{"id":314,"date":"2023-03-16T11:10:44","date_gmt":"2023-03-16T03:10:44","guid":{"rendered":"https:\/\/www.xgnd.net\/?p=314"},"modified":"2025-11-30T16:04:24","modified_gmt":"2025-11-30T08:04:24","slug":"%e6%9c%80%e5%b0%8f%e7%94%9f%e6%88%90%e6%a0%91%e5%81%9a%e9%a2%98%e7%ac%94%e8%ae%b0","status":"publish","type":"post","link":"https:\/\/www.xgnd.net\/index.php\/2023\/03\/16\/%e6%9c%80%e5%b0%8f%e7%94%9f%e6%88%90%e6%a0%91%e5%81%9a%e9%a2%98%e7%ac%94%e8%ae%b0\/","title":{"rendered":"\u300c\u505a\u9898\u7b14\u8bb0\u300d\u6700\u5c0f\u751f\u6210\u6811"},"content":{"rendered":"

<!-- wp:heading {"level":3} -->
\n<h3><a href="https:\/\/www.luogu.com.cn\/problem\/P2916<\/a>" target="_blank" rel="noreferrer noopener">P2916 [USACO08NOV] Cheering up the Cow G<\/a><\/h3>
\n<!-- \/wp:heading -->
\n<!-- wp:paragraph -->
\n<p>\u677f\u5b50\u9898\uff0c\u8003\u8651\u6bcf\u6761\u8fb9\u7684\u8d21\u732e\uff0c\u7531\u4e8e\u6bcf\u6761\u8fb9\u5fc5\u7136\u4f1a\u88ab\u7ecf\u8fc7\u4e24\u6b21\uff0c\u5219\u5bf9\u4e8e\u8fd9\u6761\u8fb9\u7684\u82b1\u8d39\u5c31\u4e3a $2w_i+cost_u+cost_v$\uff0c\u5c06\u8fb9\u6743\u66ff\u6362\u4e3a\u6b64\u82b1\u8d39\uff0c\u8dd1\u4e00\u904dKruskal\u5373\u53ef\u3002\u6700\u540e\u8fd8\u8981\u52a0\u4e0a\u8d77\u70b9\u7684\u82b1\u8d39\uff0c\u56e0\u4e3a\u662f\u4efb\u610f\u8d77\u70b9\uff0c\u9009\u82b1\u8d39\u6700\u5c0f\u7684\u4f5c\u4e3a\u8d77\u70b9\u5c31\u884c\u4e86\u3002<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:html -->
\n<details>
\n<summary>Code<\/summary>
\n<pre class="wp-block-code"><code>#include<bits\/stdc++.h>
\nusing namespace std;
\ntypedef long long ll;
\nconst int maxn=10005;
\nint n,m;
\nll c[maxn];
\nll sum;<\/p>\n

struct edge{
\nll u,v,w;
\n}e[maxn*10];<\/p>\n

int f[maxn];<\/p>\n

int dsu_find(int x){
\nreturn x==f[x]?x:f[x]=dsu_find(f[x]);
\n}<\/p>\n

bool cmp(edge x,edge y){
\nreturn x.w<y.w;
\n}<\/p>\n

void kruskal(){
\nfor(int i=1;i<=n;i++)f[i]=i;
\nsort(e+1,e+1+m,cmp);
\nint cnt=0;
\nfor(int i=1;i<=m;i++){
\nint u=dsu_find(e[i].u),v=dsu_find(e[i].v);
\nif(f[u]==f[v])continue;
\nf[u]=v;
\nsum+=e[i].w;
\n\/\/cout<<e[i].u<<" "<<e[i].v<<endl;
\nif(++cnt==n-1)break;
\n}
\n}<\/p>\n

int main(){
\nios::sync_with_stdio(0);
\ncin>>n>>m;
\nll mi=0x3f3f3f3f;
\nfor(int i=1;i<=n;i++)cin>>c[i],mi=min(mi,c[i]);<\/p>\n

for(int i=1;i&lt;=m;i++){\n    int x;\n    cin&gt;&gt;e[i].u&gt;&gt;e[i].v&gt;&gt;x;\n    e[i].w=2*x+c[e[i].u]+c[e[i].v];\n}\nkruskal();\ncout&lt;&lt;(sum+mi)&lt;&lt;endl;\nreturn 0;<\/code><\/pre>\n
}<\/code><\/pre>
\n<\/details>
\n<!-- \/wp:html -->
\n<!-- wp:heading {"level":3} -->
\n<h3><a href="https:\/\/www.luogu.com.cn\/problem\/P1967<\/a>" target="_blank" rel="noreferrer noopener">P1967 [NOIP2013 \u63d0\u9ad8\u7ec4] \u8d27\u8f66\u8fd0\u8f93<\/a><\/h3>
\n<!-- \/wp:heading -->
\n<!-- wp:paragraph -->
\n<p>\u9898\u76ee\u5b9e\u9645\u662f\u8981\u4f7f\u5f97\u56fe\u4e2d\u4e24\u70b9\u95f4\u8def\u5f84\u4e2d\u7684\u8fb9\u6743\u6700\u5c0f\u503c\u5c3d\u53ef\u80fd\u5927\uff0c\u8003\u8651\u7528Kruskal\u6c42\u4e00\u4e2a\u6700\u5927\u751f\u6210\u6811\uff0c\u6b64\u65f6\u56fe\u4e2d\u7684\u8fb9\u6743\u90fd\u5c3d\u53ef\u80fd\u5927\u4e86\u3002<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:paragraph -->
\n<p>\u7531\u4e8e\u53f8\u673a\u8981\u4ece\u4e00\u5730\u5230\u53e6\u4e00\u5730\uff0c\u53ef\u4ee5\u7528LCA\u5904\u7406\u4e24\u70b9\u95f4\u8def\u5f84\uff0c\u518d\u7528LCA\u9884\u5904\u7406\u65f6\u987a\u5e26\u9884\u5904\u7406\u51faLCA\u8def\u5f84\u4e0a\u7684\u8fb9\u6743\u6700\u5c0f\u503c\u5373\u53ef\uff0c\u4f46\u8981\u6ce8\u610f\u7684\u662f\u56fe\u4e0d\u4e00\u5b9a\u8fde\u901a\uff0c\u53ef\u80fd\u6709\u591a\u4e2a\u8fde\u901a\u5757\uff0c\u8981\u4ece\u6bcf\u4e00\u4e2a\u6839\u8282\u70b9\u5f00\u59cb\u9884\u5904\u7406\u3002<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:html -->
