{"id":152,"date":"2019-01-23T00:00:04","date_gmt":"2019-01-22T16:00:04","guid":{"rendered":"http:\/\/wwwwodddd.com\/?p=152"},"modified":"2019-05-04T20:33:44","modified_gmt":"2019-05-04T12:33:44","slug":"usaco-2019-jan","status":"publish","type":"post","link":"https:\/\/wwwwodddd.com\/wordpress\/usaco-2019-jan\/","title":{"rendered":"USACO 2019 JAN"},"content":{"rendered":"

<\/p>\n

Bronze<\/h1>\n

B1 \/ 843<\/h2>\n

\u8fd8\u662f$3$\u4e2a\u53d8\u91cf\uff0c\u6a21\u62df\u4ea4\u6362\uff0c\u7528\u6570\u7ec4\u8ba1\u6570\u5373\u53ef\u3002<\/p>\n

import sys\nsys.stdin = open('shell.in', 'r')\nsys.stdout = open('shell.out', 'w')\nn = input()\na = [0, 1, 2, 3]\nc = [0, 0, 0, 0]\nfor i in range(n):\n    x, y, z = map(int, raw_input().split())\n    a[x], a[y] = a[y], a[x]\n    c[a[z]] += 1\nprint max(c)\n<\/code><\/pre>\n
B2 \/ 844<\/h2>\n
\u672a\u88ab\u64cd\u4f5c\u7684\u90e8\u5206\u5fc5\u987b\u662f\u4e00\u4e2a\u5355\u8c03\u589e\u52a0\u7684\u540e\u7f00\u3002<\/p>\n
import sys\nsys.stdin = open('sleepy.in', 'r')\nsys.stdout = open('sleepy.out', 'w')\nn = input()\na = map(int, raw_input().split())\nfor i in range(n)[::-1]:\n    if i == 0 or a[i-1] > a[i]:\n        print i\n        break\n<\/code><\/pre>\n
B3 \/ 845<\/h2>\n
\u679a\u4e3e\u4e24\u4e2a\u4e0d\u540c\u7684\u96c6\u5408\uff0c\u96c6\u5408\u6c42\u4ea4\uff0c\u7136\u540e\u7528\u4ea4\u96c6\u5927\u5c0f\u66f4\u65b0\u7b54\u6848\u3002<\/p>\n
import sys\nsys.stdin = open('guess.in', 'r')\nsys.stdout = open('guess.out', 'w')\nn = input()\na = []\nfor i in range(n):\n    a.append(set(raw_input().split()[2:]))\nz = 0\nfor i in range(n):\n    for j in range(i):\n        z = max(z, len(a[i] & a[j]))\nprint z + 1\n<\/code><\/pre>\n
Silver<\/h1>\n
S1 \/ 846<\/h2>\n
\u7edf\u8ba1\u6bcf\u4e2a\u70b9\u5ea6\u6570\uff0c\u6700\u5927\u7684\u5ea6\u6570+1\u5c31\u662f\u7b54\u6848\u3002
\n\u6bd4\u4e0a\u4e2a\u6708\u7b80\u5355\u597d\u591a\u3002<\/p>\n
#include <bits\/stdc++.h>\nusing namespace std;\nint n, x, y;\nint c[100020];\nint main() {\n    freopen(\"planting.in\", \"r\", stdin);\n    freopen(\"planting.out\", \"w\", stdout);\n    scanf(\"%d\", &n);\n    for (int i = 1; i < n; i++) {\n        scanf(\"%d%d\", &x, &y);\n        c[x]++;\n        c[y]++;\n    }\n    int cnt = 0;\n    for (int i = 0; i < n; i++) {\n        cnt = max(cnt, c[i] + 1);\n    }\n    printf(\"%d\\n\", cnt);\n    return 0;\n}\n<\/code><\/pre>\n
S2 \/ 847<\/h2>\n
https:\/\/www.luogu.org\/problemnew\/show\/P1451 \u8ba1\u7b97\u6bcf\u4e2a\u533a\u57df\u9762\u79ef\u548c\u5468\u957f
\n\u76f4\u63a5DFS<\/p>\n
#include <bits\/stdc++.h>\nusing namespace std;\nchar s[1002][1002];\nbool v[1002][1002];\nint dx[] = {0, 0, -1, 1};\nint dy[] = {-1, 1, 0, 0};\nint n, area, perimeter;\npair<int, int> ans;\nbool in(int x, int y) {\n    return 0 <= x && x < n && 0 <= y && y < n;\n}\n\nvoid dfs(int x, int y) {\n    if (v[x][y]) {\n        return;\n    }\n    v[x][y] = true;\n    area++;\n    for (int i = 0; i < 4; i++) {\n        int nx = x + dx[i];\n        int ny = y + dy[i];\n        if (in(nx, ny) && s[nx][ny] == '#') {\n            dfs(nx, ny);\n        } else {\n            perimeter++;\n        }\n    }\n}\n\nint main() {\n    freopen(\"perimeter.in\", \"r\", stdin);\n    freopen(\"perimeter.out\", \"w\", stdout);\n    scanf(\"%d\", &n);\n    for (int i = 0; i < n; i++) {\n        scanf(\"%s\", s[i]);\n    }\n    for (int i = 0; i < n; i++) {\n        for (int j = 0; j < n; j++) {\n            if (s[i][j] == '#' && !v[i][j]) {\n                area = 0;\n                perimeter = 0;\n                dfs(i, j);\n                ans = max(ans, make_pair(area, -perimeter));\n            }\n        }\n    }\n    printf(\"%d %d\\n\", ans.first, -ans.second);\n    return 0;\n}\n<\/code><\/pre>\n
