{"id":146,"date":"2020-11-19T04:49:00","date_gmt":"2020-11-19T04:49:00","guid":{"rendered":"https:\/\/imwarming.com\/?p=146"},"modified":"2020-11-19T04:49:00","modified_gmt":"2020-11-19T04:49:00","slug":"%e5%b9%b6%e6%9f%a5%e9%9b%86","status":"publish","type":"post","link":"https:\/\/imwarming.com\/?p=146","title":{"rendered":"\u5e76\u67e5\u96c6"},"content":{"rendered":"

\u5e76\u67e5\u96c6\u5c31\u662f\u7ed9\u4f60\u4e00\u4e2a\u56fe\uff0c\u91cc\u9762\u6709\u5f88\u591a\u70b9\uff0c\u5e76\u5c31\u662f\u628a\u70b9\u5408\u5e76\u4e00\u4e2a\u96c6\u5408\uff0c\u628aa\u70b9\u641e\u4e3ab\u70b9\u7236\u4eb2\uff1b\u67e5\u5c31\u662f\u67e5\u70b9\u5728\u54ea\u4e2a\u96c6\u5408\uff0c\u67e5a\u70b9\u7684\u7236\u4eb2\u7956\u5148\u662f\u8c01\u3002<\/p>\n

\u521d\u59cb\u5316\u70b9\u7684\u7236\u4eb2\u662f\u81ea\u5df1<\/p>\n

\n
int<\/span> find(int<\/span> x){\n    <\/span>if<\/span>(father[x] != x)\/\/<\/span>\u5982\u679c\u7236\u4eb2\u4e0d\u662f\u81ea\u5df1\uff0c\u90a3\u5c31\u9012\u5f52\u627e\u7236\u4eb2<\/span>\n        father[x] = find(father[x]);\/\/<\/span>\u627e\u4ed6\u7236\u4eb2\u65f6\u628a\u5176\u513f\u5b50\u4e5f\u8fde\u4e0a,\u5927\u591a\u6570\u8fd9\u6837\u538b\u7f29\u4e0b\u5c31\u884c\uff0c\u4e5f\u53ef\u4ee5\u5199find(father[x])\u4f46\u6ca1\u538b\u7f29<\/span>\n    return<\/span> father[x];\/\/<\/span>\u627e\u5230\u7236\u4eb2\u8fd4\u56de\u4ed6<\/span>\n}\n\n<\/span>\/\/<\/span>\u67e5\u627e\u9012\u5f52\u6808\u7206\u4e86\u7684\u8bdd\u7528\u8fed\u4ee3<\/span>\nint<\/span> find(int<\/span> x){\n    <\/span>int<\/span> y = x;\n    <\/span>while<\/span>(father[y] != y){\n        y <\/span>= father[y];\/\/<\/span>\u628a\u539fx\u7684\u7238\u7238\u8d4b\u503c\u7ed9y\uff0c\u518d\u56de\u68c0\u67e5y\u7684\u7238\u7238\u662f\u5426\u7b49\u4e8ey<\/span>\n    }\n    <\/span>\/\/<\/span>\u538b\u7f29\uff0c\u7238\u7238\u76f4\u63a5\u4e00\u6b65\u5230\u4f4d<\/span>\n    int<\/span> p = x, j;\n    <\/span>while<\/span>(p != y){\/\/<\/span>\u5c31\u662f\u628a\u4ecex\u7684\u7236\u4eb2\u7684\u7236\u4eb2\u7684...\u7684\u7236\u4eb2(\u5982\u679c\u6709)\u5168\u90e8\u76f4\u63a5\u4e00\u6b65\u5230\u7956\u5148\uff0c<\/span>\n        j = father[p];\/\/<\/span>\u4e0d\u7528\u4e00\u6b65\u6b65\u627e<\/span>\n        father[p] = y;\n        p <\/span>= j;\n    }\n    <\/span>return<\/span> y;\n}\n\n<\/span>void<\/span> union(int<\/span> x, int<\/span> y){\n    <\/span>int<\/span> p = find(x);\/\/<\/span>\u627ex\u7236\u4eb2<\/span>\n    int<\/span> q = find(y);\/\/<\/span>\u627ey\u7236\u4eb2<\/span>\n    if<\/span>(p != q){\n        father[p] <\/span>= q;\/\/<\/span>\u5982\u679c\u4e0d\u662f\u540c\u4e00\u4e2a\u7236\u4eb2\uff0c\n        <\/span>\/\/<\/span>\u90a3\u5c31\u628aq\u4f5c\u4e3ap\u7236\u4eb2\uff0cfather[q]=p\u4e5f\u53ef\u4ee5<\/span>\n    }\n}\n\n<\/span>\/\/<\/span>\u542f\u53d1\u5f0f\u5408\u5e76\u4f18\u5316\uff0c\u52a0\u4e2arank\u6570\u7ec4\u521d\u59cb\u5316\u4e3a0\uff0c\u5b58\u4ed6\u67e5\u627e\u7684\u6df1\u5ea6\uff0c\u628a\u6df1\u5ea6\u5c0f\u6302\u5728\u5927\u7684\u4e0a<\/span>\nvoid<\/span> union(int<\/span> x, int<\/span> y, int<\/span> rank[]){\n    <\/span>int<\/span> p = find(x);\n    <\/span>int<\/span> q = find(y);\n    <\/span>if<\/span>(p != q){\n        <\/span>if<\/span>(rank[p] < rank[q]){\n            father[p] <\/span>= q;\/\/<\/span>\u8fd9\u6837\u5c31\u4e0d\u4f1a\u52a0\u6df1\u5ea6<\/span>\n        }\n        <\/span>else<\/span> if<\/span>(rank[p] > rank[q]){\n            father[q] <\/span>= p;\/\/<\/span>\u540c\u4e0a<\/span>\n        }\n        <\/span>else<\/span>{\n            father[q] <\/span>= p;\/\/<\/span>\u968f\u4fbf\u641e\u4e2a\u7236\u4eb2\uff0c\u7236\u4eb2\u6df1\u5ea6\u52a01<\/span>\n            rank[p]++;\n        }\n    }\n}<\/span><\/pre>\n<\/div>\n
\u4f8b\uff1aluogu p1525<\/a>\u5e76\u67e5\u96c6\u65f6\u533a\u5206\u654c\u53cb<\/p>\n
\n
#include<bits\/stdc++.h>\nusing<\/span> namespace<\/span> std;\ntypedef <\/span>long<\/span> long<\/span> ll;\n<\/span>const<\/span> int<\/span> maxn = 2e5 + 5<\/span>;\nll n, m, k, sum;\n<\/span>string<\/span> s;\npriority_queue<\/span><int<\/span>, vector<int<\/span>>, greater<int<\/span>> >q;\n\n<\/span>struct<\/span> node{\n    <\/span>int<\/span> x, y, z;\/\/<\/span>z\u4e3a\u6028\u6c14\u503c<\/span>\n}a[maxn];\n<\/span>int<\/span> f[maxn], b[maxn];\n\n<\/span>void<\/span> initialise(){\/\/<\/span>f\u521d\u59cb\u5316\uff0c\u5404\u81ea\u5728\u81ea\u5df1\u76d1\u72f1<\/span>\n    for<\/span>(int<\/span> i = 0<\/span>; i < maxn; i++){\n        f[i] <\/span>= i;\n    }\n}\n\n<\/span>int<\/span> find(int<\/span> x){\n    <\/span>if<\/span>(f[x] != x){\n        f[x] <\/span>= find(f[x]);\n    }\n    <\/span>return<\/span> f[x];\n}\n\n<\/span>bool<\/span> cmp(node a, node b){\/\/<\/span>sort\u6392\u5e8f<\/span>\n    return<\/span> a.z > b.z;\n}\n\n<\/span>void<\/span> union(int<\/span> x, int<\/span> y){\n    <\/span>int<\/span> p = find(x);\n    <\/span>int<\/span> q = find(y);\n    <\/span>if<\/span>(p != q){\n        f[p] <\/span>= q;\n    }\n}\n\n<\/span>int<\/span> main(){\n    <\/span>\/\/<\/span>ios_base::sync_with_stdio(0);\n    <\/span>\/\/<\/span>cin.tie(); cout.tie();<\/span>\n    cin>>n>>m;\n    initialise();\n    <\/span>for<\/span>(int<\/span> i = 1<\/span>; i <= m; i++)\n        cin<\/span>>>a[i].x>>a[i].y>>a[i].z;\n    