\n<details>
\n<summary>Code<\/summary>
\n<pre class="wp-block-code"><code>#include<bits\/stdc++.h>
\nusing namespace std;
\nconst int maxn1=50005,maxn2=10005;
\nconst int INF=0x3f3f3f3f;<\/p>\n
int log2n;
\nint n,m,f[maxn2];
\nint de[maxn2],fa[maxn2][22],dp[maxn2][22];<\/p>\n
struct edge{
\nint u,v,z;
\n}e[maxn1];<\/p>\n
struct edge2{
\nint to;
\nint v;
\n};
\nvector<edge2> g[maxn2];<\/p>\n
bool cmp(edge x,edge y){
\nreturn x.z>y.z;
\n}<\/p>\n
int dsu_find(int x){
\nreturn f[x]==x ? x : f[x]=dsu_find(f[x]);
\n}<\/p>\n
bool kruskal(){
\nsort(e+1,e+1+m,cmp);
\nfor(int i=1;i<=n;i++)f[i]=i;
\nint s=0,cnt=0;
\nfor(int i=1;i<=m;i++){
\nint fu=dsu_find(e[i].u);
\nint fv=dsu_find(e[i].v);
\nif(fu==fv)continue;
\nf[fu]=fv;
\nedge2 u={e[i].v,e[i].z};
\ng[e[i].u].push_back(u);
\nu={e[i].u,e[i].z};
\ng[e[i].v].push_back(u);
\nif(++cnt==n-1)break;
\n}
\n}<\/p>\n
void dfs(int x,int fath) {<\/p>\n
for(int i=1;i&lt;log2n;i++){\n\n    fa[x][i]=fa[fa[x][i-1]][i-1];\n\n    dp[x][i]=min(dp[x][i-1],dp[fa[x][i-1]][i-1]);\n}\nfor(int i=0;i&lt;g[x].size();i++){\n    int to=g[x][i].to;\n    if(to==fath)continue;\n    fa[to][0]=x;\n    dp[to][0]=g[x][i].v;\n    de[to]=de[x]+1;\n    dfs(to,x);\n}<\/code><\/pre>\n
}<\/p>\n
int lca(int x,int y){
\nint ans=INF;
\nif(de[x]<de[y])swap(x,y);
\nfor(int i=log2n;~i;i--){
\nif(de[fa[x][i]]>=de[y] and fa[x][i]){
\nans=min(ans,dp[x][i]);
\nx=fa[x][i];
\n}
\n}
\nif(x==y)return ans;<\/p>\n
for(int i=log2n;~i;i--){\n    if(fa[x][i]!=fa[y][i]){\n        ans=min(ans,min(dp[x][i],dp[y][i]));\n        x=fa[x][i];\n        y=fa[y][i];\n    }\n}\nans=min(ans,min(dp[x][0],dp[y][0]));\nreturn ans;<\/code><\/pre>\n
}<\/p>\n
int main(){
\nios::sync_with_stdio(0);
\ncin>>n>>m;<\/p>\n
for(int i=1;i&lt;=m;i++){\n    cin&gt;&gt;e[i].u&gt;&gt;e[i].v&gt;&gt;e[i].z;\n}\n\nkruskal();\n\nlog2n=log(n)\/log(2)+1;\n\nfor(int i=1;i&lt;=n;i++){\n    if(dsu_find(f[i])==i){\n        dfs(i,0);\n    }\n}\n\nint q;\ncin&gt;&gt;q;\nfor(int i=1;i&lt;=q;i++){\n    int x,y;\n    cin&gt;&gt;x&gt;&gt;y;\n    if(dsu_find(f[x])!=dsu_find(f[y])){\n        cout&lt;&lt;-1&lt;&lt;endl;\n    }\n    else{\n        cout&lt;&lt;lca(x,y)&lt;&lt;endl;\n    }\n}\n\nreturn 0;<\/code><\/pre>\n
}<\/code><\/pre>
\n<\/details>
\n<!-- \/wp:html -->
\n<!-- wp:heading {"level":3} -->
\n<h3><a href="https:\/\/www.luogu.com.cn\/problem\/P2323<\/a>" target="_blank" rel="noreferrer noopener">P2323 [HNOI2006] \u516c\u8def\u4fee\u5efa\u95ee\u9898<\/a><\/h3>
\n<!-- \/wp:heading -->
\n<!-- wp:paragraph -->
\n<p>\u9898\u76ee\u4e2d\u8bf4\u5fc5\u987b\u8981\u4fee\u591fk\u6761\u4e00\u7ea7\u516c\u8def\uff0c\u4f7f\u5f97\u82b1\u8d39\u6700\u591a\u7684\u4e00\u6761\u516c\u8def\u7684\u82b1\u8d39\u5c3d\u53ef\u80fd\u5c11\uff0c\u56e0\u6b64\u663e\u7136\u53ef\u4ee5\u77e5\u9053\uff0c\u8fd9k\u6761\u4e00\u7ea7\u516c\u8def\u5fc5\u987b\u8981\u4fee\uff0c\u5e76\u4e14\u82b1\u8d39\u5c3d\u53ef\u80fd\u5c0f\uff0c\u53ea\u8981\u7528Kruskal\u5bf9\u4e00\u7ea7\u516c\u8def\u6c42\u4e00\u4e2a\u6700\u5c0f\u751f\u6210\u6811\uff0c\u6309\u987a\u5e8f\u53d6\u5176\u4e2dk\u6761\u8fb9\uff0c\u5e76\u8bb0\u5f55\u8fb9\u53ca\u8fb9\u6743\u6700\u5927\u503c\u3002\u5269\u4e0b\u7684\u7528\u540c\u6837\u65b9\u6cd5\u5bf9\u4e8c\u7ea7\u516c\u8def\u7528Kruskal\u52a0\u8fb9\uff0c\u66f4\u65b0\u6700\u5927\u503c\u5373\u53ef\u3002<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:paragraph -->
\n<p>\u4e00\u4e2a\u60e8\u75db\u7684\u6559\u8bad\uff1a\u5728\u4e00\u4e2a\u56fe\u91cc\u591a\u6b21\u8dd1Kruskal\u7684\u65f6\u5019\uff0c\u5343\u4e07\u4e0d\u8981\u6bcf\u8dd1\u4e00\u6b21\u524d\u5c31\u521d\u59cb\u5316\u4e00\u6b21\u5e76\u67e5\u96c6\uff0c\u4e00\u5f00\u59cb\u521d\u59cb\u5316\u4e00\u904d\u5c31\u591f\u4e86\uff01\uff01\uff01<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:html -->