S3 \/ 848<\/h2>\n
\u5c06\u6bcf\u4e2a(x, y)\u53d8\u6210\u533a\u95f4(x-y, x+y)
\n\u7136\u540e\u95ee\u9898\u53d8\u6210\u4e86\u9009\u6700\u591a\u7684\u533a\u95f4\uff0c\u4f7f\u5f97\u4e0d\u51fa\u73b0\u5305\u542b\u7684\u60c5\u51b5\u3002
\nhttps:\/\/www.luogu.org\/problemnew\/show\/P1803 \u5982\u679c\u4e0d\u80fd\u9009\u76f8\u4e92\u5305\u542b\u7684\u533a\u95f4\uff08\u9009\u53d6\u7684\u591a\u4e2a\u533a\u95f4\u8981\u4e48\u76f8\u79bb\u8981\u4e48\u76f8\u4ea4\uff09\uff0c\u6700\u591a\u9009\u591a\u5c11\u4e2a\uff1f
\n\u6309\u5de6\u7aef\u70b9\u4ece\u5c0f\u5230\u5927\u6392\u5e8f\uff0c\u5982\u679c\u5de6\u7aef\u70b9\u76f8\u540c\uff0c\u53f3\u7aef\u70b9\u4ece\u5927\u5230\u5c0f\u6392\u5e8f\u3002
\n\u8fd9\u6837\u5bf9\u4e8e\u4e24\u4e2a\u533a\u95f4i\u548cj\uff0c\u5982\u679ci < j \u4e14 r[i] >= r[j]\u90a3\u4e48\u533a\u95f4i\u5305\u542b\u533a\u95f4j\u3002
\n\u8d2a\u5fc3\u9009\u62e9\u5373\u53ef\u3002<\/p>\n
#include <bits\/stdc++.h>\nusing namespace std;\nint n, x, y;\npair<int, int> a[100020];\nint main() {\n    freopen(\"mountains.in\", \"r\", stdin);\n    freopen(\"mountains.out\", \"w\", stdout);\n    scanf(\"%d\", &n);\n    for (int i = 0; i < n; i++) {\n        scanf(\"%d%d\", &x, &y);\n        a[i].first = x - y;\n        a[i].second = -x - y;\n    }\n    sort(a, a + n);\n    int cnt = 0, l = -2e9;\n    for (int i = 0; i < n; i++) {\n        if (l < -a[i].second) {\n            l = -a[i].second;\n            cnt++;\n        }\n    }\n    printf(\"%d\\n\", cnt);\n    return 0;\n}\n<\/code><\/pre>\n
Gold<\/h1>\n
G1 \/ 849<\/h2>\n
\u80cc\u5305\uff0c\u5148\u6c42\u51fa\u4ee5\u6bcf\u4e2a\u97f5\u7ed3\u5c3e\u7684\u53e5\u5b50\u6570\u3002
\n\u6700\u540e\u5bf9\u4e8e\u6bcf\u4e2a\u5927\u5199\u5b57\u6bcd\u8ba1\u6570\uff0c<\/p>\n
#include <bits\/stdc++.h>\nusing namespace std;\nint n, m, l, p = 1000000007;\nint f[5020];\nint s[5020];\nint c[5020];\nint v[26];\nint z[5020];\nint pw(int x, int y) {\n    int re = 1;\n    for (; y > 0; y >>= 1) {\n        if (y & 1) {\n            re = (long long)re * x % p;\n        }\n        x = (long long)x * x % p;\n    }\n    return re;\n}\nint main() {\n    freopen(\"poetry.in\", \"r\", stdin);\n    freopen(\"poetry.out\", \"w\", stdout);\n    scanf(\"%d%d%d\", &n, &m, &l);\n    for (int i = 0; i < n; i++) {\n        scanf(\"%d%d\", &s[i], &c[i]);\n    }\n    f[0] = 1;\n    for (int i = 1; i <= l; i++) {\n        for (int j = 0; j < n; j++) {\n            if (i >= s[j]) {\n                f[i] = (f[i] + f[i - s[j]]) % p;\n            }\n        }\n    }\n    for (int i = 0; i < n; i++) {\n        z[c[i]] = (z[c[i]] + f[l - s[i]]) % p;\n    }\n    for (int i = 0; i < m; i++) {\n        char ch;\n        scanf(\" %c\", &ch);\n        v[ch - 'A']++;\n    }\n    int ans = 1;\n    for (int i = 0; i < 26; i++) {\n        if (v[i] == 0) {\n            continue;\n        }\n        int tmp = 0;\n        for (int j = 1; j <= n; j++) {\n            tmp = (tmp + pw(z[j], v[i])) % p;\n        }\n        ans = (long long)ans * tmp % p;\n    }\n    printf(\"%d\\n\", ans);\n    return 0;\n}\n<\/code><\/pre>\n
G2 \/ 850<\/h2>\n
\u6811\u72b6\u6570\u7ec4\u3002<\/p>\n
#include <bits\/stdc++.h>\nusing namespace std;\nint n;\nint c[1000020];\nint a[1000020];\nint z[1000020];\nint v[1000020];\nvoid change(int x, int y) {\n    for (int i = x; i <= n; i += i & -i) {\n        c[i] += y;\n    }\n}\nint query(int x) {\n    int re = 0;\n    for (int i = x; i > 0; i -= i & -i) {\n        re += c[i];\n    }\n    return re;\n}\nint main() {\n    freopen(\"sleepy.in\", \"r\", stdin);\n    freopen(\"sleepy.out\", \"w\", stdout);\n    scanf(\"%d\", &n);\n    for (int i = 0; i < n; i++) {\n        scanf(\"%d\", &a[i]);\n        change(a[i], 1);\n    }\n    int ans = -1;\n    for (int i = n - 1; i >= 0; i--) {\n        if (i == 0 || a[i - 1] > a[i]) {\n            ans = i;\n            break;\n        }\n    }\n    printf(\"%d\\n\", ans);\n    for (int i = ans - 1; i >= 0; i--) {\n        change(a[i], -1);\n        z[i] = query(a[i]) + ans - 1 - i;\n    }\n    if (ans == 0) {\n        printf(\"\\n\");\n    } else {\n        for (int i = 0; i < ans; i++) {\n            printf(\"%d%c\", z[i], i == ans - 1 ? '\\n' : ' ');\n        }\n    }\n    return 0;\n}\n<\/code><\/pre>\n