sort(a <\/span>+ 1<\/span>, a + m + 1<\/span>, cmp);\/\/<\/span>\u6309\u4ed6\u6028\u6c14\u503c\u5927\u5c0f\u6392\u5e8f\uff0c\u5927\u7684\u5728\u524d<\/span>\n    for<\/span>(int<\/span> i = 1<\/span>; i <= m; i++){\n        <\/span>int<\/span> p = find(a[i].x);\n        <\/span>int<\/span> q = find(a[i].y);\n        <\/span>if<\/span>(p == q){\/\/<\/span>\u5982\u679c\u540c\u4e2a\u76d1\u72f1\uff0c\u76f4\u63a5\u8f93\u51fa\u6028\u6c14\u503c\uff0c\u56e0\u4e3a\u6392\u4e86\u5e8f<\/span>\n            cout<<a[i].z;\n            <\/span>return<\/span> 0<\/span>;\n        }\n        <\/span>\/\/<\/span>\u5982\u679ca[i].x\u6ca1\u6709\u654c\u4eba\uff0c\u628aa[i].y\u8bbe\u4e3a\u4ed6\u654c\u4eba\u4e92\u4e3a\u654c\u4eba\u4e0d\u80fd\u5173\u4e00\u8d77<\/span>\n        if<\/span>(!b[a[i].x]){\n            b[a[i].x] <\/span>= a[i].y;\n        }\n        <\/span>else<\/span>{\/\/<\/span>a[i].x\u6709\u654c\u4eba(\u5c31\u662fb[a[i].x]),\u628a\u4ed6\u654c\u4eba\u548ca[i].y\u5173\u4e00\u8d77\uff0c\u8fd9\u6837\u5173\u4e00\u8d77\u7684\u6028\u6c14\u503c\u80af\u5b9a\u6ca1\u548c\u539f\u5148\u9ad8\uff0c\u56e0\u4e3a\u6392\u4e86\u5e8f<\/span>\n            union(b[a[i].x], a[i].y);\n        }\n        <\/span>if<\/span>(!b[a[i].y]){\/\/<\/span>\u540c\u4e0a<\/span>\n            b[a[i].y] = a[i].x;\n        }\n        <\/span>else<\/span>{\/\/<\/span>\u540c\u4e0a<\/span>\n            union(b[a[i].y], a[i].x);\n        }\n    }\n    cout<\/span><<0<\/span>;\n    <\/span>return<\/span> 0<\/span>;\n}<\/span><\/pre>\n<\/div>\n
\u4f8b\uff1aluogu p2024<\/a>\u540c\u4e0a\u9898\uff0c\u4e0d\u8fc7\u662f3\u4e2a\u7c7b<\/p>\n
\n
#include<bits\/stdc++.h>\nusing<\/span> namespace<\/span> std;\ntypedef <\/span>long<\/span> long<\/span> ll;\n<\/span>const<\/span> int<\/span> maxn = 3e5 + 5<\/span>;\n<\/span>int<\/span> n, m, k, sum;\n<\/span>string<\/span> s;\nqueue<\/span><int<\/span>> q;\n<\/span>int<\/span> f[maxn];\/\/<\/span>\u4e00\u500d\u5b58\u81ea\u5df1\uff0c\u4e24\u500d\u5b58\u670b\u53cb\uff0c\u4e09\u500d\u5b58\u654c\u4eba\uff0c\u5728\u8fd9\u4e00\u500d\u662fa\u7c7b\uff0c2\u500d\u662fb\u7c7b\uff0c3\u500d\u662fc\u7c7b\n<\/span>\/\/<\/span>\u5404\u81ea\u500d\u7684\u5982\u679c\u662f\u540c\u96c6\u5408\uff0c\u8bf4\u660e\u76f8\u4e92\u662f\u654c\u4eba\uff1b\u540c\u500d\u7684\u5728\u540c\u4e00\u96c6\u5408\uff0c\u8bf4\u660e\u662f\u81ea\u5df1\u4eba<\/span>\nvoid<\/span> initialise(){\n    <\/span>for<\/span>(int<\/span> i = 0<\/span>; i < maxn; i++){\n        f[i] <\/span>= i;\n    }\n}\n\n<\/span>int<\/span> find(int<\/span> x){\n    <\/span>if<\/span>(f[x] != x){\n        f[x] <\/span>= find(f[x]);\n    }\n    <\/span>return<\/span> f[x];\n}\n\n<\/span>void<\/span> union(int<\/span> x, int<\/span> y){\n    <\/span>int<\/span> p = find(x);\n    <\/span>int<\/span> q = find(y);\n    <\/span>if<\/span>(p != q){\n        f[p] <\/span>= q;\/\/<\/span>\u8fd9\u662fp\u5403q\u7684\u610f\u601d\uff0c\u4e5f\u53ef\u4ee5f[q]=p,\u770b\u6307\u5411\u7238\u7238\u662f\u54ea\u79cd\u610f\u601d<\/span>\n    }\n}\n\n<\/span>int<\/span> main(){\n    <\/span>\/\/<\/span>ios_base::sync_with_stdio(0);\n    <\/span>\/\/<\/span>cin.tie(); cout.tie();<\/span>\n    initialise();\n    cin<\/span>>>n>>m;\n    <\/span>int<\/span> x, y, z;\n    <\/span>for<\/span>(int<\/span> i = 1<\/span>; i <= m; i++){\n        cin<\/span>>>z>>x>>y;\n        <\/span>if<\/span>(x > n || y > n){\/\/<\/span>\u4f9d\u9898\u610f\uff0c\u5047\u8bdd<\/span>\n            sum++;continue<\/span>;\n        }\n        <\/span>if<\/span>(z == 1<\/span>){\/\/<\/span>\u540c\u7c7b\u7684\u8bdd\uff0c\u627e\u4e00\u500d\u7684x\u548c\u57282\u500d\u7684y\uff0c\u548c\u4e00\u500dx\u548c\u4e09\u500dy\u662f\u4e0d\u662f\u540c\u96c6\u5408\uff0c\u540c\u96c6\u5408\u90a3\u5c31\u4e0d\u662f\u540c\u7c7b<\/span>\n            if<\/span>(find(x) == find(y + n) || find(x) == find(y + n + n)){\n                sum<\/span>++;continue<\/span>;\n            }\n            <\/span>\/\/<\/span>\u4e0d\u7b26\u5408\u4e0a\u9762\u7684\u60c5\u51b5\u8bf4\u660e\u662f\u771f\u8bdd\uff0c\u90a3\u628a\u5404\u81ea\u540c\u500d(\u4e5f\u5c31\u662f\u5404\u81ea\u7c7b)\u7684\u5408\u5e76\u4e00\u8d77<\/span>\n            union(x, y);\n            union(x <\/span>+ n, y + n);\n            union(x <\/span>+ n + n, y + n + n);\n        }\n        <\/span>else<\/span> if<\/span>(z == 2<\/span>){\/\/<\/span>x\u5403y\uff0c\u90a3\u5224\u65ad\u4e0b\u540c\u500dxy\u5728\u4e0d\u5728\u540c\u96c6\u5408\uff0c\u662f\u7684\u8bdd\u5c31\u5047\u8bdd\uff1b\u8fd8\u5224\u65ad\u662f\u4e0d\u662fy\u5403x\uff0c\u627e\u4e09\u500dy\u548c\u4e00\u500dx\u5728\u4e0d\u5728\u540c\u96c6\u5408\uff0c\u5728\u5c31\u662fy\u5403x<\/span>\n            if<\/span>(find(x) == find(y) || find(x) == find(y + n + n)){\n                sum<\/span>++;continue<\/span>;\n            }\n            <\/span>\/\/<\/span>\u4e0d\u7b26\u5408\u4e0a\u9762\u7684\u8bdd\u4ee3\u8868\u662f\u771f\u8bdd<\/span>\n            union(x + n + n, y);\/\/<\/span>c\u7c7bx\u5403a\u7c7b\u7684y(\u4e5f\u5c31\u662f\u4e09\u500d\u7684x\u5403\u4e00\u500d\u7684y)<\/span>\n            union(x, y + n);\/\/<\/span>a\u7c7bx\u5403b\u7c7by(\u4e5f\u5c31\u662f\u4e00\u500d\u7684x\u5403\u4e8c\u500d\u7684y)<\/span>\n            union(x + n, y + n + n);\/\/<\/span>b\u7c7bx\u5403c(\u4e5f\u5c31\u662f\u4e8c\u500d\u7684x\u5403\u4e09\u500d\u7684y)<\/span>\n        }\n    }\n    cout<\/span><<sum;\n    <\/span>return<\/span> 0<\/span>;\n}<\/span><\/pre>\n<\/div>\n
