{"id":524,"date":"2020-08-24T22:33:48","date_gmt":"2020-08-24T14:33:48","guid":{"rendered":"http:\/\/nocriz.com\/?p=524"},"modified":"2021-09-08T20:20:07","modified_gmt":"2021-09-08T12:20:07","slug":"%e6%9d%ad%e7%94%b5%e5%a4%9a%e6%a0%a1%e7%ac%ac%e4%b9%9d%e5%9c%ba-1010-jump","status":"publish","type":"post","link":"https:\/\/nocriz.com\/?p=524","title":{"rendered":"\b\b\u676d\u7535\u591a\u6821\u7b2c\u4e5d\u573a-1010-Jump"},"content":{"rendered":"\n

\u8fd9\u573a\u6bd4\u8d5b\u662f\u6211\u4eec\u961f\u56de\u5230\u897f\u5b89\u4e4b\u540e\u6253\u7684\u7b2c1\u573a\u591a\u6821\u6bd4\u8d5b\u3002\u8fd9\u573a\u6bd4\u8d5b\u96be\u5ea6\u6bd4\u8f83\u5927\uff0c\u9898\u76ee\u597d\u50cf\u6211\u4e5f\u6ca1\u600e\u4e48\u8865\u3002\u6240\u4ee5\u505a\u4e865\u9898\u5c31\u62ff\u5230\u4e86\u7b2c2\u540d\uff0c\u7b2c1\u540d\u597d\u50cf\u67096\u9898\uff0c\u7136\u540e\u540e\u9762\u7684\u961f\u5c31\u90fd\u662f4\u9898\u5bf9\u3002\u8fd9\u573a\u6bd4\u8d5b\u6211\u53d1\u6325\u7684\u4e0d\u9519\uff0c\u6700\u540e\u7684\u4e24\u9053\u9898\u90fd\u662f\u6211\u505a\u7684\u3002\u5176\u4e2d\u4e00\u9053\u5c31\u662f\u8fd9\u4e00\u9053\u53ea\u6709\u4e00\u4e2a\u4eba\u8fc7\u76841010\u3002<\/p>\n\n\n\n

\u9898\u610f\uff1a\u6709\u4e00\u68f5\u6811\uff0c\u8fb9\u6709\u8fb9\u6743\u3002\u4f60\u73b0\u5728\u7ef4\u62a4\u4e00\u4e2a\u70b9\u7684\u5e8f\u5217\uff0c\u64cd\u4f5c\u6709\u4e24\u79cd\uff1a 1.\u5c06[l,r]\u533a\u95f4\u4e2d\u6240\u6709\u70b9\u90fd\u53d8\u4e3a\u5176\u7236\u8282\u70b9\uff08\u6839\u7684\u7236\u8282\u70b9\u4e3a\u6839\u8282\u70b9\uff092.\u67e5\u8be2[l,r]\u533a\u95f4\u4e2d\u6240\u6709\u70b9\u7684\u6df1\u5ea6\u6700\u5c0f\u503c<\/p>\n\n\n\n\n\n\n\n

\u8003\u8651sqrt\u5206\u5757\uff0c\u5219\u6211\u4eec\u9700\u8981\u5904\u7406\u56db\u79cd\u64cd\u4f5c\uff1a<\/p>\n\n\n\n

1.\u6574\u5757\u53d8\u4e3a\u7236\u8282\u70b9
2.\u5757\u4e2d\u90e8\u5206\u8282\u70b9\u53d8\u4e3a\u7236\u8282\u70b9
3.\u6574\u5757\u8be2\u95ee
4.\u90e8\u5206\u8282\u70b9\u8be2\u95ee<\/p>\n\n\n\n