G3 \/ 851<\/h2>\n
\u88f8\u6700\u77ed\u8def\u6570\uff0c\u7528dijkstra\u66f4\u65b0\u7684\u65f6\u5019\uff0c\u4e0d\u4ec5\u8981\u8bb0\u5f55\u6700\u77ed\u8def\uff0c\u8fd8\u8981\u8bb0\u5f55\u6bcf\u4e2a\u70b9\u662f\u88ab\u54ea\u4e2a\u70b9\u66f4\u65b0\u7684\u3002<\/p>\n
#include <bits\/stdc++.h>\nusing namespace std;\nvector<pair<int, int> > a[10020];\nint n, m, t;\nint c[10020];\nint d[10020];\nint f[10020];\nset<pair<int, int> > s;\nvector<int> q;\nint main() {\n    freopen(\"shortcut.in\", \"r\", stdin);\n    freopen(\"shortcut.out\", \"w\", stdout);\n    scanf(\"%d%d%d\", &n, &m, &t);\n    for (int i = 1; i <= n; i++) {\n        scanf(\"%d\", &c[i]);\n    }\n    for (int i = 0; i < m; i++) {\n        int x, y, z;\n        scanf(\"%d%d%d\", &x, &y, &z);\n        a[x].push_back(make_pair(y, z));\n        a[y].push_back(make_pair(x, z));\n    }\n    memset(d, 0x3f, sizeof d);\n    d[1] = 0;\n    s.insert(make_pair(d[1], 1));\n    while (s.size()) {\n        int u = s.begin() -> second;\n        q.push_back(u);\n        s.erase(s.begin());\n        for (int i = 0; i < a[u].size(); i++) {\n            if (d[a[u][i].first] > d[u] + a[u][i].second) {\n                s.erase(make_pair(d[a[u][i].first], a[u][i].first));\n                d[a[u][i].first] = d[u] + a[u][i].second;\n                f[a[u][i].first] = u;\n                s.insert(make_pair(d[a[u][i].first], a[u][i].first));\n            } else if (d[a[u][i].first] == d[u] + a[u][i].second) {\n                f[a[u][i].first] = min(f[a[u][i].first], u);\n            }\n        }\n    }\n    long long ans = 0;\n    for (int i = q.size() - 1; i > 0; i--) {\n        ans = max(ans, (long long)c[q[i]] * (d[q[i]] - t));\n        c[f[q[i]]] += c[q[i]];\n    }\n    printf(\"%lld\\n\", ans);\n    return 0;\n}\n<\/code><\/pre>\n
Platinum<\/h1>\n
P1 \/ 852<\/h2>\n
\u5f88\u5bb9\u6613\u5f97\u5230\u4e00\u4e2a\u65f6\u95f4\u590d\u6742\u5ea6\u4e3ank\u7684\u52a8\u6001\u89c4\u5212<\/p>\n
    for (int i = 1; i <= n; i++) {\n        f[i] = f[i - 1] + 1;\n        for (int j = max(i - m, 0); j < i; j++) {\n            if (i - 2 * s[i] > j - 2 * s[j]) {\n                f[i] = min(f[i], f[j]);\n            } else {\n                f[i] = min(f[i], f[j] + 1);\n            }\n        }\n    }\n<\/code><\/pre>\n
\u5148\u7528 max(i – m, 0) \u5230 i-1 \u7684\u6bcf\u4e2aj \u7684f[j] + 1\u66f4\u65b0f[i]
\n\u8fd9\u4e2a\u662f\u533a\u95f4\u6700\u503c\uff0c\u53ef\u4ee5\u7528\u7ebf\u6bb5\u6811\u6216\u8005\u5355\u8c03\u961f\u5217\u89e3\u51b3
\n\u7136\u540e\u8003\u8651\u6ee1\u8db3i – 2 * s[i] > j – 2 * s[j] \u7684 f[j]\u6765\u66f4\u65b0f[i] \uff08\u8fd9\u91cc\u4e0d+1\uff0c\u6240\u4ee5\u66f4\u4f18\uff09
\n\u6240\u4ee5\u8bf4\u6bcf\u6b21\u5f97\u5230\u4e00\u4e2af[i]\uff0c\u5c31\u628a\u4ed6\u653e\u5728i – 2 * s[i]\u7684\u4f4d\u7f6e\u4e0a\uff0c\u7136\u540e\u53d8\u6210\u4e86\u8be2\u95ee\u5c0f\u4e8ei – 2 * s[i]\u7684\u4f4d\u7f6e\u4e0a\uff0c\u6700\u5c0f\u503c\u662f\u591a\u5c11\u7684\u95ee\u9898\u3002
\n\u8fd9\u91cc\u6ce8\u610f\u4e00\u4e2a\u4f4d\u7f6e\u4e0a\u53ef\u80fd\u88ab\u52a0\u591a\u4e2a\u503c
\n\u5e76\u4e14\u52a0\u4e0a\u7684\u503c\u8fd8\u5fc5\u987b\u652f\u6301\u5220\u9664\uff08i – j > m\u7684\u8bdd\u5c31\u8981\u628aj\u5220\u6389\u4e86\uff09
