
        {
            res+=1<<i;
            p=son[p][!s];
        }
        else p=son[p][s];
    }
    return res;
}
signed main()
{
    quick_cin();
    cin>>n;
    rep2(i,1,n)
    {
        cin>>a[i];
        insert(a[i]);
    }
    int ans=0;
    rep2(i,1,n)
    {
        ans=max(ans,search(a[i]));
    }
    dbug(ans);
    return 0;
}

4，n-皇后问题

对角线及反对角线的状态表示；

正对角线就是y+x，该线上y+x都一样

反对角线y-x都一样，但是数组下标不能为0，故统一加n；

#pragma GCC optimize(3)
#include<bits/stdc++.h>
#define rep1(i,a,n) for( int i=(a);i<(n);++i)
#define rep2(i,a,n) for( int i=(a);i<=(n);++i)
#define per1(i,n,a) for( int i=(n);i>(a);i--)
#define per2(i,n,a) for( int i=(n);i>=(a);i--)
#define quick_cin() cin.tie(0),cout.tie(0),ios::sync_with_stdio(false)
#define memset(a,i,b) memset((a),(i),sizeof (b))
#define memcpy(a,i,b) memcpy((a),(i),sizeof (b))
#define endl "\n"
#define lowbit(m) ((-m)&(m))
#define dbug(y) cout<<(y)<<"\n"
#define dbug2(a,b) cout<<(a)<<" "<<(b)<<"\n"
#define dbug3(a,b,c) cout<<(a)<<" "<<(b)<<" "<<(c)<<"\n"
#define dbug4(a,b,c,d) cout<<(a)<<" "<<(b)<<" "<<(c)<<" "<<(d)<<"\n"
#define tulun int e[N],ne[N],h[N],w[N],idx
#define T_solve() int T;cin>>T;while(T--)solve()
#define pi 3.14159265358979323846
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int,int> PII;
typedef pair<long long,long long> PLL;
typedef double dob;
const int N=1e2+10,mod=1e6+3,base=131;
int n;
char g[N][N];
int col[N],dg[N],udg[N];
void dfs(int u)
{
    if(u==n)
    {
        rep1(i,0,n)dbug(g[i]);
        cout<<endl;
        return;
    }
    int x=u;
    rep1(y,0,n)
    {
        if(col[y]||dg[y+x]||udg[y-x+n])continue;
        col[y]=dg[y+x]=udg[y-x+n]=1;
        g[x][y]='Q';
        dfs(x+1);
        g[x][y]='.';
        
        col[y]=dg[y+x]=udg[y-x+n]=0;
    }
}
signed main()
{
    quick_cin();
    cin>>n;
    rep1(i,0,n)
    rep1(j,0,n)g[i][j]='.';
    dfs(0);
    return 0;
}

5，走迷宫；

走到终点的最短路径，第一次走到的一定是最短的！因为是层向拓展，所以第一次走到的一定是最短的！；

#pragma GCC optimize(3)
#include<bits/stdc++.h>
#define rep1(i,a,n) for( int i=(a);i<(n);++i)
#define rep2(i,a,n) for( int i=(a);i<=(n);++i)
#define per1(i,n,a) for( int i=(n);i>(a);i--)
#define per2(i,n,a) for( int i=(n);i>=(a);i--)
#define quick_cin() cin.tie(0),cout.tie(0),ios::sync_with_stdio(false)
#define memset(a,i,b) memset((a),(i),sizeof (b))
#define memcpy(a,i,b) memcpy((a),(i),sizeof (b))
#define endl "\n"
#define lowbit(m) ((-m)&(m))
#define dbug(y) cout<<(y)<<"\n"
#define dbug2(a,b) cout<<(a)<<" "<<(b)<<"\n"
#define dbug3(a,b,c) cout<<(a)<<" "<<(b)<<" "<<(c)<<"\n"
#define dbug4(a,b,c,d) cout<<(a)<<" "<<(b)<<" "<<(c)<<" "<<(d)<<"\n"
#define tulun int e[N],ne[N],h[N],w[N],idx
#define T_solve() int T;cin>>T;while(T--)solve()
#define pi 3.14159265358979323846
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int,int> PII;
typedef pair<long long,long long> PLL;
typedef double dob;
const int N=1e2+10,mod=1e6+3,base=131;
int n,m;
int a[N][N];
int d[N][N];
int dx[]={-1,0,1,0},dy[]={0,1,0,-1};
void bfs()
{
    queue<PII>q;
    q.push({1,1});
    d[1][1]=1;
    while(q.size())
    {
        auto t=q.front();
        q.pop();
        int x=t.first,y=t.second;
        rep1(i,0,4)
        {
            int xx=x+dx[i];
            int yy=y+dy[i];
            if(xx>=1&&xx<=n&&yy>=1&&yy<=m&&!a[xx][yy]&&!d[xx][yy])
            {
                d[xx][yy]=d[x][y]+1;
                q.push({xx,yy});
            }
        }
    }
    dbug(d[n][m]-1);
}
signed main()
{
    quick_cin();
    cin>>n>>m;
    rep2(i,1,n)
    rep2(j,1,m)cin>>a[i][j];
    bfs();
    return 0;
}