\n<details>
\n<summary>Code<\/summary>
\n<pre class="wp-block-code"><code>#include<bits\/stdc++.h>
\nusing namespace std;
\nconst int maxn=20005;
\nint n,m,k,f[maxn],bj[maxn];
\nint s=0,tot=0;<\/p>\n
struct edge{
\nint t,u,v,c1,c2;
\n}e[maxn];<\/p>\n
struct node{
\nint bh,gl;
\n}ans[maxn];<\/p>\n
int dsu_find(int x){
\nreturn f[x]==x ? x : f[x]=dsu_find(f[x]);
\n}<\/p>\n
bool cmp1(edge x,edge y){
\nreturn x.c1<y.c1;
\n}<\/p>\n
bool cmp2(edge x,edge y){
\nreturn x.c2<y.c2;
\n}<\/p>\n
bool cmp3(node x,node y){
\nreturn x.bh<y.bh;
\n}<\/p>\n
void kruskal1(){
\nint cnt=0;<\/p>\n
for(int i=1;i&lt;m;i++){\n    int fu=dsu_find(e[i].u),fv=dsu_find(e[i].v);\n    if(fu==fv or bj[e[i].t])continue;\n    f[fv]=fu;\n    bj[e[i].t]=1;\n    ans[++tot].bh=e[i].t;\n    ans[tot].gl=1;\n    s=max(s,e[i].c1);\n    if(++cnt==k)break;\n}<\/code><\/pre>\n
}<\/p>\n
void kruskal2(){
\nint cnt=0;<\/p>\n
for(int i=1;i&lt;m;i++){\n    int fu=dsu_find(e[i].u),fv=dsu_find(e[i].v);\n    if(fu==fv or bj[e[i].t])continue;\n    f[fv]=fu;\n    bj[e[i].t]=1;\n    ans[++tot].bh=e[i].t;\n    ans[tot].gl=2;\n    s=max(s,e[i].c2);\n    if(++cnt==n-1-k)break;\n}<\/code><\/pre>\n
}<\/p>\n
int main(){
\nios::sync_with_stdio(0);
\ncin>>n>>k>>m;
\nfor(int i=1;i<=n;i++)f[i]=i;
\nfor(int i=1;i<m;i++){
\ncin>>e[i].u>>e[i].v>>e[i].c1>>e[i].c2;
\ne[i].t=i;
\n}<\/p>\n
sort(e+1,e+m,cmp1);\nkruskal1();\nsort(e+1,e+m,cmp2);\nkruskal2();\nsort(ans+1,ans+n,cmp3);\ncout&lt;&lt;s&lt;&lt;endl;\nfor(int i=1;i&lt;n;i++){\n    cout&lt;&lt;ans[i].bh&lt;&lt;\" \"&lt;&lt;ans[i].gl&lt;&lt;endl;\n}\n\nreturn 0;<\/code><\/pre>\n
}<\/code><\/pre>
\n<\/details>
\n<!-- \/wp:html -->
\n<!-- wp:heading {"level":3} -->
\n<h3><a href="https:\/\/www.luogu.com.cn\/problem\/P3623<\/a>" target="_blank" rel="noreferrer noopener">P3623 [APIO2008] \u514d\u8d39\u9053\u8def<\/a><\/h3>
\n<!-- \/wp:heading -->
\n<!-- wp:paragraph -->
\n<p>\u9898\u76ee\u5927\u610f\u5176\u5b9e\u5c31\u662f\u6709\u8fb9\u6743\u4e3a0\u548c1\u7684\u8fb9\uff0c\u6c42\u8fb9\u6743\u603b\u548c\u4e3ak\u7684\u751f\u6210\u6811\u3002<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:paragraph -->
\n<p>\u8003\u8651\u5148\u4ece0\u8fb9\u5f00\u59cb\u8dd1\u4e00\u904dKruskal\uff0c\u5982\u679c\u6b64\u65f6\u56fe\u6ca1\u6709\u8fde\u901a\uff0c\u8bf4\u660e\u6b64\u65f6\u8fd8\u9700\u52a0\u5165\u4e00\u4e9b1\u8fb9\u624d\u80fd\u4f7f\u56fe\u8fde\u901a\uff0c\u800c\u8fd9\u4e9b1\u8fb9\u5c31\u662f\u751f\u6210\u6811\u5fc5\u987b\u8981\u6709\u7684\u8fb9\uff0c\u7531\u6b64\u786e\u5b9a\u4e86\u4e00\u90e8\u52061\u8fb9\u3002<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:paragraph -->
\n<p>\u7531\u4e8e\u5df2\u7ecf\u786e\u5b9a\u4e86\u4e00\u90e8\u52061\u8fb9\uff0c\u751f\u6210\u6811\u4e5f\u53ef\u4ee5\u57fa\u672c\u786e\u5b9a\uff0c\u6b64\u65f6\u7b2c\u4e8c\u904d\u4ece1\u8fb9\u5f00\u59cb\u8dd1Kruskal\uff08\u8dd1\u4e4b\u524d\u8981\u5148\u5c06\u5df2\u786e\u5b9a\u76841\u8fb9\u52a0\u5165\uff09\uff0c\u9009\u591fk\u67611\u8fb9\u540e\u518d\u90090\u8fb9\uff0c\u5373\u53ef\u6c42\u51fa\u751f\u6210\u6811\u3002<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:paragraph -->
\n<p>\u65e0\u89e3\u60c5\u51b5\uff1a<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:list -->
\n<ul><li>\u9009\u76841\u8fb9\u6570\u5927\u4e8e\u6216\u5c0f\u4e8ek<\/li><li>\u56fe\u4e0d\u8fde\u901a<\/li><\/ul>
\n<!-- \/wp:list -->
\n<!-- wp:html -->
\n<details>
\n<summary>Code<\/summary>
\n<pre class="wp-block-code"><code>#include<bits\/stdc++.h>
\nusing namespace std;
\nconst int maxn=1e5+10;
\nconst int inf=0x3f3f3f3f;
\nint n,m,k;
\nint f[20005];<\/p>\n
struct edge{