\n\u6240\u4ee5\u7528\u7ebf\u6bb5\u6811\uff0c\u6bcf\u4e2a\u53f6\u5b50\u8282\u70b9\u7ef4\u62a4\u4e00\u4e2aset\u5373\u53ef\u3002<\/p>\n
#include <bits\/stdc++.h>\nusing namespace std;\nint n, m;\nchar c[300020];\nint f[300020];\nint s[300020];\nint qq[300020], bb, ff;\nmultiset<int> ms[600020];\nint mn[2400020];\nint inf = 1e9;\nvoid build(int x, int L, int R) {\n    if (L == R - 1) {\n        mn[x] = inf;\n        return;\n    }\n    int M = (L + R) \/ 2;\n    build(x * 2, L, M);\n    build(x * 2 + 1, M, R);\n    mn[x] = min(mn[x * 2], mn[x * 2 + 1]);\n}\nint query(int x, int L, int R, int l, int r) {\n    if (r <= L || R <= l) {\n        return inf;\n    }\n    if (l <= L && R <= r) {\n        return mn[x];\n    }\n    int M = (L + R) \/ 2;\n    return min(query(x * 2, L, M, l, r), query(x * 2 + 1, M, R, l, r));\n}\nvoid insert(int x, int L, int R, int p, int v) {\n    if (L == R - 1) {\n        ms[L].insert(v);\n        mn[x] = *ms[L].begin();\n        return;\n    }\n    int M = (L + R) \/ 2;\n    if (p < M) {\n        insert(x * 2, L, M, p, v);\n    } else {\n        insert(x * 2 + 1, M, R, p, v);\n    }\n    mn[x] = min(mn[x * 2], mn[x * 2 + 1]);\n}\nvoid erase(int x, int L, int R, int p, int v) {\n    if (L == R - 1) {\n        multiset<int>::iterator it = ms[L].find(v);\n        assert(it != ms[L].end());\n        ms[L].erase(it);\n        if (ms[L].size() > 0) {\n            mn[x] = *ms[L].begin();\n        } else {\n            mn[x] = inf;\n        }\n        return;\n    }\n    int M = (L + R) \/ 2;\n    if (p < M) {\n        erase(x * 2, L, M, p, v);\n    } else {\n        erase(x * 2 + 1, M, R, p, v);\n    }\n    mn[x] = min(mn[x * 2], mn[x * 2 + 1]);\n}\nint main() {\n    freopen(\"redistricting.in\", \"r\", stdin);\n    freopen(\"redistricting.out\", \"w\", stdout);\n    scanf(\"%d%d\", &n, &m);\n    scanf(\"%s\", c);\n    for (int i = 0; i < n; i++) {\n        s[i + 1] = s[i] + (c[i] == 'G');\n    }\n    qq[ff++] = 0;\n    build(1, 0, 2 * n + 1);\n    insert(1, 0, 2 * n + 1, n, 0);\n    for (int i = 1; i <= n; i++) {\n        while (qq[bb] < i - m) {\n            bb++;\n        }\n        {\n            int u = i - m - 1;\n            if (u >= 0) {\n                erase(1, 0, 2 * n + 1, n + u - 2 * s[u], f[u]);\n            }\n        }\n        assert(bb < ff);\n        f[i] = f[qq[bb]] + 1;\n        int tmp = query(1, 0, 2 * n + 1, 0, n + i - 2 * s[i]);\n        f[i] = min(f[i], tmp);\n        insert(1, 0, 2 * n + 1, n + i - 2 * s[i], f[i]);\n        while (bb < ff && f[qq[ff - 1]] >= f[i]) {\n            ff--;\n        }\n        qq[ff++] = i;\n\/*\n        for (int j = max(i - m, 0); j < i; j++) {\n            if (i - 2 * s[i] > j - 2 * s[j]) {\n                f[i] = min(f[i], f[j]);\n            } else {\n                f[i] = min(f[i], f[j] + 1);\n            }\n        }\n*\/\n\/\/      cerr << i << ' ' << f[i] << endl;\n    }\n    printf(\"%d\\n\", f[n]);\n    return 0;\n}\n<\/code><\/pre>\n
P2 \/ 853<\/h2>\n
\u5168\u90e8\u7684\u8def\u5f84\u6570 – \u6ca1\u6709\u516c\u5171\u70b9\uff08\u663e\u7136\u4e0d\u4f1a\u6709\u516c\u5171\u8fb9\uff09\u7684\u8def\u5f84\u5bf9\u6570 – \u53ea\u6709\u516c\u5171\u70b9\u800c\u6ca1\u6709\u516c\u5171\u8fb9\u7684\u8def\u5f84\u5bf9\u6570<\/p>\n
\u5168\u90e8\u7684\u8def\u5f84\u6570 = C(m, 2)  m\u4e3a\u975e\u6811\u8fb9\u7684\u4e2a\u6570<\/p>\n
\u6ca1\u6709\u516c\u5171\u70b9\uff08\u663e\u7136\u4e0d\u4f1a\u6709\u516c\u5171\u8fb9\uff09\u7684\u8def\u5f84\u5bf9\u6570
\n\u8003\u8651\u8f83\u6df1\u7684\u8def\u5f84\u7684lca\u7684\u7236\u4eb2\u65b9\u5411\u7684\u8fb9\uff0c\u6211\u4eec\u5e0c\u671b\u6bcf\u4e00\u5bf9\u8def\u5f84\u90fd\u5728\u8fd9\u4e2a\u4f4d\u7f6e\u88ab\u7edf\u8ba1\u5230\u3002
