2019陕西省赛题解

A 数位dp

B 欧拉路径判定

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> pll;
const int N=500005;
const int inf=0x3f3f3f3f;
int p[N];
int n,m;
vector<char> g[N];
int in[N],out[N];
int num;
int find(int x){
    if(p[x]!=x){
        p[x]=find(p[x]);
    }
    return p[x];
}
int main(){
    int t;
    ios::sync_with_stdio(false);
    cin>>t;
    while(t--){
        cin>>n>>m;
        int i,j;
        num=0;
        for(i=0;i<n*m;i++){
            p[i]=i;
            g[i].clear();
            in[i]=out[i]=0;
        }
        for(i=0;i<n;i++){
            for(j=0;j<m;j++){
                char c;
                cin>>c;
                g[i].push_back(c);
            }
        }
        for(i=0;i<n;i++){
            for(j=0;j<m;j++){
                int x;
                cin>>x;
                int dx,dy;
                if(g[i][j]=='u'){
                    dx=i-x;
                    dy=j;
                }
                else if(g[i][j]=='d'){
                    dx=i+x;
                    dy=j;
                }
                else if(g[i][j]=='r'){
                    dx=i;
                    dy=j+x;
                }
                else{
                    dx=i;
                    dy=j-x;
                }
                if(dx<0||dx>=n||dy<0||dy>=m)
                    continue;
                int tmp1=dx*m+dy;
                int tmp2=i*m+j;
                int pa=find(tmp1);
                int pb=find(tmp2);
                in[tmp1]++,out[tmp2]++;
                if(pa!=pb){
                    p[pa]=pb;
                    num++;
                }
            }
        }
        int sig1=0;
        int sig2=0;
        for(i=0;i<n*m;i++)
            if(in[i]>out[i]) sig1+= in[i]-out[i];
            else sig2 += out[i]-in[i];
        if(num==n*m-1&&sig1<=1&&sig2<=1)cout<<"Yes"<<endl;
        else cout<<"No"<<endl;
    }
    return 0;
}

C 思维字符串去重

#include<cstdio>
#include<cstring>
#define LL long long
const int maxn=1e6+5;
char s[maxn];
LL a[5]={0};
int main()
{
    int T;
    scanf("%d",&T);
    while(T--)
    {
        memset(a,0,sizeof a);
        scanf("%s",s);
        LL l=(LL)strlen(s);
        for(int i=0;s[i]!='\0';i++)
        {
            if(s[i]=='0')
                a[0]++;
            if(s[i]=='6')
                a[1]++;
            if(s[i]=='8')
                a[2]++;
            if(s[i]=='9')
                a[3]++;
        }
        LL ans=(l+1)*l/2;
        LL x=a[0]*(a[0]+1)/2;
        LL y=a[2]*(a[2]+1)/2;
        LL z=a[1]*a[3];
        ans=ans-x-y-z;
        if(!(a[1]==l||a[3]==l))
            ans++;
        printf("%lld\n",ans);
    }
    return 0;
}

E 二分check

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=3e5+10;
int n,k;
string s;
bool check(int x){
    int i;
    int cnt=0;
    for(i=n;i>=1;){
        if(s[i]=='1'){
            cnt++;
            i=i-x;
        }
        else{
            i--;
        }
    }
    return cnt<=k;
}
int main(){
    ios::sync_with_stdio(false);
    int t;
    cin>>t;
    while(t--){
        cin>>n>>k;
        cin>>s;
        s=" "+s;
        int l=1,r=n;
        int num=0;
        for(int i=1;i<=n;i++){
            if(s[i]=='0')
                num++;
        }
        if(num==n){
            cout<<0<<endl;
            continue;
        }
        while(l<r){
            int mid=l+r>>1;
            if(check(mid))
                r=mid;
            else
                l=mid+1;
        }
        cout<<l<<endl;
    }
}

F 思维签到

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=5005;
const int inf=0x3f3f3f3f;
const ll  y=2e9;
int main(){
    ll a,b,c;
    int t;
    scanf("%d",&t);
    while(t--){
        scanf("%lld%lld%lld",&a,&b,&c);
        if(c>a+b){
            printf("-1\n");
            continue;
        }
        if(c==a+b){
            printf("%lld\n",a+b+1);
            continue;
        }
        ll x=a+b-c;
        int f=0;
        for(ll i=1;i<=sqrt(x);i++){
            if((x/i)<=a||(x/i)<=c)break;
            if(x%i==0){
                    f=1;
                    printf("%lld\n",x/i);
                break;
            }
        }
        if(!f)printf("-1\n");
    }
    return 0;
}

