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某模拟题题解

　　第一道题还是比较简单,只不过做的时候手贱写错了一个字母，然后活活RE掉了40分

　　先处理处最终的图，然后从后往前用并查集完成询问。至于之前的删边可以排个序，

然后建一个长度和它一样的boolean数组标志这条边又没被删，删除的时候就lower_bound

就可以了，只不过注意重复的边。如果这一位上为false（这条边被删掉了）应该往后找到

第一个为true的地方，然后将它改为false

Code

  1 #include<iostream>
  2 #include<cstdio>
  3 #include<fstream>
  4 #include<cstdlib>
  5 #include<queue>
  6 #include<set>
  7 #include<map>
  8 #include<cctype>
  9 #include<algorithm>
 10 #include<cstring>
 11 #include<string>
 12 #include<stack>
 13 using namespace std;
 14 typedef bool boolean;
 15 #define smin(a, b) a = min(a, b)
 16 #define smax(a, b) b = max(a, b)
 17 template<typename T>
 18 inline void readInteger(T& u) {
 19     char x;
 20     while(!isdigit(x = getchar()));
 21     for(u = x - '0'; isdigit((x = getchar())); u = (u << 3) + (u << 1) + x - '0');
 22     ungetc(x, stdin);
 23 }
 24 
 25 typedef class union_found{
 26     public:
 27         int *f;
 28         union_found():f(NULL) {}
 29         union_found(int points) {
 30             f = new int[(const int)(points + 1)];
 31             for(int i = 0; i <= points; i++)
 32                 f[i] = i;
 33         }
 34         int find(int x) {
 35             if(f[x] != x)    return f[x] = find(f[x]);
 36             return f[x];
 37         }
 38         void unit(int fa, int so) {
 39             int ffa = find(fa);
 40             int fso = find(so);
 41             f[fso] = ffa;
 42         }
 43         boolean connected(int a, int b) {
 44             return find(a) == find(b);
 45         }
 46 }union_found;
 47 
 48 typedef class _edge{
 49     public:
 50         int from;
 51         int end;
 52         _edge(const int a = 0, const int b = 0) {
 53             from = min(a, b);
 54             end = max(a, b);
 55         }
 56         boolean operator <(_edge another) const {
 57             if(this->from != another.from)    return this->from < another.from;
 58             return this->end < another.end;
 59         }
 60 }_edge;
 61 
 62 typedef class _question{
 63     public:
 64         boolean isCut;
 65         int a;
 66         int b;
 67 }_question;
 68 
 69 inline void readQues(_question& que){
 70     int c;
 71     readInteger(c);
 72     if(c == 1)    que.isCut = true;
 73     else que.isCut = false;
 74     readInteger(que.a);
 75     readInteger(que.b);
 76 }
 77 
 78 int n, m, q;
 79 union_found uf;
 80 _edge* es;
 81 boolean* enable;
 82 _question *ques;
 83 stack<int> s;
 84 
 85 #define MAP_IT multiset<_edge>::iterator
 86 
 87 inline void init() {
 88     int lastEdge;
 89     readInteger(n);
 90     readInteger(m);
 91     readInteger(q);
 92     es = new _edge[(const int)(m + 1)];
 93     uf = union_found(n);
 94     ques = new _question[(const int)(q + 1)];
 95     enable = new boolean[(const int)(m + 1)];
 96     lastEdge = m;
 97     memset(enable, true, sizeof(boolean) * (m + 1));
 98     for(int i = 1, a, b; i <= m; i++){
 99         readInteger(a);
100         readInteger(b);
101         es[i] = _edge(a, b);
102     }
103     sort(es + 1, es + m + 1);
104     for(int i = 1; i <= q; i++){
105         readQues(ques[i]);
106         ques[i].a ^= lastEdge;
107         ques[i].b ^= lastEdge;
108         if(ques[i].isCut){
109 //            es.erase(es.lower_bound(_edge(ques[i].a, ques[i].b)));
110             int rank = lower_bound(es + 1, es + m + 1, _edge(ques[i].a, ques[i].b)) - es;
111             while(!enable[rank]) rank++;
112             enable[rank] = false;
113             lastEdge--;
114         }
115     }
116     for(int i = 1; i <= m; i++){
117         if(enable[i])
118             uf.unit(es[i].from, es[i].end);
119     }
120 }
121 
122 void solve() {
123     for(int i = q; i > 0; i--){
124         if(ques[i].isCut){
125             uf.unit(ques[i].a, ques[i].b);
126         }else{
127             boolean result = uf.connected(ques[i].a, ques[i].b);
128             if(result)    s.push(1);
129             else s.push(0);
130         }
131     }
132     while(!s.empty()){
133         printf("%d
", s.top());
134         s.pop();
135     }
136 }
137 
138 int main(){
139     freopen("graph.in", "r", stdin);
140     freopen("graph.out", "w", stdout);
141     init();
142     solve();
143     fclose(stdin);
144     fclose(stdout);
145     return 0;
146 }