\n\u6240\u4ee5\u9700\u8981\u5904\u7406\u5bf9\u4e8e\u6bcf\u4e2a\u70b9\uff0c\u6709\u591a\u5c11\u4e2a\u70b9\u4ee5\u4ed6\u4e3aLCA\u3002
\n\u6bcf\u4e2a\u70b9\u5bf9\u5e94\u7684\u5b50\u6811\uff0c\u5185\u90e8\u6709\u591a\u5c11\u6761\u8def\u5f84
\n\u5b50\u6811\u5185\u90e8\u7684\u8def\u5f84\u6709\u4e24\u79cd\u542b\u4e49\uff0c
\n\u7b2c\u4e00\u79cd\u662f\u6307\u8def\u5f84\u5b8c\u5168\u5728\u5b50\u6811\u5185\u90e8\uff08\u8def\u5f84\u7684LCA\u5728\u5b50\u6811\u5185\u90e8\uff09
\n\u7b2c\u4e8c\u79cd\u662f\u6307\u8def\u5f84\u4e00\u4e2a\u7aef\u70b9\u5728\u5b50\u6811\u5185\u90e8\uff0c\u4e00\u4e2a\u7aef\u70b9\u5728\u5b50\u6811\u5916\u90e8\u3002
\n\u7b54\u6848 += \u4ee5\u5f53\u524d\u70b9\u4e3aLCA\u7684\u8def\u5f84\u6570 * (m – \u8def\u5f84\u5b8c\u5168\u5728\u5b50\u6811\u5185\u90e8\u7684\u4e2a\u6570 – \u8def\u5f84\u4e00\u4e2a\u7aef\u70b9\u5728\u5b50\u6811\u5185\u90e8\u7684\u4e2a\u6570)
\n(m – \u8def\u5f84\u5b8c\u5168\u5728\u5b50\u6811\u5185\u90e8\u7684\u4e2a\u6570 – \u8def\u5f84\u4e00\u4e2a\u7aef\u70b9\u5728\u5b50\u6811\u5185\u90e8\u7684\u4e2a\u6570) \u76f8\u5f53\u4e8e\u662f\u4e0d\u5728\u5b50\u6811\u5185\u90e8\u7684\u8def\u5f84\u4e2a\u6570<\/p>\n
\u4f46\u662f\u8fd9\u6837\u4f1a\u6709\u4e00\u4e2a\u95ee\u9898\uff0c\u5982\u679c\u4e00\u5bf9\u8def\u5f84\uff0c\u5206\u5c5e\u4e0d\u540c\u5b50\u6811\uff0c\u90a3\u4e48\u7b54\u6848\u4e2d\u4ed6\u4eec\u4f1a\u88ab\u7edf\u8ba1\u4e24\u6b21\uff0c\u9700\u8981\u628a\u8fd9\u79cd\u60c5\u51b5\u51cf\u6389\u3002
\n\u8fd9\u4e2a\u51cf\u53bb\u7684\u8fc7\u7a0b\u4f1a\u5728\u6240\u6709\u70b9\u7684LCA\u5904\u88ab\u51cf\u53bb\u3002<\/p>\n
\u53ea\u6709\u516c\u5171\u70b9\u800c\u6ca1\u6709\u516c\u5171\u8fb9\u7684\u8def\u5f84\u5bf9\u6570\uff0c\u8003\u8651\u4e00\u6761\u8def\u5f84\u548c\u4e00\u4e2a\u70b9\u7684\u5173\u7cfb\u6709\u54ea\u4e9b
\n\u53ef\u80fd\u662f\u5b8c\u5168\u65e0\u5173\uff0c\u8def\u5f84\u4e0d\u901a\u8fc7\u8fd9\u4e2a\u70b9\uff08\u8fd9\u4e0d\u9700\u8981\u8003\u8651\uff09
\n\u53ef\u80fd\u662f\u901a\u8fc7\u8fd9\u4e2a\u70b9\uff0c\u548c\u8fd9\u4e2a\u70b9\u76f8\u90bb\u7684\u4e24\u6761\u8fb9\u6709\u4ea4\u96c6\u3002
\n\u53ef\u80fd\u662f\u8fd9\u4e2a\u70b9\u662f\u7aef\u70b9\u4e4b\u4e00\uff0c\u548c\u8fd9\u4e2a\u70b9\u76f8\u90bb\u7684\u4e00\u6761\u8fb9\u6709\u4ea4\u96c6\u3002<\/p>\n
\u7136\u540e\u9700\u8981\u8003\u8651 \u6709\u591a\u5c11\u5bf9\u8fb9\u96c6\uff08\u8fb9\u96c6\u5927\u5c0f<=2\uff09\uff0c\u4ea4\u96c6\u4e3a\u7a7a\u3002
\n\u505a\u6cd5\u975e\u5e38\u7ecf\u5178\uff1a
\n\u4ea4\u96c6\u4e3a\u7a7a\u7684\u8fb9\u96c6\u5bf9\u6570 = C(\u4ea4\u96c6\u5305\u542b\u7a7a\u96c6\u7684\u96c6\u5408\u6570, 2) – C(\u4ea4\u96c6\u5305\u542b\u5927\u5c0f\u4e3a1\u7684\u96c6\u5408\u6570, 2) + C(\u4ea4\u96c6\u5305\u542b\u5927\u5c0f\u4e3a2\u7684\u96c6\u5408\u6570, 2)
\n\u5927\u5c0f\u4e3a1\u7684\u96c6\u5408 \u548c \u5927\u5c0f\u4e3a2\u7684\u96c6\u5408 \u5747\u9700\u8981\u679a\u4e3e\u6240\u6709\u53ef\u80fd\u6027\u3002<\/p>\n
\u5927\u5c0f\u4e3a0\u7684\u96c6\u5408 \u5373\u679a\u4e3e\u6240\u6709\u70b9\uff0c\u5bf9\u4e8e\u6bcf\u4e2a\u70b9\u8ba1\u7b97\u6709\u591a\u5c11\u6761\u8def\u5f84\u7ecf\u8fc7\u4ed6\u3002
\n\u5927\u5c0f\u4e3a1\u7684\u96c6\u5408 \u5373\u679a\u4e3e\u6240\u6709\u8fb9\uff0c\u5bf9\u4e8e\u6bcf\u6761\u8fb9\u8ba1\u7b97\u6709\u591a\u5c11\u6761\u8def\u5f84\u7ecf\u8fc7\u4ed6\u3002<\/p>\n
\u4ee5\u4e0a\u4e24\u4e2a\u95ee\u9898\u51e0\u4e4e\u4e00\u6837\uff0c\u4f46\u662f\u6ce8\u610f\u6bcf\u6761\u8fb9\u5e94\u8be5\u5728\u5b69\u5b50\u8282\u70b9\u548c\u7236\u4eb2\u8282\u70b9\u5404\u88ab\u8ba1\u7b97\u4e00\u904d\u3002<\/p>\n
\u5927\u5c0f\u4e3a2\u7684\u96c6\u5408\uff0c\u5373\u679a\u4e3e\u6240\u6709\u76f8\u90bb\u7684\u4e24\u6761\u8fb9\uff0c\u5bf9\u4e8e\u6bcf\u7ec4\u8ba1\u7b97\u6709\u591a\u5c11\u6761\u8def\u5f84\u7ecf\u8fc7\u4ed6\u3002
\n\u4f46\u662f\u8fd9\u6837\u4f1a\u8d85\u65f6\uff0c\u9700\u8981\u60f3\u4e00\u4e9b\u5176\u4ed6\u7684\u529e\u6cd5\u3002<\/p>\n
