{"id":136,"date":"2018-11-20T12:00:38","date_gmt":"2018-11-20T04:00:38","guid":{"rendered":"http:\/\/wwwwodddd.com\/?p=136"},"modified":"2019-01-23T14:46:15","modified_gmt":"2019-01-23T06:46:15","slug":"noip2018day1","status":"publish","type":"post","link":"https:\/\/wwwwodddd.com\/wordpress\/noip2018day1\/","title":{"rendered":"NOIP2018Day1"},"content":{"rendered":"

<\/p>\n

NOIP 2018 Day1<\/h1>\n

\u7b80\u4ecb<\/h2>\n

\u7b2c\u4e00\u5929\u9898\u76ee\u603b\u4f53\u6765\u8bf4\u662f\u8fd9\u4e9b\u5e74\u4e2d\u6bd4\u8f83\u7b80\u5355\u7684\u3002
\n\u4e09\u4e2a\u9898\u76ee\u90fd\u88ab\u8bf4\u662f\u539f\u9898\u3002
\n\u725b\u5ba2\u7248\u7684\u6570\u636e<\/a><\/p>\n

T1 \u94fa\u8bbe\u9053\u8def<\/h2>\n

\u9898\u76ee\u80cc\u666f<\/h3>\n

\u672c\u9898\u4e3b\u8981\u8003\u5bdf\u4e86\u6570\u5b66\u3002
\n \u672c\u9898\u548cNOIP2013\u7b2c\u4e00\u5929\u7b2c\u4e00\u9898\u4e00\u6a21\u4e00\u6837\uff0c\u6570\u636e\u8303\u56f4\uff0c\u8f93\u5165\u8f93\u51fa\u683c\u5f0f\uff0c\u6807\u7a0b\u505a\u6cd5\uff0c\u9898\u76ee\u4e3b\u4eba\u516c\u3002
\n \u53ea\u662f\u9898\u610f\u6709\u5fae\u5c0f\u7684\u5dee\u522b\u3002<\/p>\n

\u9898\u76ee\u5927\u610f<\/h3>\n

\u8f93\u5165\u4e00\u4e2a\u6570\u7ec4$a_i$\uff0c\u6bcf\u6b21\u53ef\u4ee5\u9009\u62e9\u4e00\u4e2a\u533a\u95f4\uff0c\u4f7f\u533a\u95f4\u5185\u7684\u6570\u5b57\u90fd\u51cf\u5c11$1$\u3002
\n \u5e0c\u671b\u628a\u6240\u6709\u6570\u5b57\u90fd\u53d8\u6210$0$\uff0c\u95ee\u6700\u5c11\u9700\u8981\u51e0\u6b21\u64cd\u4f5c\u3002<\/p>\n

\u9898\u76ee\u505a\u6cd5<\/h3>\n

\u6c42\u5dee\u5206\uff0c\u8003\u8651\u5dee\u5206\u4e2d\u6240\u6709\u6b63\u6570\u7684\u548c\u3002\uff08\u540c\u65f6\u4e5f\u662f\u6240\u6709\u8d1f\u6570\u548c\u7684\u76f8\u53cd\u6570\uff09<\/p>\n