　　第二道相对于第一道题就没有那么友好了，这次真的只能用在线算法，于是我决定用暴力碰碰运气

结果真的AC了。。。（这数据太水，没办法）

　　思路很简单，这道题是树，所以，两点之间的连线断开后，就成了两个联通块，然后我给每个连通块

一个编号，然后每次删边就去dfs一遍修改这个值。

2018-2-17

　　现在想了想，其实直接写一个LCT没多大毛病。

　　记得标程用的树链剖分。于是考虑树链剖分怎么做。

　　对于删边操作，如果删掉的是轻边，那么只需要更改father信息，如果删掉的是重边，那么需要修改重链上一段的重链顶，这个可以用线段树来维护。

　　对于查询操作，两个点沿着重链一直往上跳，看最后跳到的点是否相同就可以判断联通了。

Code

  1 #include<iostream>
  2 #include<cstdio>
  3 #include<fstream>
  4 #include<cstdlib>
  5 #include<queue>
  6 #include<set>
  7 #include<map>
  8 #include<cctype>
  9 #include<algorithm>
 10 #include<cstring>
 11 #include<string>
 12 using namespace std;
 13 typedef bool boolean;
 14 #define smin(a, b) a = min(a, b)
 15 #define smax(a, b) b = max(a, b)
 16 template<typename T>
 17 inline void readInteger(T& u) {
 18     char x;
 19     while(!isdigit(x = getchar()));
 20     for(u = x - '0'; isdigit((x = getchar())); u = (u << 3) + (u << 1) + x - '0');
 21     ungetc(x, stdin);
 22 }
 23 
 24 ///Linked Map Template Starts
 25 typedef class Edge{
 26     public:
 27         int next;
 28         int end;
 29         Edge(const int next = 0, const int end = 0):next(next), end(end){    }
 30 }Edge;
 31 typedef class MapManager{
 32     public:
 33         int *h;
 34         Edge* edge;
 35         int ce;
 36         MapManager():h(NULL), edge(NULL), ce(0) { }
 37         MapManager(int point, int edges):ce(0){
 38             h = new int[(const int)(point + 1)];
 39             edge = new Edge[(const int)(edges + 1)];
 40             memset(h, 0, sizeof(int) * (point + 1));
 41         }
 42         inline void addEdge(int from, int end) {
 43             edge[++ce] = Edge(h[from], end);
 44             h[from] = ce;
 45         }
 46 }MapManager;
 47 ///Linked Map Template Ends
 48 
 49 int n, q;
 50 MapManager tree;
 51 int* fa;
 52 int* value;
 53 int* types;
 54 int ct;
 55 
 56 inline void init() {
 57     ct = 1;
 58     readInteger(n);
 59     readInteger(q);
 60     value = new int[(const int)(n + 1)];
 61     fa = new int[(const int)(n + 1)];
 62     tree = MapManager(n, 2 * n);
 63     types = new int[(const int)(n + 1)];
 64     fill(types + 1, types + n + 1, 1);
 65     for(int i = 1; i <= n; i++)    readInteger(value[i]);
 66     for(int i = 1, a, b; i < n; i++){
 67         readInteger(a);
 68         readInteger(b);
 69         tree.addEdge(a, b);
 70         tree.addEdge(b, a);
 71     }
 72 }
 73 
 74 void buildTree(int node, int lastNode){
 75     fa[node] = lastNode;
 76     for(int i = tree.h[node]; i != 0; i = tree.edge[i].next){
 77         int& end = tree.edge[i].end;
 78         if(end == lastNode)    continue;
 79         buildTree(end, node);
 80     }
 81 }
 82 
 83 void update(int node, int lastNode, const int newType){
 84     if(fa[node] != lastNode) return;
 85     types[node] = newType;
 86     for(int i = tree.h[node]; i != 0; i = tree.edge[i].next){
 87         int& end = tree.edge[i].end;
 88         if(end == lastNode)    continue;
 89         update(end, node, newType);
 90     }
 91 }
 92 
 93 int lastans;
 94 
 95 inline void solve() {
 96     buildTree(1, 0);
 97     for(int i = 1, c, a, b; i <= q; i++){
 98         readInteger(c);
 99         readInteger(a);
100         readInteger(b);
101         a ^= lastans;
102         b ^= lastans;
103         int s;
104         switch(c){
105         case 1:
106             if(fa[a] == b){
107                 s = a;
108             }else{
109                 s = b;
110             }
111             fa[s] = 0;
112             update(s, 0, ++ct);
113             break;
114         case 2:
115             if(types[a] == types[b]){
116                 lastans = value[a] * value[b];
117             } else {
118                 lastans = value[a] + value[b];
119             }
120             printf("%d
", lastans);
121             break;
122         case 3:
123             value[a] = b;
124             break;
125         default:
126 //            throw c;
127             break;
128         }
129     }
130 }
131 
132 int main(){
133     freopen("tree.in", "r", stdin);
134     freopen("tree.out", "w", stdout);
135     init();
136     solve();
137     return 0;
138 }