\u6211\u4eec\u5148\u8003\u8651\u53ea\u67091\u30013\u30014\u64cd\u4f5c\u7684\u60c5\u5f62\u3002\u6211\u4eec\u8003\u8651\u5efa\u7acb\u5757\u4e2d\u6240\u6709\u8282\u70b9\u7684\u865a\u6811\uff0c\u6709\u7956\u5148\u8282\u70b9\u4e5f\u5728\u5757\u4e2d\u7684\u8282\u70b9\u5219\u662f\u6c38\u8fdc\u4e0d\u4f1a\u6210\u4e3a\u6df1\u5ea6\u6700\u5c0f\u7684\u70b9\u7684\u3002\u6211\u4eec\u53bb\u6389\u8fd9\u4e9b\u70b9\uff0c\u5c31\u5f97\u5230\u4e86\u53ea\u6709\u53f6\u5b50\u8282\u70b9\u662f\u5757\u4e2d\u8282\u70b9\u7684\u4e00\u9897\u865a\u6811\u3002\u7ef4\u62a4\u8fd9\u4e9b\u8282\u70b9\uff0c\u6bcf\u6b21\u64cd\u4f5c1\u65f6\u90fd\u5c06\u6240\u6709\u70b9\u66b4\u529b\u53d8\u4e3a\u7236\u8282\u70b9\uff0c\u5e76\u68c0\u67e5\u6b64\u65f6\u662f\u5426\u6709\u8282\u70b9\u662f\u5176\u4ed6\u8282\u70b9\u7684\u7956\u5148\u8282\u70b9\uff0c\u53ca\u65f6\u5220\u9664\u6ca1\u6709\u7528\u7684\u8282\u70b9\u3002<\/p>\n\n\n\n

\u7531\u4e8e\u6bcf\u4e00\u4e2a\u8282\u70b9\u53ea\u4f1a\u53d8\u6210\u5176\u7236\u8282\u70b9\u4e00\u6b21\uff0c\u6bcf\u4e2a\u5757\u603b\u7684\u64cd\u4f5c\u6b21\u6570\u5c06\u4e0d\u8d85\u8fc7n\u3002\u5982\u679c\u5728\u66f4\u65b0\u65f6\u5019\u7ef4\u62a4\u7b54\u6848\uff0c\u5c31\u53ef\u4ee5\u76f4\u63a5\u56de\u7b543\u7c7b\u64cd\u4f5c\u3002\u6211\u4eec\u8bb0\u5f55\u6574\u4e2a\u5757\u88ab\u64cd\u4f5c1\u8fdb\u884c\u4e86\u51e0\u6b21\uff0c\u5e76\u4f7f\u7528\u67d0\u4e9b\u5bfb\u627e\u6bcf\u4e2a\u8282\u70b9\u7684k\u7956\u5148\u7684\u65b9\u6cd5\u5c31\u53ef\u4ee5\u56de\u7b544\u7c7b\u64cd\u4f5c\u3002<\/p>\n\n\n\n

\u8003\u86512\u7c7b\u64cd\u4f5c\uff0c\u53ef\u4ee5\u6bcf\u6b21\u66b4\u529b\u91cd\u6784\u3002<\/p>\n\n\n\n

\u4e8b\u5b9e\u4e0a\uff0c\u4e0d\u9700\u8981\u663e\u5f0f\u5730\u5efa\u7acb\u865a\u6811\uff0c\u53ea\u9700\u8981\u628a\u6709\u53ef\u80fd\u6210\u4e3a\u7b54\u6848\u7684\u70b9\u6309\u7167dfs\u5e8f\u6392\u5e8f\u5b58\u5728vector\u91cc\u9762\u5373\u53ef\u3002\u7531\u4e8e\u5c06\u6240\u6709\u8282\u70b9\u53d8\u4e3a\u7236\u8282\u70b9\uff0cdfs\u5e8f\u7684\u76f8\u5bf9\u987a\u5e8f\u6539\u53d8\u662f\u6709\u9650\u7684\uff0c\u56e0\u6b64\u53ef\u4ee5\u7ebf\u6027\u8fdb\u884c\u8fd9\u6837\u7684\u64cd\u4f5c\u3002\u4e0b\u9762\u662f\u5c06\u4e00\u4e2a\u8fd9\u6837\u7684vector\u5168\u90e8\u53d8\u4e3a\u5176\u7236\u8282\u70b9\u7684\u51fd\u6570\u7684\u7ebf\u6027\u5b9e\u73b0\uff1a<\/p>\n\n\n\n

