知识点扫盲加基本板子总结

知识点扫盲加基本板子总结

数据结构

并查集

#include<bits/stdc++.h>
#define N 105
using namespace std;
int fa[N];
int n;
int find(int x)
{
    if (x==fa[x]) return x; else return (fa[x]=find(fa[x]));
}
void merge(int x,int y)
{
    int fx=find(x),fy=find(y);
    if (fx!=fy) fa[fx]=fy;
}
void init()
{   scanf("%d",&n);
    for (int i=1; i<=n; i++) fa[i]=i;
}
int main()
{
    return 0;
}

图论

Floyd

题目链接['http://codeforces.com/contest/296/problem/D']

#include<bits/stdc++.h>
#define N 505
#define ll long long
#define inf 100000000000000LL
using namespace std;
int n;
int b[N];
ll f[N][N],ans[N];
bool vis[N];
void init()
{
    scanf("%d",&n);
    for (int i=1; i<=n; i++)
    {
        for (int j=1; j<=n; j++) scanf("%lld",&f[i][j]);
    }
    for (int i=1; i<=n; i++) scanf("%d",&b[i]);

}
void floyd()
{
    for (int i=n; i>=1; i--)
    {
        vis[b[i]]=1;

        for (int j=1; j<=n; j++)
            for (int k=1; k<=n; k++)
            {
                f[j][k]=min(f[j][k],f[j][b[i]]+f[b[i]][k]);
            }
        ll sum=0;
        for (int j=1; j<=n; j++)
            for (int k=1; k<=n; k++)
            {
                if (!vis[j] || !vis[k]) continue;
                sum+=f[j][k];
            }
        ans[i]=sum;
    }
}
void print()
{
    for (int i=1; i<=n; i++) printf("%lld ",ans[i]);
}
int main()
{
    init();
    floyd();
    print();
    return 0;
}

堆优化Dijkstra

题目链接['http://codeforces.com/contest/20/problem/C']

#include<bits/stdc++.h>
#define N 100005
#define M 100005
#define inf 100000000000000000LL
#define ll long long
using namespace std;
int n,m,st,ed;
ll dis[N];
ll path[N];
bool vis[N];
vector<pair<ll,ll> >E[M+10];
priority_queue<pair<ll,ll> > Q;
void insedge(int u,int v,ll val)
{
    E[u].push_back(make_pair(v,val));
}
void init()
{
    scanf("%d%d",&n,&m);
    for (int i=1; i<=m; i++)
    {
        int u,v;
        ll val;
        scanf("%d%d%lld",&u,&v,&val);
        insedge(u,v,val);
        insedge(v,u,val);
    }
    st=1; ed=n;
    for (int i=1; i<=n; i++) dis[i]=inf;
    dis[st]=0;
}
void  dijkstra()
{
    Q.push(make_pair(dis[st],st));
    while (!Q.empty())
    {
        int  v=Q.top().second;
        ll val=-Q.top().first;
        Q.pop();
        if (val!=dis[v]) continue;
        if (vis[v]) continue;
        vis[v]=1;
        for (int i=0; i<E[v].size(); i++)
        {
            int u=E[v][i].first;
            ll cost=E[v][i].second;
            if (dis[u]>dis[v]+cost)
            {
                dis[u]=dis[v]+cost;
                path[u]=v;
                Q.push(make_pair(-dis[u],u));
            }
        }

    }
}
void dfs(int x)
{
    if (x!=st) dfs(path[x]);
    printf("%d ",x);
}
void print()
{
    if (dis[ed]==inf) printf("-1\n");
    else
    {
        int x=ed;
        dfs(x);
    }
}
int main()
{
    init();
    dijkstra();
    print();
    return 0;
}

SPFA

题目链接['http://codeforces.com/contest/20/problem/C']

#include<bits/stdc++.h>
#define mp(a,b) make_pair(a,b)
#define ll long long
#define inf 100000000000000000LL
#define N 200005
using namespace std;
vector<pair<int,ll> > E[N];
int path[N];
ll dis[N];
queue<int>q;
bool vis[N];
int n,m;
void insedge(int u,int v,ll val)
{
    E[u].push_back(mp(v,val));
}
void spfa()
{
    q.push(1);
    while (!q.empty())
    {
        int u=q.front(); q.pop();
        vis[u]=0;
        for (int i=0; i<E[u].size(); i++)
        {
            int v=E[u][i].first;
            ll cost=E[u][i].second;
            if (dis[v]>dis[u]+cost)
            {
                dis[v]=dis[u]+cost; path[v]=u;
                if (dis[v]>dis[n]) continue;
                if (!vis[v])
                {
                    q.push(v); vis[v]=1;
                }
            }
        }
    }
}
void init()
{
    scanf("%d%d",&n,&m);
    for (int i=1; i<=m; i++)
    {
        int u,v; ll val;
        scanf("%d%d%lld",&u,&v,&val);
        insedge(u,v,val); insedge(v,u,val);
    }
    for (int i=1; i<=n; i++) dis[i]=inf;
    dis[1]=0;
}
void dfs(int x)
{
    if (x!=1) dfs(path[x]);
    printf("%d ",x);
}
void print()
{
    if (dis[n]==inf) printf("-1\n");
    else
    {
        int x=n;
        dfs(x);
    }
}
int main()
{
    init();
    spfa();
    print();
    return 0;
}

最小生成树Kruskal

题目链接['http://acm.hdu.edu.cn/showproblem.php?pid=1863']

#include<bits/stdc++.h>
#define N 100005
#define ll long long
using namespace std;
int n,m;
int fa[N];
struct Edge
{
    int u,v; long long val;
    operator < ( Edge a){
        return this->val<a.val;
    }
}a[N];
int find(int x)
{
    if (x==fa[x]) return x; else return (fa[x]=find(fa[x]));
}
int  merge(int x,int y)
{
    int fx=find(x),fy=find(y);
    if (fx!=fy)
    {
        fa[fx]=fy; return 1;
    }
    return 0;
}
int main()
{
    while (scanf("%d%d",&n,&m)!=EOF)
    {
        if (n==0 ) break;
        for (int i=1; i<=n; i++)
            scanf("%d%d%lld",&a[i].u,&a[i].v,&a[i].val);
        sort(a+1,a+n+1);
        //for (int i=1; i<=n; i++)
           // cout<<a[i].u<<" "<<a[i].v<<" "<<a[i].val<<endl;
        int sum=0; ll ans=0;
        for (int i=0; i<=m; i++) fa[i]=i;
        for (int i=1; i<=n; i++)
        {
            int flag=merge(a[i].u,a[i].v);
            if (flag==1) sum++,ans+=a[i].val;
          //  if (sum==m-1) break;
        }
        if (sum!=(m-1)) printf("?\n");
        else printf("%lld\n",ans);
    }

    return 0;
}

最小生成树prim算法

题目链接[]