{"id":76037,"date":"2026-02-13T21:05:24","date_gmt":"2026-02-13T13:05:24","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/76037.html"},"modified":"2026-02-13T21:05:24","modified_gmt":"2026-02-13T13:05:24","slug":"%e3%80%90%e6%8b%86%e4%bd%8d%e6%b3%95%e3%80%91p9277-agm-2023-%e8%b5%84%e6%a0%bc%e8%b5%9b-%e5%8f%8d%e8%bd%ac%e6%99%ae%e5%8f%8a","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/76037.html","title":{"rendered":"\u3010\u62c6\u4f4d\u6cd5\u3011P9277 [AGM 2023 \u8d44\u683c\u8d5b] \u53cd\u8f6c|\u666e\u53ca+"},"content":{"rendered":"

\u672c\u6587\u6d89\u53ca\u77e5\u8bc6\u70b9<\/h2>\n

\u4f4d\u8fd0\u7b97\u3001\u72b6\u6001\u538b\u7f29\u3001\u679a\u4e3e\u5b50\u96c6\u6c47\u603b<\/p>\n

P9277 [AGM 2023 \u8d44\u683c\u8d5b] \u53cd\u8f6c<\/h2>\n

\u9898\u76ee\u63cf\u8ff0<\/h3>\n

\u7ed9\u5b9a\u957f\u5ea6\u4e3a <\/p>\n

N<\/p>\n

N<\/p>\n

<\/span><\/span>N<\/span><\/span><\/span><\/span><\/span> \u7684\u5e8f\u5217 <\/p>\n

a<\/p>\n

a<\/p>\n

<\/span><\/span>a<\/span><\/span><\/span><\/span><\/span> \u6ee1\u8db3\u6bcf\u4e2a\u6570\u90fd\u5c0f\u4e8e <\/p>\n

2<\/p>\n

K<\/p>\n

2^K<\/p>\n

<\/span><\/span>2<\/span><\/span>K<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u4f60\u9700\u8981\u6267\u884c\u6070\u597d <\/p>\n

P<\/p>\n

P<\/p>\n

<\/span><\/span>P<\/span><\/span><\/span><\/span><\/span> \u6b21\u64cd\u4f5c，\u6bcf\u6b21\u64cd\u4f5c\u662f\u628a\u5176\u4e2d\u4e00\u4e2a\u6570\u7684\u67d0\u4e00\u4e2a\u4e8c\u8fdb\u5236\u4f4d\u53cd\u8f6c\u3002\u6700\u7ec8\u4f60\u9700\u8981\u4f7f\u5f97<\/p>\n

<\/p>\n

\u2211<\/p>\n

i<\/p>\n

\u2211<\/p>\n

j<\/p>\n

a<\/p>\n

i<\/p>\n

\u2295<\/p>\n

a<\/p>\n

j<\/p>\n

(<\/p>\n

i<\/p>\n

<<\/p>\n

j<\/p>\n

)<\/p>\n

\\\\sum_i\\\\sum_j a_i\\\\oplus a_j(i<j)<\/p>\n

<\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2295<\/span><\/span><\/span><\/span>a<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>i<\/span><\/span><<\/span><\/span><\/span><\/span>j<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u6700\u5927，\u5176\u4e2d <\/p>\n

\u2295<\/p>\n

\\\\oplus<\/p>\n

<\/span><\/span>\u2295<\/span><\/span><\/span><\/span><\/span> \u4e3a\u6309\u4f4d\u5f02\u6216\u8fd0\u7b97\u3002<\/p>\n

\u8f93\u5165\u683c\u5f0f<\/h3>\n

\u7b2c\u4e00\u884c\u5305\u542b\u6574\u6570 <\/p>\n

N<\/p>\n

\u3001<\/p>\n

K<\/p>\n

\u3001<\/p>\n

P<\/p>\n

N\u3001K\u3001P<\/p>\n

<\/span><\/span>N<\/span>\u3001<\/span>K<\/span>\u3001<\/span>P<\/span><\/span><\/span><\/span><\/span>，\u4fdd\u8bc1 <\/p>\n