vector<int> cns(vector<int> Fr){\n        sort(all(Fr),cmp);\n        vector<int> nxt;\n        for(auto ct:Fr){\n            if(!nxt.size()){\n                nxt.PB(ct);\n                continue;\n            }\n            if(!subtree(nxt.back(),ct))nxt.PB(ct);\n        }\n        return nxt;\n    }<\/code><\/pre>\n\n\n\n
\u6211\u4f7f\u7528\u7684\u627e\u5230\u7956\u5148\u8282\u70b9\u7684\u65b9\u6cd5\u662f\u500d\u589e\uff0c\u56e0\u6b64\u590d\u6742\u5ea6\u662fn sqrt(n log n)\u7684\uff1f\u5982\u679c\u6539\u6210O(1)\u7684\u65b9\u6cd5\uff0c\u53ef\u80fd\u53ef\u4ee5\u8fbe\u5230n sqrt n\uff0c\u4f46\u662f\u6211\u6ca1\u8bd5\u8fc7\u3002<\/p>\n\n\n\n
\u9898\u89e3\u7ed9\u51fa\u7684\u505a\u6cd5\u5982\u4e0b\uff0c\u548c\u6211\u7684\u505a\u6cd5\u5e76\u4e0d\u76f8\u540c\uff0c\u590d\u6742\u5ea6\u597d\u50cf\u548c\u6211\u5dee\u4e0d\u591a\u3002<\/p>\n\n\n\n
\u9996\u5148\u6211\u4eec\u56de\u987e\u4e00\u4e0b\u4e00\u4e2a\u4e8b\u5b9e\uff0c\u5c31\u662f\u5982\u679c\u6211\u4eec\u6bcf\u6b21\u5220\u9664\u5f53\u524d\u6811\u4e0a\u6240\u6709\u5ea6\u6570\u4e3a1\u7684\u70b9\uff0c\u90a3\u4e48\u7ecf\u8fc7O(T)\u8f6e\u4e4b \u540e\uff0c\u6811\u4e0a\u7684\u5ea6\u6570\u4e3a1\u7684\u70b9\u4e0d\u4f1a\u8d85\u8fc7O(n\/ T) \u4e2a\uff0c\u6211\u4eec\u8bb0\u8fd9\u4e9b\u70b9\u4e3a\u5173\u952e\u70b9\uff0c\u90a3\u4e48\u53ef\u4ee5\u53d1\u73b0\uff0c\u5982\u679c\u4e00\u4e2a\u70b9\u5f80\u4e0a \u8df3\u4e86O(T)\u8f6e\uff0c\u90a3\u4e48\u4e00\u5b9a\u5728\u67d0\u4e2a\u5173\u952e\u70b9\u4e4b\u4e0a\uff0c\u800c\u4e00\u4e2a\u5173\u952e\u70b9\u4e4b\u4e0a\u7684\u70b9\u5728\u4e00\u6761\u94fe\u4e0a\uff0c\u90a3\u4e48\u6700\u6d45\u70b9\u5f88\u5bb9\u6613\u7ef4 \u62a4\u3002
\u6240\u4ee5\u7b97\u6cd5\u5927\u81f4\u4e0a\u662f\u8fd9\u6837\u7684\uff0c\u9996\u5148\u6bcf\u4e2a\u70b9\u5230\u5173\u952e\u70b9\u4e4b\u524d\u7684\u8fd9\u4e00\u6bb5\uff0c\u6211\u4eec\u66b4\u529b\u8df3\u3002\u4e4b\u540e\u6211\u4eec\u5bf9\u4e8e\u6bcf\u4e2a\u5173\u952e\u70b9 \u5206\u522b\u6700\u6d45\u7684\u70b9\uff0c\u7b49\u4ef7\u4e8e\u533a\u95f4\u51cf\uff0c\u533a\u95f4\u6700\u5c0f\u503c\u3002
\u524d\u9762\u90e8\u5206\u9700\u8981\u505aO(nT) \u6b21\u5355\u70b9\u4fee\u6539\uff0cO(n)\u6b21\u533a\u95f4\u67e5\u8be2\uff0c\u800c\u540e\u9762\u90e8\u5206\u9700\u8981\u505aO \"\left(n^{2} / T\right)\" \u6b21\u4fee\u6539\u548c\u67e5\u8be2\uff0c\u8fd9 \u91cc\u6211\u4eec\u5047\u8bbe \"n, q\" \u540c\u9636\u3002\u524d\u9762\u90e8\u5206\u53ef\u4ee5\u7528\u5206\u5757\u5c06\u590d\u6742\u5ea6\u5e73\u8861\u6210\u4e3a \"O(n T)+O\left(n^{1.5}\right),\" \u540e\u9762\u90e8\u5206\u65f6\u95f4\u590d\u6742\u5ea6 \u4e3a \"O\left(n^{2} \log n / T\right),\" \u6240\u4ee5\u603b\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \"O(n \sqrt{n \log n})\"<\/p>\n\n\n\n
\u4ee3\u7801\u5982\u4e0b\u3002<\/p>\n\n\n\n