\u53c2\u8003\u4ee3\u7801<\/h3>\n
#include <bits\/stdc++.h>\nusing namespace std;\nint n, z, x, l;\nint main() {\n    scanf(\"%d\", &n);\n    for (int i = 0; i < n; i++) {\n        scanf(\"%d\", &x);\n        z += max(x - l, 0);\n        l = x;\n    }\n    printf(\"%d\\n\", z);\n    return 0;\n}\n<\/code><\/pre>\n
T2 \u8d27\u5e01\u7cfb\u7edf<\/h2>\n
\u9898\u76ee\u80cc\u666f<\/h3>\n
\u672c\u9898\u4e3b\u8981\u8003\u5bdf\u4e86\u5b8c\u5168\u80cc\u5305\u548c\u52a8\u6001\u89c4\u5212\u3002
\n \u8fd9\u4e2a\u9898\u88ab\u8bf4BZOJ 2914\u4e00\u6837\uff0c\u6211\u89c9\u5f97\u8fd9\u4e2a\u9898\u6bd4BZOJ 2914\u7b80\u5355\u8bb8\u591a\u3002<\/p>\n
\u9898\u76ee\u5927\u610f<\/h3>\n
\u8f93\u5165$n$\u4e2a\u9762\u503c$a_i$\u8fd9\u4e9b\u9762\u503c\u53ef\u4ee5\u51d1\u51fa\u4e00\u4e9b\u91d1\u989d\u3002
\n \u95ee\u80fd\u51d1\u51fa\u8fd9\u6837\u7684\u91d1\u989d\u81f3\u5c11\u9700\u8981\u51e0\u4e2a\u9762\u503c\u3002
\n $n \\leq 100, a_i \\leq 25000$<\/p>\n
\u9898\u76ee\u505a\u6cd5<\/h3>\n
\u5c06\u6240\u6709\u9762\u503c\u6392\u5e8f\u3002
\n \u9762\u503c\u6700\u5c0f\u7684\u4e00\u5b9a\u8981\u9009\u3002
\n \u5982\u679c\u7528\u9762\u503c\u6700\u5c0f\u7684\u51d1\u4e0d\u51fa\u9762\u503c\u7b2c\u4e8c\u5c0f\u7684\uff0c\u90a3\u4e48\u8981\u9009\u7b2c\u4e8c\u5c0f\u7684\u3002\uff08\u5982\u679c\u51d1\u7684\u51fa\uff0c\u5c31\u4e0d\u7528\u9009\uff09
\n \u5bf9\u4e8e\u9762\u503c$x$\uff0c\u5982\u679c\u7528\u6bd4$x$\u5c0f\u7684\u9762\u503c\u51d1\u4e0d\u51fa$x$\uff0c\u5c31\u9700\u8981\u9009$x$\uff08\u5982\u679c\u51d1\u7684\u51fa\uff0c\u5c31\u4e0d\u7528\u9009\uff09
\n \u51d1\u5f97\u51fa\u51d1\u4e0d\u51fa\uff0c\u8fd9\u662f\u4e00\u4e2a\u5b8c\u5168\u80cc\u5305\u95ee\u9898\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u662f$O(n \\times a_i)$\u3002<\/p>\n
\u8fd8\u6709\u53e6\u4e00\u4e2a\u505a\u6cd5\uff0c\u76f4\u63a5\u5b8c\u5168\u80cc\u5305DP\u51fa\u51d1\u51fa\u6bcf\u4e2a\u91d1\u989d\u7684\u65b9\u6848\u6570\uff0c\u5224\u65ad\u6bcf\u4e2a\u9762\u503c\u7684\u65b9\u6848\u6570\u662f\u5426\u4e3a1\uff0c\u65b9\u6848\u6570\u8981\u53d6\u6a21\uff0c\u6216\u8005\u662f\u81ea\u7531\u8d8a\u754c\u3002\u8fd9\u4e2a\u65b9\u6cd5\u5e94\u8be5\u662f\u53ef\u4ee5\u88ab\u5361\u6389\u7684\uff0c\u4f46\u662f\u51fa\u9898\u4eba\u653e\u8fc7\u53bb\u4e86\u3002<\/p>\n
\u53c2\u8003\u4ee3\u7801<\/h3>\n
\u6392\u5e8fDP\u7684\u505a\u6cd5\u3002<\/p>\n
#include <bits\/stdc++.h>\nusing namespace std;\nint f[25020];\nint a[120];\nint t, n;\nint main() {\n    scanf(\"%d\", &t);\n    for (int tt = 0; tt < t; tt++) {\n        scanf(\"%d\", &n);\n        for (int i = 0; i < n; i++) {\n            scanf(\"%d\", &a[i]);\n        }\n        sort(a, a + n);\n        memset(f, 0, sizeof f);\n        f[0] = 1;\n        int z = 0;\n        for (int i = 0; i < n; i++) {\n            if (f[a[i]] == 0) {\n                z++;\n                for (int j = a[i]; j <= a[n - 1]; j++) {\n                    f[j] |= f[j - a[i]];\n                }\n            }\n        }\n        printf(\"%d\\n\", z);\n    }\n    return 0;\n}\n<\/code><\/pre>\n
\u65b9\u6848\u6570\u7684\u505a\u6cd5<\/p>\n
#include <bits\/stdc++.h>\nusing namespace std;\nint f[25020];\nint a[120];\nint t, n;\nint main() {\n    scanf(\"%d\", &t);\n    for (int tt = 0; tt < t; tt++) {\n        scanf(\"%d\", &n);\n        for (int i = 0; i < n; i++) {\n            scanf(\"%d\", &a[i]);\n        }\n        sort(a, a + n);\n        memset(f, 0, sizeof f);\n        f[0] = 1;\n        int z = 0;\n        for (int i = 0; i < n; i++) {\n            for (int j = a[i]; j <= a[n - 1]; j++) {\n                f[j] = (f[j] + f[j - a[i]]) % 10007;\n            }\n        }\n        for (int i = 0; i < n; i++) {\n            if (f[a[i]] == 1) {\n                z++;\n            }\n        }\n        printf(\"%d\\n\", z);\n    }\n    return 0;\n}\n<\/code><\/pre>\n
T3 \u8d5b\u9053\u4fee\u5efa<\/h2>\n
\u9898\u76ee\u80cc\u666f<\/h3>\n
\u672c\u9898\u4e3b\u8981\u8003\u5bdf\u4e86\u4e8c\u5206\u548c\u6811\u5f62\u52a8\u6001\u89c4\u5212\u3002