\nint u,v,w,bj=0;
\n}e[maxn];<\/p>\n
int dsu_find(int x){
\nreturn f[x]==x ? x : f[x]=dsu_find(f[x]);
\n}<\/p>\n
bool cmp1(edge x,edge y){
\nreturn x.w<y.w;
\n}<\/p>\n
bool cmp2(edge x,edge y){
\nif(x.w==y.w)return x.bj>y.bj;
\nreturn x.w>y.w;
\n}<\/p>\n
void kruskal1(){
\nint cnt=0;
\nfor(int i=1;i<=n;i++)f[i]=i;
\nfor(int i=1;i<=m;i++){
\nint fu=dsu_find(e[i].u),fv=dsu_find(e[i].v);
\nif(fu==fv)continue;
\nf[fv]=fu;
\nif(e[i].w==1)e[i].bj=1;
\nif(++cnt==n-1)break;
\n}
\n}<\/p>\n
void kruskal2(){
\nint cnt=0,kk=k;
\nfor(int i=1;i<=n;i++)f[i]=i;
\nfor(int i=1;i<=m;i++){
\nif(e[i].bj){
\nf[dsu_find(e[i].v)]=dsu_find(e[i].u);
\ncnt++;
\nkk--;
\ncontinue;
\n}
\nint fu=dsu_find(e[i].u),fv=dsu_find(e[i].v);
\nif(fu==fv)continue;<\/p>\n
    f[fv]=fu;\n    e[i].bj=1;\n    if(e[i].w)kk--;\n    if(!kk)for(;e[i].w;i++);\n    if(++cnt==n-1)break;\n}\n\nif(kk&gt;0){\n    cout&lt;&lt;\"no solution\"&lt;&lt;endl;\n    exit(0);\n}<\/code><\/pre>\n
}<\/p>\n
int main(){
\nios::sync_with_stdio(0);
\ncin>>n>>m>>k;<\/p>\n
for(int i=1;i&lt;=m;i++){\n    int ww;\n    cin&gt;&gt;e[i].u&gt;&gt;e[i].v&gt;&gt;ww;\n    e[i].w=1-ww;\n}\nsort(e+1,e+1+m,cmp1);\nkruskal1();\n\nsort(e+1,e+1+m,cmp2);\nkruskal2();\n\nfor(int i=1;i&lt;=m;i++){\n\n    if(e[i].bj){\n        cout&lt;&lt;e[i].u&lt;&lt;\" \"&lt;&lt;e[i].v&lt;&lt;\" \"&lt;&lt;(1-e[i].w)&lt;&lt;endl;\n    }\n}\n\nreturn 0;<\/code><\/pre>\n
}<\/code><\/pre>
\n<\/details>
\n<!-- \/wp:html -->
\n<!-- wp:heading {"level":3} -->
\n<h3><a href="https:\/\/www.luogu.com.cn\/problem\/P1550<\/a>" target="_blank" rel="noreferrer noopener">P1550 [USACO08OCT] Watering Hole G<\/a><\/h3>
\n<!-- \/wp:heading -->
\n<!-- wp:paragraph -->
\n<p>\u7a0d\u5fae\u62bd\u8c61\u4e00\u4e0b\u9898\u610f\uff0c\u65e0\u5411\u56fe\u6709\u4e00\u5806\u5e26\u6743\u503c\u7684\u8fb9\u548c\u70b9\uff0c\u5f53\u9009\u5b9a\u4e86\u4e00\u4e2a\u70b9\u65f6\uff0c\u4e0e\u5b83\u8fde\u901a\u7684\u70b9\u5c31\u4e0d\u7528\u8ba1\u5b83\u7684\u6743\u503c\uff0c\u4e0d\u96be\u770b\u51fa\uff0c\u53ef\u4ee5\u5c06\u70b9\u6743\u8f6c\u5316\u4e3a\u8fb9\u6743\uff0c\u4e5f\u5c31\u662f\u5efa\u7acb\u4e00\u4e2a\u8d85\u7ea7\u6e90\u70b9\uff0c\u4e0e\u5176\u4ed6\u6bcf\u4e2a\u70b9\u90fd\u6709\u8fde\u8fb9\uff0c\u8be5\u8fb9\u7684\u8fb9\u6743\u5c31\u662f\u8fde\u5411\u7684\u70b9\u7684\u70b9\u6743\uff0c\u8fd9\u6837\u5c31\u80fd\u628a\u6240\u6709\u6743\u503c\u90fd\u7edf\u4e00\u4e3a\u8fb9\u6743\u3002<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:paragraph -->
\n<p>\u9898\u76ee\u8981\u6c42\u4f7f\u5f97\u56fe\u8fde\u901a\u7684\u6700\u5c11\u94b1\u6570\uff0c\u8dd1\u4e2aKruskal\u5373\u53ef\u3002<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:html -->
\n<details>
\n<summary>Code<\/summary>
\n<pre class="wp-block-code"><code>#include<bits\/stdc++.h>
\nusing namespace std;
\ntypedef long long ll;
\nconst int maxn=305;
\nint n,m,tot;
\nint c[maxn],f[maxn];
\nll sum;<\/p>\n
struct edge{
\nint u,v,w;
\n}e[maxn*maxn];<\/p>\n
int dsu_find(int x){
\nreturn x==f[x]?x:f[x]=dsu_find(f[x]);
\n}<\/p>\n
bool cmp(edge x,edge y){
\nreturn x.w<y.w;
\n}<\/p>\n
void kruskal(){
\nfor(int i=0;i<=n;i++)f[i]=i;
\nsort(e+1,e+1+tot,cmp);
\nint cnt=0;
\nfor(int i=1;i<=tot;i++){
\nint fu=dsu_find(e[i].u),fv=dsu_find(e[i].v);
\nif(fu==fv)continue;
\nf[fu]=fv;
\nsum+=e[i].w;
\nif(++cnt==n)break;
\n}
\n}<\/p>\n
int main(){
\nios::sync_with_stdio(0);
\ncin>>n;<\/p>\n
for(int i=1;i&lt;=n;i++){\n    int x;\n    cin&gt;&gt;x;\n    e[++tot]={0,i,x};\n}\n\nfor(int i=1;i&lt;=n;i++){\n    for(int j=1;j&lt;=n;j++){\n        int x;\n        cin&gt;&gt;x;\n        if(i&lt;j){\n            e[++tot].u=i;\n            e[tot].v=j;\n            e[tot].w=x;\n        }\n    }\n}\nkruskal();\ncout&lt;&lt;sum&lt;&lt;endl;\n\nreturn 0;<\/code><\/pre>\n