#include <bits\/stdc++.h>\nusing namespace std;\n\ntemplate <typename A, typename B>string to_string(pair<A, B> p);template <typename A, typename B, typename C>string to_string(tuple<A, B, C> p);template <typename A, typename B, typename C, typename D>string to_string(tuple<A, B, C, D> p);string to_string(const string& s) {  return '\"' + s + '\"';}string to_string(const char* s) {  return to_string((string) s);}string to_string(bool b) {  return (b ? \"true\" : \"false\");}string to_string(vector<bool> v) {  bool first = true;  string res = \"{\";  for (int i = 0; i < static_cast<int>(v.size()); i++) {    if (!first) {      res += \", \";    }    first = false;    res += to_string(v[i]);  }  res += \"}\";  return res;}template <size_t N>string to_string(bitset<N> v) {  string res = \"\";  for (size_t i = 0; i < N; i++) {    res += static_cast<char>('0' + v[i]);  }  return res;}template <typename A>string to_string(A v) {  bool first = true;  string res = \"{\";  for (const auto &x : v) {    if (!first) {      res += \", \";    }    first = false;    res += to_string(x);  }  res += \"}\";  return res;}template <typename A, typename B>string to_string(pair<A, B> p) {  return \"(\" + to_string(p.first) + \", \" + to_string(p.second) + \")\";}template <typename A, typename B, typename C>string to_string(tuple<A, B, C> p) {  return \"(\" + to_string(get<0>(p)) + \", \" + to_string(get<1>(p)) + \", \" + to_string(get<2>(p)) + \")\";}template <typename A, typename B, typename C, typename D>string to_string(tuple<A, B, C, D> p) {  return \"(\" + to_string(get<0>(p)) + \", \" + to_string(get<1>(p)) + \", \" + to_string(get<2>(p)) + \", \" + to_string(get<3>(p)) + \")\";}void debug_out() { cerr << endl; }template <typename Head, typename... Tail>void debug_out(Head H, Tail... T) {  cerr << \" \" << to_string(H);  debug_out(T...);}\n\n#ifdef LOCAL\n#define debug(...) cerr << \"[\" << #__VA_ARGS__ << \"]:\", debug_out(__VA_ARGS__)\n#else\n#define debug(...) 42\n#endif\n\n#define set0(x) memset(x,0,sizeof(x))\n#define F first\n#define S second\n#define PB push_back\n#define MP make_pair\n#define rep(i, a, b) for(int i = a; i < (b); ++i)\n#define trav(a, x) for(auto& a : x)\n#define all(x) x.begin(), x.end()\n#define sz(x) (int)(x).size()\n\ntypedef long long ll;\ntypedef pair<int,int> pii;\ntypedef pair<ll,ll> pll;\ntemplate<typename T> void read(T &x){\n    x = 0;char ch = getchar();ll f = 1;\n    while(!isdigit(ch)){if(ch == '-')f*=-1;ch=getchar();}\n    while(isdigit(ch)){x = x*10+ch-48;ch=getchar();}x*=f;\n}\ntemplate<typename T, typename... Args> void read(T &first, Args& ... args) {\n    read(first);\n    read(args...);\n}\n\nint T,n,m,rt,u,v,d,opt,l,r;\nint val[450020],dfn[450020],sz[450020],d1[450020],ff[450020][20];\nll d2[450020];\n\nvector<pii> G[450020];\n\nint tim;\nvoid dfs(int num,int fa = -1){\n    ff[num][0] = fa;if(fa == -1)ff[num][0] = num;\n    for(int i=1;i<20;i++) ff[num][i] = ff[ff[num][i-1]][i-1];\n    tim+=1;\n    sz[num] = 1;\n    dfn[num] = tim;\n    for(auto ct:G[num]){\n        if(ct.F == fa)continue;\n        d1[ct.F] = d1[num]+1;\n        d2[ct.F] = d2[num]+ct.S;\n        dfs(ct.F,num);\n        sz[num]+=sz[ct.F];\n    }\n}\ninline bool subtree(int a,int b){\n    return dfn[b]<dfn[a]+sz[a] && dfn[b]>=dfn[a];\n}\nbool cmp(int a,int b){\n    return dfn[a]<dfn[b];\n}\nstruct block{\n    int l = 1e9,r = -1,up = 0,changed = 1;\n    ll cache = 0;\n    vector<int> A,sig;\n    