\n \u8fd9\u4e2a\u9898\u88ab\u8bf4BZOJ 2067\u4e00\u6837\uff0c\u6211\u89c9\u5f97\u8fd9\u4e2a\u9898\u6bd4BZOJ 2067\u975e\u5e38\u7c7b\u4f3c\u3002
\n \u90fd\u662f\u5148\u4e8c\u5206\uff0c\u518d\u6811\u5f62DP\uff0c\u6bcf\u4e2a\u70b9\u518d\u9700\u8981\u4e8c\u5206\u66f4\u65b0\u3002<\/p>\n
\u9898\u76ee\u5927\u610f<\/h3>\n
\u8f93\u5165\u4e00\u68f5$n$\u4e2a\u70b9\u7684\u6811\uff0c\u6709\u8fb9\u6743\uff0c\u4ece\u4e2d\u627e\u51fa$m$\u4e2a\u8fb9\u4e0d\u76f8\u4ea4\u7684\u94fe\uff08\u70b9\u53ef\u4ee5\u76f8\u4ea4\uff09\uff0c\u4f7f\u5f97\u6700\u77ed\u7684\u94fe\u6700\u957f\u3002
\n $n \\leq 50000, m < n$<\/p>\n
\u9898\u76ee\u505a\u6cd5<\/h3>\n
\u9996\u5148\u770b\u5230\u6700\u77ed\u7684\u94fe\u6700\u957f\uff0c\u663e\u7136\u60f3\u5230\u662f\u4e00\u4e2a\u4e8c\u5206\u3002
\n \u7136\u540e\u770b\u5230$n$\u7684\u8303\u56f4\uff0c\u6bcf\u4e2a\u70b9\u5e94\u8be5\u53ea\u6709\u5e38\u6570\u4e2a\u72b6\u6001\u3002
\n \u8fd9\u4e2a\u9898\u76ee\u5728DFS\u4e2d\u6709\u4e00\u4e2a\u6392\u5e8f\uff0c\u4e4b\u540e\u7684\u90e8\u5206\u4e00\u4e2a\u6bd4\u8f83\u7b80\u7b54\u7684\u5199\u6cd5\u662f\u4e8c\u5206
\n \uff08\u56e0\u4e3a\u5df2\u7ecf\u6709\u6392\u5e8f\u4e86\uff0c\u5e76\u4e0d\u589e\u52a0\u590d\u6742\u5ea6\uff09
\n \u53e6\u4e00\u4e2a\u60f3\u6cd5\u5c31\u662f\u53c2\u8003\u4ee3\u7801\u4e2d\u7684\u76f4\u63a5\u626b\u4e24\u904d\u3002<\/p>\n
\u53c2\u8003\u4ee3\u7801<\/h3>\n
#include <bits\/stdc++.h>\nusing namespace std;\nint n, m, x, y, z, M, cnt;\nvector<pair<int, int> > a[50020];\n\nint dfs(int x, int y) {\n    vector<int> b;\n    for (int i = 0; i < a[x].size(); i++) {\n        if (a[x][i].first != y) {\n            int l = dfs(a[x][i].first, x) + a[x][i].second;\n            if (l >= M) {\n                cnt++;\n            } else {\n                b.push_back(l);\n            }\n        }\n    }\n    b.push_back(0);\n    sort(b.begin(), b.end(), greater<int>());\n    int res = 0, ret = -1;\n    int L = 0, R = b.size() - 1;\n    while (L < R) {\n        if (b[L] + b[R] >= M) {\n            L++;\n            R--;\n            res++;\n        } else {\n            R--;\n        }\n    }\n    cnt += res;\n    L = res;\n    R = res + 1;\n    int tmp = 0;\n    while (R <= 2 * res) {\n        if (b[L] + b[R] >= M) {\n            L--;\n            R++;\n        } else {\n            if (tmp == 0) {\n                tmp++;\n                ret = b[L];\n                L--;\n            } else if (tmp == 1) {\n                tmp++;\n                break;\n            }\n        }\n    }\n    if (tmp == 0) {\n        return b[0];\n    } else if (tmp == 1) {\n        return ret;\n    }\n    L = 0;\n    R = 2 * res;\n    while (L < R) {\n        if (b[L] + b[R] >= M) {\n            L++;\n            R--;\n        } else {\n            return b[R];\n        }\n    }\n    return b[R];\n}\nbool ok() {\n    cnt = 0;\n    dfs(1, 0);\n    return cnt >= m;\n}\nint main() {\n    scanf(\"%d%d\", &n, &m);\n    for (int i = 1; i < n; i++) {\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    int L = 0, R = 1e9;\n    while (L < R - 1) {\n        M = (L + R) \/ 2;\n        if (ok()) {\n            L = M;\n        } else {\n            R = M;\n        }\n    }\n    printf(\"%d\\n\", L);\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":[],"class_list":["post-136","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wwwwodddd.com\/wordpress\/wp-json\/wp\/v2\/posts\/136","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=136"}],"version-history":[{"count":0,"href":"https:\/\/wwwwodddd.com\/wordpress\/wp-json\/wp\/v2\/posts\/136\/revisions"}],"wp:attachment":[{"href":"https:\/\/wwwwodddd.com\/wordpress\/wp-json\/wp\/v2\/media?parent=136"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wwwwodddd.com\/wordpress\/wp-json\/wp\/v2\/categories?post=136"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wwwwodddd.com\/wordpress\/wp-json\/wp\/v2\/tags?post=136"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}