题目描述:
给一个点数为N(N<1,000)的图,Q次询问. 每次询问如果第i条边的值变为v, 这条边是否可能会在最小生成树中.
吐槽:
1. 由于边比较稠密,所以这两种方法差不多....
算法分析:
其实和次小生成树没什么关系额...
就是prim求mst的时候顺便把max[u][v],求出来. max[u][v]指的是u到v的最大边.
求法就是 : 在考虑点v的时候, 假设之间遍历的点的max值已经两两求出了...
则有max[u][v] = max_value(max[u][P[v]], edge[u][v]);
询问的时候就比较更新的值和max[u][v]就好了....
树链剖分就是在线求max[u][v](ps: 支持更新的哦~~~)...
prim版:
因为写这个是拿来对拍的,所以写的不是很好...
1 #include<iostream>
2 #include<cstdio>
3 #include<cassert>
4 using namespace std;
5 #define re(i,n) for(int i=0;i<n;i++)
6 #define re1(i,n) for(int i=1;i<=n;i++)
7 const int V = 1005;
8 const int E = 1000005;
9 template <typename T> inline void chkmax (T &a, T b) {if(a<b) a=b;}
10 int G[V][V],mx[V][V],low[V],vis[V],P[V];
11 struct edge{
12 int u,v;
13 edge(int U=0,int V=0) : u(U), v(V) {}
14 } num[E];
15 const int inf = ~0u>>2;
16 int n,m,q;
17 void prim(){
18 for(int i=0;i<n;i++){
19 low[i] = inf;
20 vis[i] = 0;
21 }
22 low[0] = 0;
23 for(int j=0;j<n;j++){
24 int s=-1, mn = inf;
25 for(int i=0;i<n;i++)
26 if(!vis[i] && mn > low[i]){
27 s = i; mn = low[i];
28 }
29 assert(s!=-1);
30 // cout<<"s: "<<s<<" "<<mn<<endl;
31 // cout<<P[s]<<endl;
32 for(int i=0;i<n;i++) if(vis[i]){
33 mx[s][i] = max(mx[i][P[s]],mn);
34 mx[i][s] = mx[s][i];
35 // cout<<"i: "<<i<<" "<<mx[i][s]<<endl;
36 }
37
38 vis[s] = 1;
39 for(int i=0;i<n;i++) if(!vis[i] && G[s][i] < low[i]){
40 low[i] = G[s][i]; P[i] = s;
41 }
42 }
43 // for(int i=0;i<n;i++) cout<<low[i]<<" "; cout<<endl;
44 }
45 int main(){
46 while(~scanf("%d%d%d",&n,&m,&q)){
47 int u,v,c;
48 for(int i=0;i<n;i++) for(int j=0;j<n;j++){
49 G[i][j] = inf;
50 mx[i][j] = 0;
51 }
52 for(int i=0;i<m;i++){
53 scanf("%d%d%d",&u,&v,&c);
54 u--;v--;
55 num[i] = edge(u,v);
56 if(c < G[u][v]) {
57 G[u][v] = G[v][u] = c;
58 }
59 }
60 prim();
61 // for(int i=0;i<n;i++) { for(int j=0;j<n;j++) cout<<mx[i][j]<<" "; cout<<endl;}
62 while(q--){
63 scanf("%d%d",&u,&v);
64 u--;
65 int a = num[u].u, b = num[u].v;
66 puts(mx[a][b] >= v?"Yes": "No");
67 }
68 }
69 }
70
剖分树版:
这个是认真写的...
