{"id":236,"date":"2026-07-28T00:20:59","date_gmt":"2026-07-27T16:20:59","guid":{"rendered":"https:\/\/huxiaole.cloud\/?p=236"},"modified":"2026-07-31T16:08:41","modified_gmt":"2026-07-31T08:08:41","slug":"d-substring","status":"publish","type":"post","link":"https:\/\/huxiaole.cloud\/index.php\/2026\/07\/28\/d-substring\/","title":{"rendered":"D. Substring"},"content":{"rendered":"\n

D. Substring<\/h1>\n\n\n\n

\u9898\u76ee\u63cf\u8ff0<\/h2>\n\n\n\n

\u7ed9\u5b9a\u4e00\u4e2a\u5305\u542b n \u4e2a\u8282\u70b9\u548c m \u6761\u6709\u5411\u8fb9\u7684\u56fe\uff0c\u6bcf\u4e2a\u8282\u70b9\u4e0a\u90fd\u6709\u4e00\u4e2a\u5c0f\u5199\u82f1\u6587\u5b57\u6bcd\u3002<\/p>\n\n\n\n

\u6211\u4eec\u5b9a\u4e49\u4e00\u6761\u8def\u5f84\u7684\u4ef7\u503c\u4e3a\uff1a\u8be5\u8def\u5f84\u4e0a\u51fa\u73b0\u6b21\u6570\u6700\u591a\u7684\u5b57\u6bcd\u7684\u51fa\u73b0\u6b21\u6570\u3002<\/p>\n\n\n\n

\u4f8b\u5982\uff0c\u4e00\u6761\u8def\u5f84\u4e0a\u7684\u5b57\u6bcd\u4f9d\u6b21\u4e3a abaca<\/code>\uff0c\u5176\u4e2d\u5b57\u6bcd a<\/code> \u51fa\u73b0\u4e86 3 \u6b21\uff0c\u56e0\u6b64\u8fd9\u6761\u8def\u5f84\u7684\u4ef7\u503c\u4e3a 3\u3002<\/p>\n\n\n\n

\u8bf7\u4f60\u6c42\u51fa\u4ef7\u503c\u6700\u5927\u7684\u8def\u5f84\u3002<\/p>\n\n\n\n

\u5982\u679c\u7b54\u6848\u53ef\u4ee5\u65e0\u9650\u5927\uff0c\u5219\u8f93\u51fa -1<\/code>\u3002<\/p>\n\n\n\n

\n\n\n\n

\u8f93\u5165\u683c\u5f0f<\/h2>\n\n\n\n

\u7b2c\u4e00\u884c\u5305\u542b\u4e24\u4e2a\u6b63\u6574\u6570 n,m\uff1a<\/p>\n\n\n\n

$1\\le n,m\\le 300000$<\/p>\n\n\n\n

\u5206\u522b\u8868\u793a\u56fe\u4e2d\u7684\u8282\u70b9\u6570\u91cf\u548c\u6709\u5411\u8fb9\u6570\u91cf\u3002<\/p>\n\n\n\n

\u7b2c\u4e8c\u884c\u5305\u542b\u4e00\u4e2a\u957f\u5ea6\u4e3a n \u7684\u5b57\u7b26\u4e32 s\uff0c\u5176\u4e2d\u53ea\u5305\u542b\u5c0f\u5199\u82f1\u6587\u5b57\u6bcd\u3002\u5b57\u7b26\u4e32\u4e2d\u7684\u7b2c i \u4e2a\u5b57\u7b26\u8868\u793a\u7b2c i \u4e2a\u8282\u70b9\u4e0a\u7684\u5b57\u6bcd\u3002<\/p>\n\n\n\n

\u63a5\u4e0b\u6765 m \u884c\uff0c\u6bcf\u884c\u5305\u542b\u4e24\u4e2a\u6574\u6570 x,y\uff1a<\/p>\n\n\n\n

$1\\le x,y\\le n$<\/p>\n\n\n\n

\u8868\u793a\u5b58\u5728\u4e00\u6761\u4ece\u8282\u70b9 x \u6307\u5411\u8282\u70b9 y \u7684\u6709\u5411\u8fb9\u3002<\/p>\n\n\n\n

\u9700\u8981\u6ce8\u610f\uff1a<\/p>\n\n\n\n

    \n
  • x \u53ef\u4ee5\u7b49\u4e8e y\uff0c\u5373\u56fe\u4e2d\u53ef\u80fd\u5b58\u5728\u81ea\u73af\uff1b<\/li>\n\n\n\n
  • \u8282\u70b9 x \u548c\u8282\u70b9 y \u4e4b\u95f4\u53ef\u80fd\u5b58\u5728\u591a\u6761\u76f8\u540c\u7684\u8fb9\uff1b<\/li>\n\n\n\n
  • \u6574\u5f20\u56fe\u4e0d\u4e00\u5b9a\u8fde\u901a\u3002<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    \u8f93\u51fa\u683c\u5f0f<\/h2>\n\n\n\n

