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476Z\"><\/path><path stroke-width=\"0\" id=\"E178-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E178-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E178-MJMATHI-6C\" d=\"M117 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422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E178-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E178-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E178-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E178-MJMATHI-6E\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E178-MJMATHI-6C\" x=\"1752\" y=\"0\"><\/use><use xlink:href=\"#E178-MJMATHI-6F\" x=\"2050\" y=\"0\"><\/use><use xlink:href=\"#E178-MJMATHI-67\" x=\"2535\" y=\"0\"><\/use><use xlink:href=\"#E178-MJMATHI-6E\" x=\"3015\" y=\"0\"><\/use><use xlink:href=\"#E178-MJMAIN-29\" x=\"3615\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(nlogn)<\/script><br \/>\n\u5206\u6cbb\u65b9\u6cd5\u2160\uff1a\u6bd4\u8d77\u7b2c\u4e8c\u79cd\u8f83\u6162\u4f46\u662f\u7801\u91cf\u5c11\u4e00\u70b9<\/p>\n<pre><code class='language-c++' lang='c++'>struct Point\n{\n    double x, y;\n};\ntypedef vector&lt;Point&gt;::iterator Iter;\nbool cmpx(const Point a, const Point b) { return a.x &lt; b.x; }\nbool cmpy(const Point a, const Point b) { return a.y &lt; b.y; }\ndouble dis(const Point a, const Point b)\n{\n    return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));\n}\nvoid slv(const Iter l, const Iter r, double &amp;d)\n{\n    if (r - l &lt;= 1) return;\n    vector&lt;Point&gt; Q;\n    Iter t = l + (r - l) \/ 2;\n    double w = t-&gt;x;\n    slv(l, t, d), slv(t, r, d), inplace_merge(l, t, r, cmpy);\n    for (Iter x = l; x != r; ++x) if (abs(w - x-&gt;x) &lt;= d) Q.push_back(*x);\n    for (Iter x = Q.begin(), y = x; x != Q.end(); ++x)\n    {\n        while (y != Q.end() &amp;&amp; y-&gt;y &lt;= x-&gt;y + d) ++y;\n        for (Iter z = x + 1; z != y; ++z) d = min(d, dis(*x, *z));\n    }\n}\nvector&lt;Point&gt; Poi; int n;\ndouble preparata()\n{\n    double ans = 1e18;\n    sort(Poi.begin(),Poi.end(), cmpx);\n    slv(Poi.begin(),Poi.end(), ans);\n    return ans;\n}\n<\/code><\/pre>\n<p>\u5206\u6cbb\u65b9\u6cd5\u2161\uff1a\u6bd4\u7b2c\u4e00\u79cd\u66f4\u5feb\u4f46\u662f\u7801\u91cf\u5927\u4e00\u70b9<\/p>\n<pre><code class='language-c++' lang='c++'>struct pt\n{\n    double x, y;\n    int id;\n};\nbool cmpx(const pt a, const pt b) { return a.x &lt; b.x; }\nbool cmpy(const pt a, const pt b) { return a.y &lt; b.y; }\nint n, ansa, ansb; \/\/ \u7b54\u6848\u5728\u8fd9\nvector&lt;pt&gt; a;     \/\/ \u4e0b\u68070\u5f00\u59cb\ndouble mindist;\nvoid upd_ans(const pt &amp;a, const pt &amp;b)\n{\n    double dist = sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));\n    if (dist &lt; mindist)\n        mindist = dist, ansa = a.id, ansb = b.id;\n}\nvoid rec(int l, int r)\n{\n    if (r - l &lt;= 3) \/\/\u70b9\u6570\u5c0f\u4e8e3\u76f4\u63a5\u66b4\u529b\u627e\n    {\n        for (int i = l; i &lt;= r; ++i)\n            for (int j = i + 1; j &lt;= r; ++j)\n                upd_ans(a[i], a[j]);\n        sort(a.begin() + l, a.begin() + r + 1, cmpy);\n        return;\n    }\n    int m = (l + r) &gt;&gt; 1;\n    double midx = a[m].x;\n    rec(l, m), rec(m + 1, r);\n    \/\/\u5f52\u5e76\u6392\u5e8f\n    inplace_merge(a.begin() + l, a.begin() + m + 1, a.begin() + r + 1, cmpy);\n    static pt t[N]; \/\/ \u7f13\u5b58\u6570\u7ec4\n    int tsz = 0;\n    for (int i = l; i &lt;= r; ++i)\n        if (abs(a[i].x - midx) &lt; mindist) \/\/\u53ef\u80fd\u662f\u6700\u8fd1\u70b9\u5bf9\n        {\n            for (int j = tsz - 1; j &gt;= 0 &amp;&amp; a[i].y - t[j].y &lt; mindist; --j) upd_ans(a[i], t[j]);\n            t[tsz++] = a[i];\n        }\n}\nvoid preparata()\n{\n    sort(a.begin(), a.end(), cmpx);\n    mindist = (ll)1e18;\n    rec(0, n - 1);\n}\n<\/code><\/pre>\n<p>\u975e\u5206\u6cbb\uff1a\u66f4\u5feb\uff08\u5e38\u6570\u5c0f\uff09<\/p>\n<p><img src = \"https:\/\/linxce.ink\/wp-content\/uploads\/2024\/03\/image-20231008084140779.png\"><\/p>\n<pre><code class='language-c++' lang='c++'>int n;\ndouble ans = 1e20;\nstruct Point\n{\n    double x, y;\n    Point(double x = 0, double y = 0) : x(x), y(y) {}\n};\nstruct cmp_y { bool operator()(const Point &amp;a, const Point &amp;b) const { return a.y &lt; b.y; } };\nvoid upd_ans(const Point &amp;a, const Point &amp;b)\n{\n    double dist = sqrt(pow((a.x - b.x), 2) + pow((a.y - b.y), 2));\n    if (ans &gt; dist) ans = dist;\n}\nPoint a[N];\/\/\u4e0b\u68070\u5f00\u59cb\nmultiset&lt;Point, cmp_y&gt; s;\nvoid preparata()\n{\n    sort(a, a + n, [&amp;](Point a, Point b) -&gt; bool { return a.x &lt; b.x || (a.x == b.x &amp;&amp; a.y &lt; b.y); });\n    for (int i = 0, l = 0; i &lt; n; i++)\n    {\n        while (l &lt; i &amp;&amp; a[i].x - a[l].x &gt;= ans) s.erase(s.find(a[l++]));\n        for (auto it=s.lower_bound({a[i].x, a[i].y - ans}); it != s.end() &amp;&amp; it-&gt;y - a[i].y &lt; ans; it++)\n            upd_ans(*it, a[i]);\n        s.insert(a[i]);\n    }\n}\n<\/code><\/pre>\n<p><\/html><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5206\u6cbb\u552f\u4e00\u771f\u795e\uff0c\u62d2\u7edd\u4eba\u7c7b\u667a\u6167 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