1 // poj 2831 by figo in 5,19,2012
2 // template
3 #include<iostream>
4 #include<algorithm>
5 #include<cassert>
6 #include<cstdio>
7 #include<cstdlib>
8 using namespace std;
9 template <typename T> inline void chkmax(T &a, T b){if(a<b) a=b;}
10 // graph
11 const int V = 1005;
12 const int E = 200005;
13 int head[V],pnt[E],nxt[E],cost[E],flag[E];
14 int n,e;
15 void add_edge(int u,int v,int c){
16 nxt[e] = head[u];
17 pnt[e] = v;
18 head[u] = e;
19 cost[e] = c;
20 e ++;
21 }
22 // kruskal
23 int parent[V];
24 struct edge{
25 int u,v,c,id;
26 edge() {}
27 edge(int U,int V,int C,int ID) : u(U), v(V), c(C), id(ID) {}
28 bool operator < (edge A) const {
29 return c < A.c;
30 }
31 } num[E];
32 int find(int x){ return x == parent[x] ? x : parent[x] = find(parent[x]);}
33 void kruskal(){
34 int len = 0;
35 for(int u = 0; u< n; u++)
36 for(int i = head[u]; i!=-1;i = nxt[i])
37 num[len++] = edge(u,pnt[i],cost[i],i);
38 assert(len == e);
39 sort(num, num+len);
40 for(int i=0;i<n;i++)
41 parent[i] = i;
42 for(int i=0;i<len;i++) flag[i] = 0;
43 for(int i = 0; i< len; i++){
44 int u = num[i].u, v = num[i].v,id = num[i].id;
45 if(find(u) == find(v)) continue;
46 flag[id] = flag[id ^ 1] = 1;
47 parent[parent[u]] = parent[v];
48 }
49 }
50 // seg_ment tree
51 int seg[V<<2], M;
52 int find(int l,int r){
53 int ans = 0;
54 for(l += M-1, r += M+1; l^r^1; l>>=1, r>>=1){
55 if(~l&1) chkmax(ans,seg[l^1]);
56 if(r&1) chkmax(ans,seg[r^1]);
57 }
58 return ans;
59 }
60 void insert(int pos, int x){
61 pos += M;
62 seg[pos] = x;
63 while(pos>>=1){
64 seg[pos] = max(seg[pos << 1] , seg[pos << 1 | 1]);
65 }
66 }
67 // prepare
68 int deep[V],size[V],heavy[V],P[V];
69 void dfs(int u,int f){
70 size[u] = 1;
71 int mx = 0, s = -1;
72 for(int i=head[u]; i!=-1;i = nxt[i]){
73 if(!flag[i] || pnt[i] == f) continue;
74 int v = pnt[i];
75 P[v] = i^1;
76 deep[v] = deep[u] + 1;
77 dfs(v,u);
78 if(size[v] > mx){
79 mx = size[v];
80 s = i;
81 }
82 size[u] += size[v];
83 }
84 heavy[u] = s;
85 if(s!=-1) parent[pnt[s]] = u;
86 }
87 void prepare(){
88 kruskal();
89 for(int i=0;i<n;i++) parent[i] = i;
90 deep[0] = 0;
91 P[0] = -1;
92 dfs(0,0);
93 for(int i=30;i;i--) if((1<<i) > n+1) M = 1<<i;
94 for(int i=0;i<2*M;i++) seg[i] = 0;
95 int len = 1;
96 for(int u = 0; u<n; u++) if(heavy[u] == -1){
97 int v = u;
98 while(v && pnt[heavy[pnt[P[v]]]] == v){
99 insert(len,cost[P[v]]);
100 flag[P[v]] = flag[P[v]^1] = len ++;
101 v = pnt[P[v]];
102 }
103 }
104 }
105 // operator
106 int lca(int u,int v){
107 while(1){
108 int a = find(u), b = find(v);
109 if(a == b) return deep[u]<deep[v] ? u : v;
110 else if(deep[a] > deep[b]) u = pnt[P[a]];
111 else v = pnt[P[b]];
112 }
113 }
114 int query(int u,int v){
115 int ans = 0;
116 // cout<<u<<" "<<v<<endl;
117 while(u != v){
118 //cout<<u<<endl;
119 int l = P[u];
120 if(pnt[heavy[pnt[P[u]]]] == u){
121 int p = find(u);
122 if(deep[p] < deep[v]) p = v;
123 // cout<<u<<" "<<p<<endl;
124 int r = heavy[p];
125 assert(flag[l] <= flag[r]);
126 int mx = find(flag[l],flag[r]);
127 chkmax(ans,mx);
128 u = p;
129 }
130 else {
131 chkmax(ans,cost[l]);
132 u = pnt[l];
133 }
134 }
135 //cout<<"ans:"<<ans<<endl;
136 return ans;
137 }
138 int ask(int E,int val){
139 int u = pnt[E<<1];
140 int v = pnt[E<<1|1];
141 int p = lca(u,v);
142 //cout<<u<<" "<<v<<" "<<p<<endl;
143 return val <= query(u,p) || val <= query(v,p);
144 }
145 // main
146 int main(){
147 int m,q,u,v,c;
148 while(~scanf("%d%d%d",&n,&m,&q)){
149 e= 0;
150 for(int i=0;i<n;i++) head[i] = -1;
151 for(int i=0;i<m;i++) {
152 scanf("%d%d%d",&u,&v,&c);
153 u--; v--;
154 add_edge(u,v,c);
155 add_edge(v,u,c);
156 }
157 prepare();
158 while(q--){
159 scanf("%d%d",&u,&v);
160 u--;
161 puts(ask(u,v) ? "Yes": "No");
162 }
163 }
164 return 0;
165 }
166
posted on 2012-05-20 15:22
西月弦 阅读(497)
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