    \u8f93\u51fa\u4e00\u4e2a\u6574\u6570\uff0c\u8868\u793a\u6240\u6709\u8def\u5f84\u4e2d\u7684\u6700\u5927\u4ef7\u503c\u3002<\/p>\n\n\n\n

    \u5982\u679c\u8def\u5f84\u7684\u4ef7\u503c\u53ef\u4ee5\u65e0\u9650\u589e\u5927\uff0c\u5219\u8f93\u51fa\uff1a<\/p>\n\n\n\n

    -1\n<\/code><\/pre>\n\n\n\n
    \n\n\n\n
    \u6837\u4f8b #1<\/h2>\n\n\n\n
    \u8f93\u5165<\/h3>\n\n\n\n
    5 4\nabaca\n1 2\n1 3\n3 4\n4 5\n<\/code><\/pre>\n\n\n\n
    \u8f93\u51fa<\/h3>\n\n\n\n
    3\n<\/code><\/pre>\n\n\n\n
    \u8bf4\u660e<\/h3>\n\n\n\n
    \u4ef7\u503c\u6700\u5927\u7684\u8def\u5f84\u4e3a\uff1a<\/p>\n\n\n\n
    $1\\rightarrow3\\rightarrow4\\rightarrow5$<\/p>\n\n\n\n
    \u8fd9\u6761\u8def\u5f84\u4e0a\u7684\u5b57\u6bcd\u4f9d\u6b21\u4e3a aaca<\/code>\uff0c\u5176\u4e2d\u5b57\u6bcd a<\/code> \u51fa\u73b0\u4e86 3 \u6b21\uff0c\u56e0\u6b64\u8def\u5f84\u7684\u4ef7\u503c\u4e3a 3\u3002<\/p>\n\n\n\n
    \n\n\n\n
    \u6837\u4f8b #2<\/h2>\n\n\n\n
    \u8f93\u5165<\/h3>\n\n\n\n
    6 6\nxzyabc\n1 2\n3 1\n2 3\n5 4\n4 3\n6 4\n<\/code><\/pre>\n\n\n\n
    \u8f93\u51fa<\/h3>\n\n\n\n
    -1\n<\/code><\/pre>\n\n\n\n
    \n\n\n\n
    \u6837\u4f8b #3<\/h2>\n\n\n\n
    \u8f93\u5165<\/h3>\n\n\n\n
    10 14\nxzyzyzyzqx\n1 2\n2 4\n3 5\n4 5\n2 6\n6 8\n6 5\n2 10\n3 9\n10 9\n4 6\n1 10\n2 8\n3 7\n<\/code><\/pre>\n\n\n\n
    \u8f93\u51fa<\/h3>\n\n\n\n
    4\n<\/code><\/pre>\n\n\n\n
    \n\n\n\n
    \u6570\u636e\u8303\u56f4<\/h2>\n\n\n\n
    $1\\le n,m\\le 300000$
    \u65f6\u95f4\u9650\u5236\uff1a$3$ \u79d2\u3002
    \u7a7a\u95f4\u9650\u5236\uff1a$256\\ \\text{MB}$\u3002<\/p>\n\n\n\n
    \u601d\u8def<\/h2>\n\n\n\n
    \u8fd9\u662f\u4e00\u9053dp+\u56fe\u8bba\u7684\u9898
    \u5982\u679c\u56fe\u4e2d\u5b58\u5728\u6709\u5411\u73af\uff0c\u5c31\u53ef\u4ee5\u6cbf\u7740\u73af\u79fb\u52a8\uff0c\u7531\u4e8e\u73af\u4e0a\u81f3\u5c11\u6709\u4e00\u4e2a\u5b57\u6bcd\uff0c\u6240\u4ee5\u8fd9\u4e2a\u5b57\u6bcd\u51fa\u73b0\u7684\u6b21\u6570\u53ef\u4ee5\u65e0\u9650\u589e\u52a0\uff0c\u7b54\u6848\u4e3a-1\u3002
    \u5b9a\u4e49
    dp[c][u]
    dp\u4e00\u7ef4\u662f\u4ee3\u886826\u4e2a\u82f1\u6587\u5b57\u6bcd\uff0c\u4e8c\u7ef4\u662f\u6bcf\u4e2a\u8282\u70b9<\/p>\n\n\n\n
    \u9996\u5148\u52a0\u5165\u5165\u5ea6\u4e3a0\u7684\u8282\u70b9\u5c31\u662f\u62d3\u6251\u8d77\u70b9\uff0c\u7136\u540e\u4ece\u6839\u8282\u70b9\u5f00\u59cb\u5411\u4e0bdp\uff0c\u5148\u8f6c\u79fb\u72b6\u6001\uff0c\u7136\u540e\u4e0b\u4e00\u4e2a\u8282\u70b9\u8981\u52a0\u4e0a\u8fd9\u4e2a\u8282\u70b9\u4e0a\u9762\u7684\u5b57\u6bcd
    \u72b6\u6001\u8f6c\u79fb\u65b9\u7a0bdp[c][v]=max(dp[c][v],dp[c][u]+[sv\u200b=c])
    \u5982\u679c\u8fd9\u4e2a\u8282\u70b9\u51fa\u961f\u5e76\u4e14\u5b8c\u6210\u5904\u7406\uff0c\u5c31\u8981\u52a0\u5165cnt\uff0c\u5982\u679ccnt!=n\uff0c\u90a3\u4e48\u5c31\u8bf4\u660e\u6709\u73af\uff0c\u4e5f\u5c31\u8f93\u51fa-1\uff0c\u5426\u5219\u8f93\u51faans\u7edf\u8ba1\u6700\u5927\u7684\u91cd\u590d\u5b57\u6bcd\u3002<\/p>\n\n\n\n
    \u4ee3\u7801<\/h2>\n\n\n\n