I dfs+线段树

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> pll;
const int N=200005;
const int inf=0x3f3f3f3f;
int h[N],ne[N],e[N],idx;
char w[N];
int dfn[N],times;
struct node{
    int l,r;
    int sum;
    int lazy;
}tr[N<<2];
int sz[N],n;
void add(int a,int b,char c){
    e[idx]=b,ne[idx]=h[a],w[idx]=c,h[a]=idx++;
}
bool solve(int u){
    int i;
    int cnt[27]={0};
    for(i=h[u];i!=-1;i=ne[i]){
        int j=e[i];
        cnt[w[i]-'a']++;
    }
    int flag=0;
    for(i=0;i<26;i++){
        if(cnt[i]>2){
            return false;
        }
        if(cnt[i]==2){
            if(flag)
                return false;
            flag++;
        }
    }
    return true;
}
bool check(){
    int i;
    for(i=1;i<=n;i++){
        if(!solve(i))
            return false;
    }
    return true;
}
void dfs(int u,int fa){
    dfn[u]=++times;
    int i;
    sz[u]=1;
    for(i=h[u];i!=-1;i=ne[i]){
        int j=e[i];
        if(j==fa)
            continue;
        dfs(j,u);
        sz[u]+=sz[j];
    }
}
void build(int u,int l,int r){
    if(l==r){
        tr[u]={l,r,0,0};
    }
    else{
        tr[u]={l,r,0,0};
        int mid=l+r>>1;
        build(u<<1,l,mid);
        build(u<<1|1,mid+1,r);
    }
}
void pushup(int u){
    tr[u].sum=tr[u<<1].sum+tr[u<<1|1].sum;
}
void pushdown(int u){
    int x=tr[u].lazy;
    tr[u<<1].sum=(tr[u<<1].r-tr[u<<1].l+1);
    tr[u<<1|1].sum=(tr[u<<1|1].r-tr[u<<1|1].l+1);
    tr[u<<1].lazy=tr[u<<1|1].lazy=x;
    tr[u].lazy=0;
}
void modify(int u,int l,int r,int k){
    if(tr[u].l>=l&&tr[u].r<=r){
        tr[u].sum=k*(tr[u].r-tr[u].l+1);
        tr[u].lazy=k;
        return ;
    }
    if(tr[u].lazy)
        pushdown(u);
    int mid=tr[u].l+tr[u].r>>1;
    if(l<=mid)
        modify(u<<1,l,r,k);
    if(r>mid)
        modify(u<<1|1,l,r,k);
    pushup(u);
}
int main(){
    ios::sync_with_stdio(false);
    int t;
    cin>>t;
    while(t--){
        cin>>n;
        int i;
        idx=0,times=0;
        for(i=0;i<=n+5;i++){
            h[i]=-1;
        }
        for(i=1;i<n;i++){
            int a,b;
            char c;
            cin>>a>>b>>c;
            add(a,b,c);
            add(b,a,c);
        }
        if(!check()){
            cout<<0<<endl;
            continue;
        }
        dfs(1,-1);
        build(1,1,n);
        for(i=1;i<=n;i++){
            map<char,int> m1;
            for(int j=h[i];j!=-1;j=ne[j]){
                int k=e[j];
                if(!m1[w[j]]){
                    m1[w[j]]=k;
                    continue;
                }
                int f1=m1[w[j]];
                int f2=k;
                if(dfn[f1]>dfn[i]&&dfn[f2]>dfn[i]){
                    if(dfn[f1]>dfn[f2])
                        swap(f1,f2);
                    modify(1,1,dfn[f1]-1,1);
                    if(dfn[f1]+sz[f1]<=n){
                        modify(1,dfn[f1]+sz[f1],dfn[f2]-1,1);
                    }
                    if(dfn[f2]+sz[f2]<=n)
                        modify(1,dfn[f2]+sz[f2],n,1);
                }
                else if(dfn[f1]>dfn[i]&&dfn[f2]<dfn[i]){
                    modify(1,dfn[i],dfn[f1]-1,1);
                    if(dfn[f1]+sz[f1]<=n)
                        modify(1,dfn[f1]+sz[f1],dfn[i]+sz[i]-1,1);
                }
                else if(dfn[f1]<dfn[i]&&dfn[f2]>dfn[i]){
                    modify(1,dfn[i],dfn[f2]-1,1);
                    if(dfn[f2]+sz[f2]<=n)
                        modify(1,dfn[f2]+sz[f2],dfn[i]+sz[i]-1,1);
                }
                break;
            }
        }
        cout<<n-tr[1].sum<<endl;
    }
    return 0;
}

K 最短路，额外维护d

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,int> pll;
const int N=2e6+10;
const int inf=0x3f3f3f3f;
int h[N],ne[N],e[N],idx;
int n,m,k;
int pos[N];
ll dis[N],st[N];
int d[N],w[N];
void add(int a,int b,int c){
    e[idx]=b,ne[idx]=h[a],w[idx]=c,h[a]=idx++;
}
void dij(){
    int i;
    for(i=1;i<=n;i++){
        dis[i]=1e18;
        st[i]=0;
    }
    priority_queue<pll,vector<pll>,greater<pll> > q;
    for(i=1;i<=k;i++){
        q.push({0,pos[i]});
        dis[pos[i]]=0;
        d[pos[i]]=0;
    }
    while(q.size()){
        auto t=q.top();
        q.pop();
        if(d[t.second]){
            d[t.second]=max(d[t.second]-1,0);
            continue;
        }
        if(st[t.second]){
            continue;
        }
        st[t.second]=1;
        dis[t.second]=t.first;
        for(i=h[t.second];i!=-1;i=ne[i]){
            int j=e[i];
            if(st[j])
                continue;
            q.push({t.first+w[i],j});
        }
    }
    if(dis[1]==1e18)
        cout<<-1<<endl;
    else
    cout<<dis[1]<<endl;
    return ;
}
int main(){
    ios::sync_with_stdio(false);
    int t;
    cin>>t;
    while(t--){
        int i;
        idx=0;
        cin>>n>>m>>k;
        for(i=1;i<=n;i++)
            h[i]=-1;
        for(i=1;i<=k;i++){
            cin>>pos[i];
        }
        for(i=1;i<=n;i++){
            cin>>d[i];
        }
        for(i=1;i<=m;i++){
            int a,b,c;
            cin>>a>>b>>c;
            add(a,b,c);
            add(b,a,c);
        }
        dij();
    }
    return 0;
}

L 签到