\u4f8b\uff1aluogu p1196<\/a>\u5e76\u67e5\u96c6\u65f6\u517c\u987e\u7ef4\u62a4<\/p>\n
\n
#include<bits\/stdc++.h>\nusing<\/span> namespace<\/span> std;\ntypedef <\/span>long<\/span> long<\/span> ll;\n<\/span>const<\/span> int<\/span> maxn = 3e4 + 5<\/span>;\nll n, m, k, sum;\n<\/span>string<\/span> s, r;\n<\/span>int<\/span> num[maxn], dis[maxn], f[maxn];\n<\/span>\/\/<\/span>num\u662f\u662f\u8be5\u6570\u5b57\u5728\u7ec4\u7684\u6210\u5458\u6570\u91cf\uff0cdis\u662f\u8be5\u6570\u79bb\u4ed6\u7ec4\u7ec4\u5934\u7684\u8ddd\u79bb<\/span>\nint<\/span> find(int<\/span> x){\n    <\/span>if<\/span>(f[x] != x){\n        <\/span>int<\/span> r = f[x];\n        f[x] <\/span>= find(f[x]);\n        dis[x] <\/span>+= dis[r];\/\/<\/span>\u5982\u679cx\u6709\u7236\u4eb2\uff0c\u5c31\u662f\u548c\u4ed6\u7236\u4eb2\u5728\u540c\u5217\uff0c\u90a3x\u5230\u961f\u5934\u7684\u8ddd\u79bb\u4e5f\u5c31\u53d8\u957f\u4e86\u6b64\u65f6dis[x]\u53ea\u4ee3\u8868\u5230\u4ed6\u7236\u4eb2\u8ddd\u79bb\uff0c\u8981\u52a0\u4e0a\u4ed6\u7236\u4eb2\u5230\u961f\u5934\u8ddd\u79bb<\/span>\n        num[x] = num[f[x]];\/\/<\/span>x\u6240\u5728\u5217\u7684\u6570\u91cf\u4e5f\u5c31\u662f\u4ed6\u7236\u4eb2\u6240\u5728\u5217\u7684\u6570\u91cf<\/span>\n    }\n    <\/span>return<\/span> f[x];\n}\n\n<\/span>void<\/span> union(int<\/span> x, int<\/span> y){\n    <\/span>int<\/span> p = find(x);\n    <\/span>int<\/span> q = find(y);\n    <\/span>if<\/span>(p != q){\n        f[p] <\/span>= q;\/\/<\/span>p\u7236\u4eb2\u662fq\uff0cp\u6240\u5728\u5217\u79fb\u52a8\u5230q\u6240\u5728\u5217<\/span>\n        dis[p] = dis[q] + num[q];\/\/<\/span>\u5408\u5e76\u8981\u79fb\u52a8\u5217\uff0cp\u5230\u961f\u5934\u8ddd\u79bb\u589e\u52a0\u5230\u539fq\u5230\u961f\u5934\u8ddd\u79bb\u52a0\u4e0aq\u6240\u5728\u5217\u7684\u539f\u6210\u5458\u6570\u91cf<\/span>\n        num[q] += num[p];\/\/<\/span>q\u6240\u5728\u5217\u6570\u91cf\u8981\u52a0\u4e0ap\u6240\u5728\u5217\u6570\u91cf<\/span>\n        num[p] = num[q];\/\/<\/span>p\u6240\u5728\u5217\u7684\u6570\u91cf\u548c\u4ed6\u7236\u4eb2\u6240\u5728\u5217\u6570\u91cf\u4e00\u6837<\/span>\n    }\n}\n\n<\/span>void<\/span> query(int<\/span> x, int<\/span> y){\n    <\/span>int<\/span> q = find(x);\n    <\/span>int<\/span> p = find(y);\n    <\/span>if<\/span>(q != p){\n        cout<\/span><<-1<\/span><<endl;\n    }\n    <\/span>else<\/span>{\/\/<\/span>\u8f93\u51fa\u4ed6\u4fe9\u4e4b\u95f4\u8ddd\u79bb\uff0c\u8bb0\u7740\u8981\u51cf\u4e00<\/span>\n        