\u8003\u8651\u4e00\u4e2a\u70b9\uff0c\u5927\u5c0f\u4e3a2\u7684\u96c6\u5408\u6709\u8fd9\u4e48\u51e0\u79cd\u53ef\u80fd
\n1. \u4ece\u4e00\u4e2a\u5b69\u5b50\u6765\uff0c\u5230\u53e6\u4e00\u4e2a\u5b69\u5b50\u53bb\uff08\u90a3\u4e48\u8bf4\u660e\u81ea\u5df1\u662fLCA\uff0c\u8fd9\u6837\u7684\u8bdd\u6bcf\u6761\u8def\u5f84\u6c42LCA\u7684\u65f6\u5019\uff0c\u6c42\u51fa\u6765\u6700\u63a5\u8fd1LCA\u76842\u4e2a\u70b9\u5373\u53ef\uff09
\n2. \u4ece\u4e00\u4e2a\u5b69\u5b50\u6765\uff0c\u5230\u7236\u4eb2\u8282\u70b9\u53bb\uff08\u56e0\u4e3a\u6bcf\u4e2a\u70b9\u7684\u5b69\u5b50\u6570\u4e0d\u592a\u591a\uff0c\u76f4\u63a5\u679a\u4e3e\u8ba1\u7b97\u5373\u53ef\uff09<\/p>\n
#include <bits\/stdc++.h>\nusing namespace std;\nint n, m;\nvector<int> a[200020];\nint f[200020][18]; \/\/ father\nint d[200020]; \/\/depth\nlong long b[200020]; \/\/ \u6709\u591a\u5c11\u6761\u8def\u5f84\u8fc7\u81ea\u5df1\u7236\u4eb2\u8fd9\u6761\u8fb9\nlong long r[200020]; \/\/ \u5f53\u524d\u70b9\u6709\u591a\u5c11\u4e2alca\nlong long c[200020]; \/\/ \u5b50\u6811\u5185\u6709\u591a\u5c11\u4e2alca\nlong long e[200020]; \/\/ \u6709\u591a\u5c11\u4e2a\u8def\u5f84\uff0c\u4ee5x\u7684\u7236\u4eb2\u8282\u70b9\u4e3alca\nlong long ans;\nmap<pair<int, int>, int> g[200020];\nvoid dfs(int x, int y) {\n    f[x][0] = y;\n    d[x] = d[y] + 1;\n    for (int i = 1; i < 18; i++) {\n        f[x][i] = f[f[x][i - 1]][i - 1];\n    }\n    for (int i: a[x]) {\n        if (i != y) {\n            dfs(i, x);\n        }\n    }\n}\n\nvoid dfs2(int x, int y) {\n    long long u = c[x];\n    r[x] = c[x];\n    long long s1 = 0;\n    long long s2 = 0;\n    for (int i: a[x]) {\n        if (i != y) {\n            dfs2(i, x);\n            c[x] += c[i];\n            b[x] += b[i];\n            s1 += c[i];\n            s2 += c[i] * c[i];\n            ans -= (b[i] - e[i]) * (b[i] - e[i] - 1) \/ 2;\n        }\n    }\n    ans -= u * (m - c[x] - b[x]);\n\/\/ \u6709\u4e00\u4e9b\u4f1a\u88ab\u51cf\u4e24\u6b21\n    ans += (s1 * s1 - s2) \/ 2;\n\/\/ \u52a0\u56de\u6765\n\n\n    ans -= (b[x] + r[x]) * (b[x] + r[x] - 1) \/ 2;\n\/\/  cerr << (b[x] + r[x]) * (b[x] + r[x] - 1) \/ 2 << endl;\n\/\/ \u51cf\u53bb\u4ea4\u96c6\u4e3a0\u7684\u5bf9\u6570\uff08\u8fc7\u70b9x\u7684\uff09\n\n    ans += (b[x]) * (b[x] - 1) \/ 2 * 2;\n\/\/  cerr << (b[x]) * (b[x] - 1) \/ 2 << endl;\n\/\/ \u52a0\u4e0a\u4ea4\u96c6\u4e3a1\u7684\u5bf9\u6570\uff08\u8fc7\u70b9x\u7236\u4eb2\u90a3\u6761\u8fb9\u7684\uff09\n\n\/\/ \u51cf\u53bb\u4ea4\u96c6\u4e3a2\u7684\uff0cLCA\u662f\u5f53\u524d\u70b9\u3002\n    for (pair<pair<int, int>, int> i: g[x]) {\n        ans -= (long long)i.second * (i.second - 1) \/ 2;\n\/\/      cerr << (long long)i.second * (i.second - 1) \/ 2 << endl;\n    }\n\/\/ \u63a5\u4e0b\u6765\u9700\u8981\u8003\u8651\u7684\u8def\u5f84\u5c31\u662f\u81ea\u5df1\u5b69\u5b50\u5230\u81ea\u5df1\u7236\u4eb2\u8282\u70b9\u8fd9\u79cd\u8def\u5f84\u4e86\n\/\/ \u7b80\u5355\u6765\u8bf4\u8fd9\u5c31\u662fb[i] ?\u4f46\u662f\u6709\u4e00\u4e9b\u8def\u5f84\u4ee5\u81ea\u5df1\u7ed3\u675f\u554a\uff0c\u518d\u5f00\u4e00\u4e2a\u6570\u7ec4\u5427\u3002\n}\n\nint lca(int x, int y) {\n    if (d[x] < d[y]) {\n        swap(x, y);\n    }\n    int dd = d[x] - d[y];\n    for (int i = 0; i < 18; i++) {\n        if (dd >> i & 1) {\n            x = f[x][i];\n        }\n    }\n    if (x == y) {\n        return x;\n    }\n    for (int i = 17; i >= 0; i--) {\n        if (f[x][i] != f[y][i]) {\n            x = f[x][i];\n            y = f[y][i];\n        }\n    }\n    return f[x][0];\n}\n\n\/*\n\u5bf9\u4e8e\u6bcf\u4e2a\u70b9\uff0c\u6bcf\u6761\u8def\u5f84\u662f\u4e00\u4e2a\u5927\u5c0f\u4e3a2\u7684\u96c6\u5408\n\u95ee\u6709\u591a\u5c11\u5bf9\u96c6\u5408\u6ca1\u6709\u4ea4\u96c6\n\u4ea4\u96c6\u4e3a0\u7684\u5bf9\u6570 - \u4ea4\u96c6\u4e3a1\u7684\u5bf9\u6570 + \u4ea4\u96c6\u4e3a2\u7684\u5bf9\u6570\n*\/\n\nint main() {\n    freopen(\"exercise.in\", \"r\", stdin);\n    freopen(\"exercise.out\", \"w\", stdout);\n    scanf(\"%d%d\", &n, &m);\n    for (int i = 1; i < n; i++) {\n        int x, y;\n        scanf(\"%d%d\", &x, &y);\n        a[x].push_back(y);\n        a[y].push_back(x);\n    }\n    dfs(1, 0);\n    m -= n - 1;\n    for (int i = 0; i < m; i++) {\n        int x, y, nx, ny;\n        scanf(\"%d%d\", &x, &y);\n        nx = x;\n        ny = y;\n        int l = lca(x, y);\n        b[x]++;\n        b[y]++;\n        b[l] -= 2;\n        c[l]++;\n        for (int i = 17; i >= 0; i--) {\n            if (d[f[nx][i]] > d[l]) {\n                nx = f[nx][i];\n            }\n            if (d[f[ny][i]] > d[l]) {\n                ny = f[ny][i];\n            }\n        }\n        if (nx > ny) {\n            swap(nx, ny);\n        }\n        if (nx != l) {\n            e[nx]++;\n        }\n        if (ny != l) {\n            e[ny]++;\n        }\n        if (nx != l && ny != l) {\n            g[l][make_pair(nx, ny)]++;\n        }\n    }\n    ans = (long long)m * (m - 1) \/ 2;\n\/*\n\u5168\u90e8 m*(m-1)\/2\n\u51cf\u53bb \u4e0d\u60f3\u4ea4\u7684\n*\/\n    dfs2(1, 0);\n\/*\n\u5230\u8fd9\u91cc\uff0c\u7b54\u6848\u5e94\u8be5\u662f\u70b9\u76f8\u4ea4\u7684\u65e0\u5e8f\u5bf9\u6570\u91cf\n\u8fd8\u9700\u8981\u51cf\u53bb\uff0c\u53ea\u76f8\u4ea4\u5728\u70b9\u4e0a\u7684\uff0c\u4e5f\u5c31\u662f -(\u4ea4\u96c6\u4e3a0\u7684\u5bf9\u6570 - \u4ea4\u96c6\u4e3a1\u7684\u5bf9\u6570 + \u4ea4\u96c6\u4e3a2\u7684\u5bf9\u6570)\n*\/\n    printf(\"%lld\\n\", ans);\n    return 0;\n}\n<\/code><\/pre>\n
P3 \/ 854<\/h2>\n
\u5bf9\u4e8e\u76f8\u90bb\u76842\u4e2a\u6570\u5b57\uff0c\u5982\u679cc[i] < c[i + 1]
\n\u90a3\u4e48\u663e\u7136a[i] = c[i]<\/p>\n
\u5982\u679cc[i] > c[i + 1]
\n\u90a3\u4e48\u663e\u7136a[i + k] = c[i + 1]<\/p>\n
\u8003\u8651\u8fd9\u6837\u7684\u6570\u636e<\/p>\n
7 3
\n1 2 2 2 3
\n\u53ef\u4ee5\u753b\u51fa7\u4e2a\u4f4d\u7f6e
\n1 _ _ 2 _ _ _
\n\u5176\u4e2d
\n\u7b2c2, 3, 4\u4e2a\u4f4d\u7f6e\uff0c\u8981\u6c42\u6bcf\u4e2a\u957f\u5ea6\u4e3a3\u7684\u533a\u95f4\u7684\u6700\u5c0f\u503c\u90fd\u662f2
\n\u7b2c5, 6, 7\u4e2a\u4f4d\u7f6e\uff0c\u8981\u6c42\u6bcf\u4e2a\u957f\u5ea6\u4e3a3\u7684\u533a\u95f4\u7684\u6700\u5c0f\u503c\u90fd\u662f3<\/p>\n
7 3
\n1 2 2 2 1
\n\u53ef\u4ee5\u753b\u51fa7\u4e2a\u4f4d\u7f6e
\n1 _ _ _ _ _ 1
\n\u5176\u4e2d
\n\u7b2c2, 3, 4, 5, 6\u4e2a\u4f4d\u7f6e\uff0c\u8981\u6c42\u6bcf\u4e2a\u957f\u5ea6\u4e3a3\u7684\u533a\u95f4\u7684\u6700\u5c0f\u503c\u90fd\u662f2<\/p>\n
7 3
\n3 2 2 2 3
\n\u53ef\u4ee5\u753b\u51fa7\u4e2a\u4f4d\u7f6e
\n_ _ _ 2 _ _ _
\n\u5176\u4e2d
\n\u7b2c1, 2, 3\u4e2a\u4f4d\u7f6e\uff0c\u8981\u6c42\u6bcf\u4e2a\u957f\u5ea6\u4e3a3\u7684\u533a\u95f4\u7684\u6700\u5c0f\u503c\u90fd\u662f3
\n\u7b2c5, 6, 7\u4e2a\u4f4d\u7f6e\uff0c\u8981\u6c42\u6bcf\u4e2a\u957f\u5ea6\u4e3a3\u7684\u533a\u95f4\u7684\u6700\u5c0f\u503c\u90fd\u662f3<\/p>\n
10 3
\n3 2 2 2 2 2 2 3
\n_ _ _ 2 _ _ 2 _ _ _
\n\u5176\u4e2d
\n\u7b2c1, 2, 3\u4e2a\u4f4d\u7f6e\uff0c\u8981\u6c42\u6bcf\u4e2a\u957f\u5ea6\u4e3a3\u7684\u533a\u95f4\u7684\u6700\u5c0f\u503c\u90fd\u662f3
\n\u7b2c8, 9, 10\u4e2a\u4f4d\u7f6e\uff0c\u8981\u6c42\u6bcf\u4e2a\u957f\u5ea6\u4e3a3\u7684\u533a\u95f4\u7684\u6700\u5c0f\u503c\u90fd\u662f3
\n\u7b2c4, 5, 6, 7\u4e2a\u4f4d\u7f6e\uff0c\u8981\u6c42\u6bcf\u4e2a\u957f\u5ea6\u4e3a3\u7684\u533a\u95f4\u7684\u6700\u5c0f\u503c\u90fd\u662f2<\/p>\n
\u53d1\u73b0\u95ee\u9898\u8f6c\u5316\u4e3a\u4e86\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u957f\u5ea6\u4e3a$n$\u7684\u6570\u7ec4\uff0c\u8981\u6c42\u6bcf\u4e2a\u957f\u5ea6\u4e3a$m$\u7684\u533a\u95f4\uff0c\u6700\u5c0f\u503c\u90fd\u662f$M – r$\u3002
\n\u5176\u4e2d$M$\u662f\u80fd\u586b\u7684\u6570\u5b57\u7684\u4e0a\u754c\u3002