vector<int> cns(vector<int> Fr){\n        sort(all(Fr),cmp);\n        vector<int> nxt;\n        for(auto ct:Fr){\n            if(!nxt.size()){\n                nxt.PB(ct);\n                continue;\n            }\n            if(!subtree(nxt.back(),ct))nxt.PB(ct);\n        }\n        return nxt;\n    }\n    void construct(){\n        sig = cns(A);\n    }\n    void solve1(int opl,int opr){\n        if(opr<l || opl>r)return;\n        changed = 1;\n        if(opl<=l && r<=opr){\n            vector<int> nxt;\n            for(auto ct:sig){\n                int cc = ff[ct][0];\n                if(!nxt.size()){\n                    nxt.PB(cc);\n                    continue;\n                }\n                if(subtree(nxt.back(),cc))continue;\n                while(nxt.size() && subtree(cc,nxt.back()))nxt.pop_back();\n                nxt.PB(cc);\n            }\n            sig = nxt;\n            up+=1;\n        }else{\n            if(up){\n                for(int i=0;i<18;i++){\n                    if((up>>i)&1){\n                        for(int j=0;j<A.size();j++)A[j] = ff[A[j]][i];\n                    }\n                }\n                up = 0;\n            }\n            for(int i= max(opl,l);i<=min(opr,r);i++){\n                A[i-l] = ff[A[i-l]][0];\n            }\n            construct();\n        }\n    }\n    ll solve2(int opl,int opr){\n        ll ans = 1e18;\n        if(opr<l || opl>r)return ans;\n        if(opl<=l && r<=opr){\n            if(!changed)return cache;\n            for(auto ct:sig)ans = min(ans,d2[ct]);\n            cache = ans;\n            changed = 0;\n        }else{\n            for(int i=0;i<18;i++){\n                if((up>>i)&1){\n                    for(int j=0;j<A.size();j++)A[j] = ff[A[j]][i];\n                }\n            }\n            up = 0;\n            for(int i= max(opl,l);i<=min(opr,r);i++){\n                ans = min(ans,d2[A[i-l]]);\n            }\n        }\n        return ans;\n    }\n};\n\nint main() {\n    read(T);\n    while(T--){\n        tim = 1;\n        read(n,m,rt);\n        d2[rt] = d1[rt] = 0;\n        for(int i=0;i<n-1;i++){\n            read(u,v,d);\n            G[u].PB(MP(v,d));\n            G[v].PB(MP(u,d));\n        }\n        vector<block> blocks(1010);\n        for(int i=1;i<=n;i++){\n            read(val[i]);\n            blocks[i\/300].r = max(blocks[i\/300].r,i);\n            blocks[i\/300].l = min(blocks[i\/300].l,i);\n            blocks[i\/300].A.PB(val[i]);\n        }\n        dfs(rt);\n        for(auto &ct:blocks)ct.construct();\n        for(int i=1;i<=m;i++){\n            read(opt,l,r);\n            if(opt == 1){\n                for(int j=l\/300;j<=r\/300;j++)blocks[j].solve1(l,r);\n            }else{\n                ll ans = 1e18;\n                for(int j=l\/300;j<=r\/300;j++)ans = min(ans,blocks[j].solve2(l,r));\n                cout<<ans<<\"\\n\";\n            }\n        }\n        for(int i=0;i<n+10;i++){\n            G[i].clear();\n        }\n    }\n    return 0;\n}<\/code><\/pre>\n ","protected":false},"excerpt":{"rendered":"
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