6，dijkstra算法；

注意continue的使用；

#pragma GCC optimize(3)
#include<bits/stdc++.h>
#define rep1(i,a,n) for( int i=(a);i<(n);++i)
#define rep2(i,a,n) for( int i=(a);i<=(n);++i)
#define per1(i,n,a) for( int i=(n);i>(a);i--)
#define per2(i,n,a) for( int i=(n);i>=(a);i--)
#define quick_cin() cin.tie(0),cout.tie(0),ios::sync_with_stdio(false)
#define memset(a,i,b) memset((a),(i),sizeof (b))
#define memcpy(a,i,b) memcpy((a),(i),sizeof (b))
#define endl "\n"
#define lowbit(m) ((-m)&(m))
#define dbug(y) cout<<(y)<<"\n"
#define dbug2(a,b) cout<<(a)<<" "<<(b)<<"\n"
#define dbug3(a,b,c) cout<<(a)<<" "<<(b)<<" "<<(c)<<"\n"
#define dbug4(a,b,c,d) cout<<(a)<<" "<<(b)<<" "<<(c)<<" "<<(d)<<"\n"
#define tulun int e[N],ne[N],h[N],w[N],idx
#define T_solve() int T;cin>>T;while(T--)solve()
#define pi 3.14159265358979323846
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int,int> PII;
typedef pair<long long,long long> PLL;
typedef double dob;
const int N=1e5+10,mod=1e6+3,base=131;
tulun;
void add(int a,int b,int c)
{
    w[idx]=c,e[idx]=b,ne[idx]=h[a],h[a]=idx++;
}
int n,m;
int dist[N];
int st[N];
void dijkstra()
{
    memset(dist,0x3f,dist);
    priority_queue<PII,vector<PII>,greater<PII>>q;
    q.push({0,1});
    dist[1]=0;
    while(q.size())
    {
        auto t=q.top();
        q.pop();
        int jl=t.first,ver=t.second;
        if(st[ver])continue;
        st[ver]=1;
        for(int i=h[ver];~i;i=ne[i])
        {
            int j=e[i];
            if(dist[j]>w[i]+jl)
            {
                dist[j]=w[i]+jl;
                q.push({dist[j],j});
            }
        }
    }
    if(dist[n]==0x3f3f3f3f)dbug(-1);
    else dbug(dist[n]);
}
signed main()
{
    quick_cin();
    memset(h,-1,h);
    cin>>n>>m;
    rep2(i,1,m)
    {
        int a,b,c;
        cin>>a>>b>>c;
        add(a,b,c);
    }
    dijkstra();
    return 0;
}

7，floyed算法；

适用数据范围小的最短路，可以求负权边；

注意初始化的方法，和dp类似，注意含义；

#pragma GCC optimize(3)
#include<bits/stdc++.h>
#define rep1(i,a,n) for( int i=(a);i<(n);++i)
#define rep2(i,a,n) for( int i=(a);i<=(n);++i)
#define per1(i,n,a) for( int i=(n);i>(a);i--)
#define per2(i,n,a) for( int i=(n);i>=(a);i--)
#define quick_cin() cin.tie(0),cout.tie(0),ios::sync_with_stdio(false)
#define memset(a,i,b) memset((a),(i),sizeof (b))
#define memcpy(a,i,b) memcpy((a),(i),sizeof (b))
#define endl "\n"
#define lowbit(m) ((-m)&(m))
#define dbug(y) cout<<(y)<<"\n"
#define dbug2(a,b) cout<<(a)<<" "<<(b)<<"\n"
#define dbug3(a,b,c) cout<<(a)<<" "<<(b)<<" "<<(c)<<"\n"
#define dbug4(a,b,c,d) cout<<(a)<<" "<<(b)<<" "<<(c)<<" "<<(d)<<"\n"
#define tulun int e[N],ne[N],h[N],w[N],idx
#define T_solve() int T;cin>>T;while(T--)solve()
#define pi 3.14159265358979323846
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int,int> PII;
typedef pair<long long,long long> PLL;
typedef double dob;
const int N=1e3+10,mod=1e6+3,base=131;
int d[N][N];
int n,m,k;
#define inf 0x3f3f3f3f
void floyed()
{
    rep2(k,1,n)
    rep2(i,1,n)
    rep2(j,1,n)
    d[i][j]=min(d[i][j],d[i][k]+d[k][j]);
}
signed main()
{
    quick_cin();
    cin>>n>>m>>k;
    rep2(i,1,n)
    rep2(j,1,m)
    {
        if(i==j)d[i][j]=0;
        else d[i][j]=inf;
    }
    rep2(i,1,m)
    {
        int a,b,c;
        cin>>a>>b>>c;
        d[a][b]=min(d[a][b],c);
    }
    floyed();
    rep2(i,1,k)
    {
        int a,b;
        cin>>a>>b;
        if(d[a][b]>inf/2)dbug("impossible");
        else dbug(d[a][b]);
    }
    return 0;
}