cout<<abs(dis[x] - dis[y]) - 1<\/span><<endl;\n    }\n}\n\n<\/span>int<\/span> main(){\n    <\/span>\/\/<\/span>ios_base::sync_with_stdio(0);\n    <\/span>\/\/<\/span>cin.tie(); cout.tie();<\/span>\n    for<\/span>(int<\/span> i = 1<\/span>; i <= maxn; i++)\n        f[i] <\/span>= i, num[i] = 1<\/span>;\n    cin<\/span>>>n;\n    <\/span>char<\/span> c;\n    <\/span>while<\/span>(n--){\n        cin<\/span>>>c>>m>>k;\n        <\/span>if<\/span>(c == '<\/span>m<\/span>'<\/span>){\n            union(m, k);\n        }\n        <\/span>else<\/span>{\n            query(m, k);\n        }\n    }\n    <\/span>return<\/span> 0<\/span>;\n}<\/span><\/pre>\n<\/div>\n
\u4f8b\uff1aluogu p2256<\/a>\u7528map\u5b57\u7b26\u4e32\u6620\u5c04<\/p>\n
\n
#include<bits\/stdc++.h>\nusing<\/span> namespace<\/span> std;\ntypedef <\/span>long<\/span> long<\/span> ll;\n<\/span>const<\/span> int<\/span> maxn = 2e5 + 5<\/span>;\nll n, m, k, sum;\n<\/span>string<\/span> s, r;\npriority_queue<\/span><int<\/span>, vector<int<\/span>>, greater<int<\/span>> >q;\nmap<\/span><string<\/span>, string<\/span>>ma;\n<\/span>string<\/span> f[maxn], a[maxn];\n<\/span>void<\/span> initialise(){\n    <\/span>for<\/span>(int<\/span> i = 0<\/span>; i < maxn; i++){\n        ma[a[i]] <\/span>= a[i];\n    }\n}\n\n<\/span>string<\/span> find(string<\/span> x){\n    <\/span>if<\/span>(ma[x] != x){\n        ma[x] <\/span>= find(ma[x]);\n    }\n    <\/span>return<\/span> ma[x];\n}\n\n<\/span>void<\/span> union(string<\/span> x, string<\/span> y){\n    <\/span>string<\/span> p = find(x);\n    <\/span>string<\/span> q = find(y);\n    <\/span>if<\/span>(p != q){\n        ma[p] <\/span>= q;\n    }\n}\n\n<\/span>int<\/span> main(){\n    <\/span>\/\/<\/span>ios_base::sync_with_stdio(0);\n    <\/span>\/\/<\/span>cin.tie(); cout.tie();<\/span>\n    cin>>n>>m;\n    <\/span>for<\/span>(int<\/span> i = 1<\/span>; i <= n; i++){\n        cin<\/span>>>a[i];\n    }\n    initialise();\n    <\/span>for<\/span>(int<\/span> i = 1<\/span>; i <= m; i++){\n        cin<\/span>>>s>>r;\n        union(s, r);\n    }\n    cin<\/span>>>k;\n    <\/span>while<\/span>(k--){\n        cin<\/span>>>s>>r;\n        <\/span>string<\/span> p = find(s);\n        <\/span>string<\/span> q = find(r);\n        <\/span>if<\/span>(p == q)\n            cout<\/span><<\"<\/span>yes.<\/span>\"<\/span><<endl;\n        <\/span>else<\/span> cout<<\"<\/span>no.<\/span>\"<\/span><<endl;\n    }\n    <\/span>return<\/span> 0<\/span>;\n}<\/span><\/pre>\n<\/div>\n
 <\/p>\n","protected":false},"excerpt":{"rendered":"
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