}<\/code><\/pre>
\n<\/details>
\n<!-- \/wp:html -->
\n<!-- wp:heading {"level":3} -->
\n<h3><a href="https:\/\/www.luogu.com.cn\/problem\/P5994<\/a>" target="blank" rel="noreferrer noopener">P5994 [PA2014] Kuglarz<\/a><\/h3>
\n<!-- \/wp:heading -->
\n<!-- wp:list -->
\n<ul><li>\u9898\u76ee\u8981\u6c42\u6bcf\u4e2a\u676f\u5b50\u5e95\u4e0b\u662f\u5426\u85cf\u6709\u7403\uff0c\u5176\u5b9e\u5c31\u662f\u60f3\u77e5\u9053\u6bcf\u4e2a\u676f\u5b50\u7684\u5947\u5076\u6027<\/li><\/ul>
\n<!-- \/wp:list -->
\n<!-- wp:paragraph -->
\n<p>\u5b9a\u4e49 $F(l,r)$ \u8868\u793a $[l,r]$ \u533a\u95f4\u7403\u7684\u603b\u6570\u3002<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:paragraph -->
\n<p>\u800c\u5982\u679c\u6211\u4eec\u60f3\u77e5\u9053 $F(l,l)$ \u7684\u5947\u5076\u6027\uff0c\u90a3\u4e48\u53ea\u9700\u8981\u77e5\u9053 $F(l+1,r)$ \u548c $F(l,r)$ \u7684\u5947\u5076\u6027\u6216\u8005\u76f4\u63a5\u82b1\u8d39 $c<\/em>{l,l}$ \u67e5\u8be2\u8be5\u70b9\uff0c\u5bf9\u4e8e $F(r,r)$ \u540c\u7406\u3002<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:paragraph -->
\n<p>\u8003\u8651\u628a $F(l,r)$ \u770b\u4f5c\u70b9 $l-1$ \u5411\u70b9 $r$ \u8fde\u4e86\u4e00\u6761\u8fb9\uff0c$F(l,l)$ \u5c31\u76f8\u5f53\u4e8e\u70b9 $l-1$ \u5411\u70b9 $l$ \u8fde\u4e86\u4e00\u6761\u8fb9\u3002\u5f53\u6240\u6709\u70b9\u90fd\u8fde\u901a\u65f6\uff0c\u90a3\u5c31\u5fc5\u7136\u53ef\u4ee5\u4ece\u76f8\u90bb\u70b9\u63a8\u51fa\u8fd9\u4e24\u70b9\u95f4\u8fb9\u7684\u5947\u5076\u6027\uff0c\u4e5f\u5c31\u662f\u77e5\u9053\u4e86 $F(l,l)$ \u7684\u5947\u5076\u6027\u3002\u8981\u4f7f\u82b1\u8d39\u6700\u5c0f\uff0c\u8dd1\u4e2aKruskal\u5373\u53ef\u3002<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:html -->
\n<details>
\n<summary>Code<\/summary>
\n<pre class="wp-block-code"><code>#include<bits\/stdc++.h>
\nusing namespace std;
\ntypedef long long ll;
\nconst int maxn=2005;
\nint n,tot;
\nll sum;
\nint f[maxn];<\/p>\n
struct edge{
\nint u,v,w;
\n}e[maxn*maxn];<\/p>\n
int dsu_find(int x){
\nreturn x==f[x]?x:f[x]=dsu_find(f[x]);
\n}<\/p>\n
bool cmp(edge x,edge y){
\nreturn x.w<y.w;
\n}<\/p>\n
void kruskal(){
\nfor(int i=0;i<=n;i++)f[i]=i;
\nsort(e+1,e+tot+1,cmp);
\nint cnt=0;
\nfor(int i=1;i<=tot;i++){
\nint fu=dsu_find(e[i].u),fv=dsu_find(e[i].v);
\nif(fu==fv)continue;
\nf[fu]=fv;
\nsum+=e[i].w;
\nif(++cnt==n)break;
\n}
\n}<\/p>\n
int main(){
\nios::sync_with_stdio(0);
\ncin>>n;
\nfor(int i=1;i<=n;i++){
\nfor(int j=i;j<=n;j++){
\ncin>>e[++tot].w;
\ne[tot].u=i-1;
\ne[tot].v=j;
\n}
\n}<\/p>\n
kruskal();\ncout&lt;&lt;sum&lt;&lt;endl;\n\nreturn 0;<\/code><\/pre>\n
}<\/code><\/pre>
\n<\/details>
\n<!-- \/wp:html -->
\n<!-- wp:heading {"level":3} -->
\n<h3><a href="https:\/\/www.luogu.com.cn\/problem\/CF1687B<\/a>" target="_blank" rel="noreferrer noopener">CF1687B Railway System<\/a><\/h3>
\n<!-- \/wp:heading -->
\n<!-- wp:paragraph -->
\n<p>\u8fd9\u9898\u5199\u4e86\u7bc7\u9898\u89e3\uff0c\u8be6\u89c1<a href="https:\/\/www.luogu.com.cn\/blog\/xgnd\/solution-cf1687b\">\u8fd9\u91cc<\/a><\/a>\u3002<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:heading {"level":3} -->
\n<h3><a href="https:\/\/www.luogu.com.cn\/problem\/CF609E<\/a>" target="_blank" rel="noreferrer noopener">CF609E Minimum spanning tree for each edge<\/a><\/h3>
\n<!-- \/wp:heading -->
\n<!-- wp:paragraph -->
\n<p>\u975e\u4e25\u683c\u6b21\u5c0f\u751f\u6210\u6811\u677f\u5b50\u9898\u3002<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:paragraph -->
\n<p>Kruskal\u6c42\u51fa\u6700\u5c0f\u751f\u6210\u6811\u540e\uff0c\u5148\u500d\u589e\u9884\u5904\u7406\u51fa\u6811\u4e0a\u4e24\u70b9\u7684\u6700\u8fd1\u516c\u5171\u7956\u5148\u548c\u8def\u5f84\u4e0a\u8fb9\u6743\u6700\u5927\u503c\u3002<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:paragraph -->