\n\uff08\u7b2c\u4e00\u4e2a\u548c\u6700\u540e\u4e00\u4e2a\u6570\u5b57\u5fc5\u987b\u662fM – r\uff0c\u5e76\u4e0d\u5f71\u54cd\u7b54\u6848\uff0c\u76f4\u63a5\u8ba9n -= 1\u5373\u53ef\uff09
\n\u8bbef[i]\u4e3a\u7b2ci\u4e2a\u6570\u5b57\u4e3aM – r\u7684\u65b9\u6848\u6570<\/p>\n
f[0] = 1 (\u4ec0\u4e48\u90fd\u6ca1\u6709)
\nf[1] = 1 (\u53ea\u586b\u4e86\u4e00\u4e2aM – r)
\nf[i] = sum(i – j <= m, f[j] * r ** (i – j – 1))
\n\u7b2ci\u4e2a\u4f4d\u7f6e\u548c\u7b2cj\u4e2a\u4f4d\u7f6e\u90fd\u5fc5\u987b\u662f$M – r$\uff0c\u671f\u95f4\u6709$i – j – 1$\u4e2a\u4f4d\u7f6e\u53ef\u4ee5\u81ea\u7531\u51b3\u5b9a\u586b$M – r + 1$\u5230$M$\u5171$r$\u4e2a\u6570\u5b57\u3002
\n\u8fd9\u4e2adp\u663e\u7136\u53ef\u4ee5\u7528\u524d\u7f00\u548c\u4f18\u5316\u3002<\/p>\n
\u628a\u539f\u9898\u53ef\u4ee5\u5212\u5206\u6210\u82e5\u5e72\u6bb5\u8fd9\u6837\u7684DP\uff0c\u7136\u540e\u5c31\u53ef\u4ee5AC\u4e86\u3002<\/p>\n
#include <bits\/stdc++.h>\nusing namespace std;\nint p = 1000000007;\nint M = 1e9;\nint n, m, ans;\nint c[200020];\nvector<pair<int, int> > b;\nlong long f[200020];\nint F(int n, int m, int r) {\n    if (n == -1) {\n        return 1;\n    }\n    if (n < 0) {\n        return 0;\n    }\n    for (int i = 0; i < n + 2; i++) {\n        f[i] = 0;\n    }\n    f[0] = 1;\n    long long u = f[0];\n    long long v = 1;\n    for (int i = 0; i < m; i++) {\n        v = v * r % p;\n    }\n    for (int i = 1; i < n + 2; i++) {\n        f[i] = u;\n        u = (u * r + f[i]) % p;\n        if (i - m >= 0) {\n            u = (u - f[i - m] * v) % p;\n        }\n        if (u < 0) {\n            u += p;\n        }\n    }\n    return f[n + 1];\n}\n\nint main() {\n    freopen(\"tracking2.in\", \"r\", stdin);\n    freopen(\"tracking2.out\", \"w\", stdout);\n\/\/  scanf(\"%d%d%d\", &n, &m, &M);\n    scanf(\"%d%d\", &n, &m);\n    for (int i = 0; i <= n - m; i++) {\n        scanf(\"%d\", &c[i]);\n    }\n    b.push_back(make_pair(0, 1));\n    for (int i = 0, j; i <= n - m; i = j) {\n        j = i;\n        while (j <= n - m && c[j] == c[i]) {\n            j++;\n        }\n        b.push_back(make_pair(c[i], j - i));\n    }\n    b.push_back(make_pair(0, 1));\n    ans = 1;\n    for (int i = 1; i < b.size() - 1; i++) {\n        if (b[i - 1].first < b[i].first && b[i].first > b[i + 1].first) {\n            ans = (long long)ans * F(b[i].second + m - 1, m, M - b[i].first) % p;\n        } else if (b[i - 1].first > b[i].first && b[i].first < b[i + 1].first) {\n            ans = (long long)ans * F(b[i].second - m - 1, m, M - b[i].first) % p;\n        } else {\n            ans = (long long)ans * F(b[i].second - 1, m, M - b[i].first) % p;\n        }\n    }\n    cout << ans << endl;\n    return 0;\n}\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[4],"class_list":["post-152","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-usaco"],"_links":{"self":[{"href":"https:\/\/wwwwodddd.com\/wordpress\/wp-json\/wp\/v2\/posts\/152","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wwwwodddd.com\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wwwwodddd.com\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wwwwodddd.com\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wwwwodddd.com\/wordpress\/wp-json\/wp\/v2\/comments?post=152"}],"version-history":[{"count":0,"href":"https:\/\/wwwwodddd.com\/wordpress\/wp-json\/wp\/v2\/posts\/152\/revisions"}],"wp:attachment":[{"href":"https:\/\/wwwwodddd.com\/wordpress\/wp-json\/wp\/v2\/media?parent=152"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wwwwodddd.com\/wordpress\/wp-json\/wp\/v2\/categories?post=152"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wwwwodddd.com\/wordpress\/wp-json\/wp\/v2\/tags?post=152"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}