　　第三题，也是最简单的一道，直接Tarjan搜强连通分量不解释

Code

  1 #include<iostream>
  2 #include<cstdio>
  3 #include<fstream>
  4 #include<cstdlib>
  5 #include<queue>
  6 #include<set>
  7 #include<map>
  8 #include<stack>
  9 #include<cctype>
 10 #include<algorithm>
 11 #include<cstring>
 12 #include<string>
 13 using namespace std;
 14 typedef bool boolean;
 15 #define smin(a, b) a = min(a, b)
 16 #define smax(a, b) b = max(a, b)
 17 template<typename T>
 18 inline void readInteger(T& u) {
 19     char x;
 20     while(!isdigit(x = getchar()));
 21     for(u = x - '0'; isdigit((x = getchar())); u = (u << 3) + (u << 1) + x - '0');
 22     ungetc(x, stdin);
 23 }
 24 ///Linked Map Template Starts
 25 typedef class Edge{
 26     public:
 27         int next;
 28         int end;
 29         Edge(const int next = 0, const int end = 0):next(next), end(end){    }
 30 }Edge;
 31 typedef class MapManager{
 32     public:
 33         int *h;
 34         Edge* edge;
 35         int ce;
 36         MapManager():h(NULL), edge(NULL), ce(0) { }
 37         MapManager(int point, int edges):ce(0){
 38             h = new int[(const int)(point + 1)];
 39             edge = new Edge[(const int)(edges + 1)];
 40             memset(h, 0, sizeof(int) * (point + 1));
 41         }
 42         inline void addEdge(int from, int end) {
 43             edge[++ce] = Edge(h[from], end);
 44             h[from] = ce;
 45         }
 46 }MapManager;
 47 ///Linked Map Template Ends
 48 
 49 MapManager g;
 50 long long result;
 51 
 52 stack<int> s;
 53 boolean* visited;
 54 boolean* inStack;
 55 int counter;
 56 int *visitID;
 57 int *exitID;
 58 
 59 inline void getMap(int end){
 60     int c_m = 0;
 61     int node;
 62     do{
 63         node = s.top();
 64         s.pop();
 65         inStack[node] = false;
 66         c_m++;
 67     }while(node != end);
 68     result += c_m * 1LL * (c_m - 1) / 2;
 69 }
 70 
 71 void Tarjan(int node){
 72     visited[node] = true;
 73     visitID[node] = exitID[node] = ++counter;
 74     s.push(node);
 75     inStack[node] = true;
 76     for(int i = g.h[node]; i != 0; i = g.edge[i].next){
 77         int e = g.edge[i].end;
 78         if(!visited[e]) {
 79             Tarjan(e);
 80             smin(exitID[node], exitID[e]);
 81         } else if(inStack[e]) {
 82             smin(exitID[node], visitID[e]);
 83         }
 84     }
 85     if(visitID[node] == exitID[node])
 86         getMap(node);
 87 }
 88 
 89 int n;
 90 int m;
 91 
 92 inline void init() {
 93     readInteger(n);
 94     readInteger(m);
 95     g = MapManager(n, m);
 96     visited = new boolean[(const int)(n + 1)];
 97     inStack = new boolean[(const int)(n + 1)];
 98     visitID = new int[(const int)(n + 1)];
 99     exitID = new int[(const int)(n + 1)];
100     memset(visited, false, sizeof(boolean) * (n + 1));
101     memset(inStack, false, sizeof(boolean) * (n + 1));
102     for(int i = 1, a, b; i <= m; i++) {
103         readInteger(a);
104         readInteger(b);
105         g.addEdge(a, b);
106     }
107 }
108 
109 inline void solve() {
110     for(int i = 1; i <= n; i++) {
111         if(!visited[i])
112             Tarjan(i);
113     }
114     cout<<result;
115 }
116 
117 int main(){
118     freopen("logic.in", "r", stdin);
119     freopen("logic.out", "w", stdout);
120     init();
121     solve();
122     return 0;
123 }

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原文地址：https://www.cnblogs.com/yyf0309/p/5933800.html