\n<p>$1$ \u5230 $m$ \u679a\u4e3e\u6bcf\u6761\u8fb9\uff0c\u82e5\u8be5\u8fb9\u5728\u6700\u5c0f\u751f\u6210\u6811\u91cc\uff0c\u76f4\u63a5\u8f93\u51fa\u5176\u6743\u503c\u548c\uff1b\u82e5\u4e0d\u5728\uff0c\u8003\u8651\u5c06\u8def\u5f84\u6743\u503c\u6700\u5927\u7684\u8fb9\u5220\u53bb\uff0c\u518d\u52a0\u5165\u8fd9\u6761\u8fb9\u65f6\uff0c\u8fb9\u6743\u548c\u6700\u5c0f\uff0c\u8fb9\u6743\u548c\u4e3a $sum+w<em>k-max<\/em>{i,j}$ \u3002\uff08 $sum$ \u4e3a\u6700\u5c0f\u751f\u6210\u6811\u8fb9\u6743\u548c\uff0c$w<em>k$ \u4e3a\u6b64\u8fb9\u8fb9\u6743\uff0c$max<\/em>{i,j}$ \u4e3a\u6811\u4e0a\u4e24\u70b9 $i$\uff0c$j$ \u8def\u5f84\u4e0a\u8fb9\u6743\u6700\u5927\u503c\uff09<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:html -->
\n<details>
\n<summary>Code<\/summary>
\n<pre class="wp-block-code"><code>#include<bits\/stdc++.h>
\nusing namespace std;
\ntypedef long long ll;
\nconst int maxn=200005;
\nint n,m;
\nll sum;
\nint f[maxn];
\nint mx[maxn][22];
\nint fa[maxn][22];
\nint dep[maxn];<\/p>\n
struct edge{
\nint u,v,w,p;
\nbool bj;
\n}e[maxn];<\/p>\n
struct edge1{
\nint to,v;
\n};
\nvector<edge1>g[maxn];<\/p>\n
int dsu_find(int x){
\nreturn x==f[x]?x:f[x]=dsu_find(f[x]);
\n}<\/p>\n
bool cmp(edge x,edge y){
\nreturn x.w<y.w;
\n}<\/p>\n
bool cmp_num(edge x,edge y){
\nreturn x.p<y.p;
\n}<\/p>\n
void kruskal(){
\nfor(int i=1;i<=n;i++)f[i]=i;
\nsort(e+1,e+1+m,cmp);
\nint cnt=0;
\nfor(int i=1;i<=m;i++){
\nint fu=dsu_find(e[i].u),fv=dsu_find(e[i].v);
\nif(fu==fv)continue;
\nf[fu]=fv;
\nsum+=e[i].w;
\ne[i].bj=1;
\ng[e[i].u].push_back({e[i].v,e[i].w});
\ng[e[i].v].push_back({e[i].u,e[i].w});
\nif(++cnt==n-1)break;
\n}
\n}<\/p>\n
void dfs(int x,int fath,int v){
\nfa[x][0]=fath;
\nmx[x][0]=v;
\ndep[x]=dep[fath]+1;<\/p>\n
for(int i=1;i&lt;=20;i++){\n    fa[x][i]=fa[fa[x][i-1]][i-1];\n    mx[x][i]=max(mx[x][i-1],mx[fa[x][i-1]][i-1]);\n}\n\nfor(int i=0;i&lt;g[x].size();i++){\n    int to=g[x][i].to;\n    if(to==fath)continue;\n    dfs(to,x,g[x][i].v);\n}<\/code><\/pre>\n
}<\/p>\n
int query(int x,int y){
\nif(dep[x]<dep[y])swap(x,y);
\nint ans=0;
\nfor(int i=20;i>=0;i--){
\nif(dep[fa[x][i]]>=dep[y]){
\nans=max(ans,mx[x][i]);
\nx=fa[x][i];
\n}
\n}
\nif(x==y)return ans;<\/p>\n
for(int i=20;i&gt;=0;i--){\n    if(fa[x][i]!=fa[y][i]){\n        ans=max(ans,max(mx[x][i],mx[y][i]));\n        x=fa[x][i],y=fa[y][i];\n    }\n}\nans=max(ans,max(mx[x][0],mx[y][0]));\nreturn ans;<\/code><\/pre>\n
}<\/p>\n
int main(){
\nios::sync_with_stdio(0);
\ncin>>n>>m;<\/p>\n
for(int i=1;i&lt;=m;i++){\n    cin&gt;&gt;e[i].u&gt;&gt;e[i].v&gt;&gt;e[i].w;\n    e[i].p=i;\n}\n\nkruskal();\ndfs(1,0,0);\nsort(e+1,e+1+m,cmp_num);\nfor(int i=1;i&lt;=m;i++){\n\n    if(e[i].bj)cout&lt;&lt;sum&lt;&lt;endl;\n    else {\n        int t=query(e[i].u,e[i].v);\n\n        cout&lt;&lt;(sum+e[i].w-t)&lt;&lt;endl;\n    }\n}\n\nreturn 0;<\/code><\/pre>\n
}<\/code><\/pre>
\n<\/details>
\n<!-- \/wp:html -->
\n<!-- wp:heading {"level":3} -->
\n<h3><a href="https:\/\/www.luogu.com.cn\/problem\/P4180<\/a>" target="_blank" rel="noreferrer noopener">P4180 [BJWC2010] \u4e25\u683c\u6b21\u5c0f\u751f\u6210\u6811<\/a><\/h3>
\n<!-- \/wp:heading -->
\n<!-- wp:paragraph -->
\n<p>\u4e25\u683c\u6b21\u5c0f\u751f\u6210\u6811\u677f\u5b50\u9898\u3002<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:paragraph -->
\n<p>\u4e0e\u975e\u4e25\u683c\u6b21\u5c0f\u751f\u6210\u6811\u7c7b\u4f3c\uff0c\u8003\u8651\u7528\u975e\u6811\u8fb9\u53bb\u66ff\u4ee3\u539f\u6700\u5c0f\u751f\u6210\u6811\u7684\u8fb9\uff0c\u4f46\u53ef\u80fd\u8fb9\u6743\u6700\u5927\u503c\u4e0e\u65b0\u52a0\u7684\u8fb9\u7684\u8fb9\u6743\u76f8\u7b49\uff0c\u56e0\u6b64\u8981\u7528\u6b21\u5927\u503c\u4ee3\u66ff\uff0c\u82e5\u6b21\u5927\u503c\u4e5f\u76f8\u7b49\uff0c\u5c31\u6362\u4e0b\u4e00\u6761\u8fb9\u518d\u8bd5\u3002\u500d\u589e\u9884\u5904\u7406\u65f6\u518d\u7ef4\u62a4\u6811\u4e0a\u4e24\u70b9\u8def\u5f84\u4e0a\u8fb9\u6743\u6b21\u5927\u503c\u5373\u53ef\u3002<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:paragraph -->