    \/\/Sunshine sunshine ladybugs awake,  \n\/\/Clap your hooves and do a little shack.  \n#include<bits\/stdc++.h>  \n#define int long long  \n#define endl \"\\n\"  \n  \nusing namespace std;  \n  \nusing PII=pair<int,int> ;  \nconst int MAXN=300005;  \nconst int mod=998244353;  \nconst int INF=0x3f3f3f3f3f3f3f3f;  \n  \nvector<int> adj[MAXN];  \nvector<int> deg(MAXN,0);  \nint dp[26][MAXN];  \nstring s;  \n  \nvoid solve(){  \n    int n,m;  \n    cin>>n>>m;  \n    cin>>s;  \n    for(int i=0;i<m;i++){  \n        int u,v;  \n        cin>>u>>v;  \n        adj[u].push_back(v);  \n        deg[v]++;  \n    }  \n    \n    int cnt=0;  \n    int ans=0;  \n    queue<int> q;  \n    for(int u=1;u<=n;u++){  \n        dp[s[u-1]-'a'][u]=1;  \n                if(deg[u]==0){  \n            q.push(u);  \n        }  \n    }  \n        while(!q.empty()){  \n        int u=q.front();  \n        q.pop();  \n        cnt++;  \n        for(int c=0;c<26;c++){  \n            ans=max(ans,dp[c][u]);  \n        }  \n        for(auto v:adj[u]){  \n            for(int c=0;c<26;c++){  \n                    dp[c][v]=max(  \n                    dp[c][v],  \n                    dp[c][u]+(s[v-1]-'a'==c)  \n                );  \n            }  \n            deg[v]--;  \n            if(deg[v]==0)q.push(v);  \n        }  \n    }  \n    \n     if(cnt<n){  \n        cout<<-1<<endl;  \n    }else{  \n        cout<<ans<<endl;  \n    }  \n}  \n  \nsigned main() {  \n    ios::sync_with_stdio(false);  \n    cin.tie(nullptr);  \n    \/\/int t;cin>>t;while(t--)  \n    solve();  \n    return 0;  \n}\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
    D. Substring \u9898\u76ee\u63cf\u8ff0 \u7ed9\u5b9a\u4e00\u4e2a\u5305\u542b n \u4e2a\u8282\u70b9\u548c m \u6761\u6709\u5411\u8fb9\u7684\u56fe\uff0c\u6bcf\u4e2a\u8282\u70b9\u4e0a\u90fd\u6709\u4e00\u4e2a\u5c0f\u5199\u82f1\u6587\u5b57 […]<\/p>\n","protected":false},"author":1,"featured_media":92,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20,17,12],"tags":[],"class_list":["post-236","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-codeforces","category-dp","category-12"],"_links":{"self":[{"href":"https:\/\/huxiaole.cloud\/index.php\/wp-json\/wp\/v2\/posts\/236","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/huxiaole.cloud\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/huxiaole.cloud\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/huxiaole.cloud\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/huxiaole.cloud\/index.php\/wp-json\/wp\/v2\/comments?post=236"}],"version-history":[{"count":1,"href":"https:\/\/huxiaole.cloud\/index.php\/wp-json\/wp\/v2\/posts\/236\/revisions"}],"predecessor-version":[{"id":237,"href":"https:\/\/huxiaole.cloud\/index.php\/wp-json\/wp\/v2\/posts\/236\/revisions\/237"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/huxiaole.cloud\/index.php\/wp-json\/wp\/v2\/media\/92"}],"wp:attachment":[{"href":"https:\/\/huxiaole.cloud\/index.php\/wp-json\/wp\/v2\/media?parent=236"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/huxiaole.cloud\/index.php\/wp-json\/wp\/v2\/categories?post=236"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/huxiaole.cloud\/index.php\/wp-json\/wp\/v2\/tags?post=236"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}