\n<p>\u6ce8\u610f\u4f1a\u6709\u91cd\u8fb9\uff0c\u53ef\u4ee5\u521d\u59cb\u5316\u7b54\u6848\u4e3a $-inf$ \u907f\u514d\u91cd\u8fb9\u3002<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:html -->
\n<details>
\n<summary>Code<\/summary>
\n<pre class="wp-block-code"><code>#include<bits\/stdc++.h>
\nusing namespace std;
\ntypedef long long ll;
\nconst int maxn=300005;
\nconst int inf=0x3f3f3f3f;
\nint n,m;
\nll sum;
\nint f[maxn];
\nint mx[maxn][22],cmx[maxn][22];
\nint fa[maxn][22];
\nint dep[maxn];<\/p>\n
struct edge{
\nint u,v,w;
\nbool bj;
\n}e[maxn];<\/p>\n
struct edge1{
\nint to,v;
\n};
\nvector<edge1>g[maxn];<\/p>\n
int dsu_find(int x){
\nreturn x==f[x]?x:f[x]=dsu_find(f[x]);
\n}<\/p>\n
bool cmp(edge x,edge y){
\nreturn x.w<y.w;
\n}<\/p>\n
void kruskal(){
\nfor(int i=1;i<=n;i++)f[i]=i;
\nsort(e+1,e+1+m,cmp);
\nint cnt=0;
\nfor(int i=1;i<=m;i++){
\nint fu=dsu_find(e[i].u),fv=dsu_find(e[i].v);
\nif(fu==fv)continue;
\nf[fu]=fv;
\nsum+=e[i].w;
\ne[i].bj=1;
\ng[e[i].u].push_back({e[i].v,e[i].w});
\ng[e[i].v].push_back({e[i].u,e[i].w});
\nif(++cnt==n-1)break;
\n}
\n}<\/p>\n
void dfs(int x,int fath){
\nfa[x][0]=fath;
\ndep[x]=dep[fath]+1;<\/p>\n
for(int i=1;i&lt;=21;i++){\n    fa[x][i]=fa[fa[x][i-1]][i-1];\n    mx[x][i]=max(mx[x][i-1],mx[fa[x][i-1]][i-1]);\n    cmx[x][i]=max(cmx[x][i-1],cmx[fa[x][i-1]][i-1]);\n    if(mx[x][i-1]&gt;mx[fa[x][i-1]][i-1])cmx[x][i]=max(cmx[x][i],mx[fa[x][i-1]][i-1]);\n    else if(mx[x][i-1]&lt;mx[fa[x][i-1]][i-1])cmx[x][i]=max(cmx[x][i],mx[x][i-1]);\n}\n\nfor(int i=0;i&lt;g[x].size();i++){\n    int to=g[x][i].to;\n    if(to==fath)continue;\n    mx[to][0]=g[x][i].v;\n    dfs(to,x);\n}<\/code><\/pre>\n
}<\/p>\n
int lca(int x,int y) {
\nif(dep[x]<dep[y]) swap(x,y);
\nfor(int i=20; ~i; i--) {
\nif(dep[fa[x][i]]>=dep[y]) {
\nx=fa[x][i];
\n}
\nif(x==y) return x;
\n}
\nfor(int i=20; ~i; i--) {
\nif(fa[x][i]!=fa[y][i]) {
\nx=fa[x][i];
\ny=fa[y][i];
\n}
\n}
\nreturn fa[x][0];
\n}<\/p>\n
int findmax(int x,int lca,int val){
\nint ans=-inf;
\nfor(int i=20;i>=0;i--){
\nif(dep[fa[x][i]]>=dep[lca]){
\nif(mx[x][i]==val)ans=max(ans,cmx[x][i]);
\nelse ans=max(ans,mx[x][i]);
\nx=fa[x][i];
\n}
\n}
\nreturn ans;
\n}<\/p>\n
int main(){
\nios::sync_with_stdio(0);
\ncin>>n>>m;<\/p>\n
for(int i=1;i&lt;=m;i++){\n    cin&gt;&gt;e[i].u&gt;&gt;e[i].v&gt;&gt;e[i].w;\n}\n\nkruskal();\ndfs(1,0);\n\nll ans=0x3f3f3f3f3f3f;\nfor(int i=1;i&lt;=m;i++){\n    if(e[i].bj)continue;\n    int l=lca(e[i].u,e[i].v);\n    int mu=findmax(e[i].u,l,e[i].w),mv=findmax(e[i].v,l,e[i].w);\n    if(max(mu,mv)!=e[i].w or max(mu,mv)&gt;-inf)ans=min(ans,(ll)sum-max(mu,mv)+e[i].w);\n}\ncout&lt;&lt;ans&lt;&lt;endl;\nreturn 0;<\/code><\/pre>\n
}<\/code><\/pre>
\n<\/details>
\n<!-- \/wp:html -->
\n<!-- wp:heading {"level":3} -->
\n<h3><a href="https:\/\/www.luogu.com.cn\/problem\/CF1305G\">CF1305G<\/a> Kuroni and Antihype<\/a><\/h3>
\n<!-- \/wp:heading -->
\n<!-- wp:paragraph -->
\n<p>update 2023.7.16<\/p>
\n<!-- \/wp:paragraph -->
\n<!-- wp:paragraph -->
\n<p>\u5148\u8003\u8651\u5efa\u51fa\u4e00\u5f20\u56fe\uff0c\u4e00\u5bf9\u670b\u53cb $(u,v)$ \u5bf9\u5e94\u56fe\u4e0a\u4e00\u5bf9\u8fb9 $u \\rightarrow v$ \u8fb9\u6743\u4e3a $a_v$ \u548c $v\\rightarrow u$ \u8fb9\u6743\u4e3a $a_u$ \uff0c\u53d1\u73b0\u56fe\u53ef\u80fd\u6709\u591a\u4e2a\u8fde\u901a\u5757\uff0c\u4e8e\u662f\u987a\u624b\u5efa\u4e00\u4e2a\u8d85\u7ea7\u6e90\u70b9\uff0c\u9898\u76ee\u5c31\u8f6c\u5316\u4e3a\u6c42\u6700\u5927\u5916\u5411\u6811\u3002<\/p>
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\n<!-- wp:paragraph -->
\n<p>\u76f4\u63a5\u6c42\u6700\u5927\u5916\u5411\u6811\u80af\u5b9a\u4e0d\u597d\u505a\uff0c\u4f46\u53d1\u73b0\u4f3c\u4e4e\u6b63\u53cd\u8fb9\u6bd4\u8f83\u5bf9\u79f0\uff0c\u53ef\u4ee5\u8003\u8651\u8f6c\u5316\uff0c\u5c06\u8fb9\u6743\u8bbe\u4e3a $a_u+a_v$ \uff0c\u90a3\u4e48\u6700\u7ec8\u7b54\u6848\u5c31\u4e3a\u6700\u5927\u751f\u6210\u6811\u6743\u503c\u548c\u51cf\u53bb $\\sum a_i$ \uff0c\u8fd9\u5c31\u5f88\u597d\u505a\u4e86\u3002<\/p>
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\n<!-- wp:paragraph -->
\n<p>\u5982\u679c\u76f4\u63a5\u5efa\u56fe\u8fde\u8fb9\uff0c\u8fb9\u6570\u4e3a $O(n^2)$ \u7ea7\u522b\uff0c\u8fd9\u4e0d\u597d\u3002\u8003\u8651\u6765\u70b9\u4f18\u5316\uff0c\u82e5\u80fd\u6a21\u62df Kruskal \u6c42\u6700\u5927\u751f\u6210\u6811\u7684\u8fc7\u7a0b\uff0c\u5c31\u4e0d\u7528\u5efa\u8fb9\u4e86\uff0c\u8fd9\u662f\u597d\u7684\u3002\u6240\u4ee5\u53ef\u4ee5\u4ece\u5927\u5230\u5c0f\u679a\u4e3e\u8fb9\u6743 $s$ \u4f9d\u6b21\u52a0\u5165\uff0c\u4f46\u5bf9\u4e8e\u4e00\u6761\u8fb9\u600e\u4e48\u77e5\u9053\u5b83\u8fde\u7684\u662f\u54ea\u4e2a\u70b9\u5462\uff1f\u6ce8\u610f\u5230\u6709\u4e00\u4e2a\u6761\u4ef6\uff0c\u6ee1\u8db3 $a_u \\& a<em>v=0$ \u7684\u70b9\u624d\u8fde\u8fb9\uff0c\u90a3\u4e48\u52a0\u6cd5\u5c31\u76f8\u5f53\u4e8e\u6216\uff0c\u6240\u4ee5\u53ef\u4ee5\u679a\u4e3e $s$ \u7684\u5b50\u96c6 $x$ \uff0c\u627e\u70b9\u6743\u4e3a $x$ \u548c $x\\; XOR\\; s$ \u7684\u70b9\u7528\u5e76\u67e5\u96c6\u8fde\u8d77\u6765\u5373\u53ef\u3002\u70b9\u6743\u76f8\u540c\u7684\u70b9\u53ef\u4ee5\u7f29\u70b9\u5f53\u4f5c\u4e00\u4e2a\u70b9\u5904\u7406\uff0c\u4e00\u6761\u8fb9\u4ea7\u751f\u7684\u8d21\u732e\u5c31\u662f $s\\times (cnt<\/em>{a<em>u}+cnt<\/em>{av}-1)$\u3002<\/p>
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\n<!-- wp:paragraph -->
\n<p>\u679a\u4e3e\u5b50\u96c6\u590d\u6742\u5ea6\u4e3a $O(3^{log\\;n})\\approx O(3^{18})$ \uff0c\u603b\u590d\u6742\u5ea6\u4e3a $O(3^{18}\\times\\alpha(n))$\u3002<\/p>
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\n<!-- wp:paragraph -->
\n<p>\u4e2a\u4eba\u8ba4\u4e3a\u8fd9\u662f\u9053\u597d\u9898\uff0c\u5b66\u5230\u4e86\u4e00\u4e9b\u5957\u8def\uff0c\u50cf\u8f6c\u5316\u8fb9\u6743\u3001\u5feb\u901f\u679a\u4e3e\u5b50\u96c6\u3001\u7f29\u70b9\u4e4b\u7c7b\u7684\uff0c\u611f\u89c9\u90fd\u6bd4\u8f83\u6709\u7528\u3002<\/p>
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\n<!-- wp:html -->
\n<details>
\n<summary>Code<\/summary>
\n<pre class="wp-block-code"><code>#include<bits\/stdc++.h>
\nusing namespace std;
\ntypedef long long ll;
\nconst int maxn=400005,INF=0x3f3f3f3f;
\nint <\/em>;
\nint t,n,mx;
\nint cnt[maxn],fa[maxn];
\nll ans;<\/p>\n
int getfa(int x){
\nreturn x==fa[x]?x:fa[x]=getfa(fa[x]);
\n}<\/p>\n
void dsu_merge(int x,int y,ll w){
\nx=getfa(x),y=getfa(y);
\nif(x==y)return;
\nfa[x]=y;
\nans+=1ll(cnt[x]+cnt[y]-1)<\/em>w;
\ncnt[y]=1;
\n}<\/p>\n
int main(){
\nios::sync_with_stdio(0);
\nint n;
\ncin>>n;<\/p>\n
cnt&#91;0]=1;\nfor(int i=1;i&lt;=n;i++){\n    int w;\n    cin&gt;&gt;w;\n    ans-=w;\n    cnt&#91;w]++;\n    mx=max(mx,w);\n}\nint mxn=1&lt;&lt;32-__builtin_clz(mx);\nfor(int i=0;i&lt;=mxn;i++)fa&#91;i]=i;\n\nfor(int i=mxn;i&gt;=0;i--){\n    for(int j=i;j;j=(j-1)&amp;i){\n        if(cnt&#91;j] and cnt&#91;j^i]){\n            dsu_merge(j,i^j,i);\n        }\n    }\n    if(cnt&#91;0] and cnt&#91;i])dsu_merge(0,i,i);\n}\n\ncout&lt;&lt;ans&lt;&lt;endl;\n\nreturn 0;<\/code><\/pre>\n
}
\n<\/code><\/pre>
\n<\/details>
\n<!-- \/wp:html --><\/p>\n","protected":false},"excerpt":{"rendered":"
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