1<\/p>\n

\u2264<\/p>\n

N<\/p>\n

\u2264<\/p>\n

10<\/p>\n

5<\/p>\n

,<\/p>\n

1<\/p>\n

\u2264<\/p>\n

K<\/p>\n

\u2264<\/p>\n

30<\/p>\n

,<\/p>\n

1<\/p>\n

\u2264<\/p>\n

P<\/p>\n

\u2264<\/p>\n

N<\/p>\n

\u00d7<\/p>\n

K<\/p>\n

1\u2264N\u226410^5,1\u2264K\u226430,1\u2264P\u2264N\\\\times K<\/p>\n

<\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>N<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>K<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>30<\/span>,<\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>P<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>N<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>K<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u4e0b\u4e00\u884c\u5305\u542b <\/p>\n

N<\/p>\n

N<\/p>\n

<\/span><\/span>N<\/span><\/span><\/span><\/span><\/span> \u4e2a\u6574\u6570，\u5373\u5e8f\u5217 <\/p>\n

a<\/p>\n

a<\/p>\n

<\/span><\/span>a<\/span><\/span><\/span><\/span><\/span>\u3002\u5bf9\u4e8e\u6240\u6709 <\/p>\n

1<\/p>\n

\u2264<\/p>\n

i<\/p>\n

\u2264<\/p>\n

N<\/p>\n

1\u2264i\u2264N<\/p>\n

<\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>i<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>N<\/span><\/span><\/span><\/span><\/span>，\u4fdd\u8bc1 <\/p>\n

0<\/p>\n

\u2264<\/p>\n

a<\/p>\n

i<\/p>\n

<<\/p>\n

2<\/p>\n

K<\/p>\n

0\u2264a_i<2^K<\/p>\n

<\/span><\/span>0<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>a<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><<\/span><\/span><\/span><\/span>2<\/span><\/span>K<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u8f93\u51fa\u683c\u5f0f<\/h3>\n

<\/p>\n

P<\/p>\n

P<\/p>\n

<\/span><\/span>P<\/span><\/span><\/span><\/span><\/span> \u884c，\u6bcf\u884c\u5305\u542b\u4e24\u4e2a\u6574\u6570 <\/p>\n

i<\/p>\n

i<\/p>\n

<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u548c <\/p>\n

j<\/p>\n

j<\/p>\n

<\/span><\/span>j<\/span><\/span><\/span><\/span><\/span>，\u6ee1\u8db3 <\/p>\n

1<\/p>\n

\u2264<\/p>\n

i<\/p>\n

\u2264<\/p>\n

N<\/p>\n

,<\/p>\n

0<\/p>\n

\u2264<\/p>\n

j<\/p>\n

<<\/p>\n

K<\/p>\n

1\u2264i\u2264N, 0\u2264j<K<\/p>\n

<\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>i<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>N<\/span>,<\/span><\/span>0<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>j<\/span><\/span><<\/span><\/span><\/span><\/span>K<\/span><\/span><\/span><\/span><\/span>，\u8868\u793a\u6570\u5b57 <\/p>\n

a<\/p>\n

i<\/p>\n

a_i<\/p>\n

<\/span><\/span>a<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u7b2c <\/p>\n

j<\/p>\n

j<\/p>\n

<\/span><\/span>j<\/span><\/span><\/span><\/span><\/span> \u4f4d\u53cd\u8f6c\u3002\u5373 <\/p>\n

a<\/p>\n

i<\/p>\n

\u2190<\/p>\n

a<\/p>\n

i<\/p>\n

\u2295<\/p>\n

2<\/p>\n

j<\/p>\n

a_i\\\\leftarrow a_i \\\\oplus 2^j<\/p>\n

<\/span><\/span>a<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2190<\/span><\/span><\/span><\/span>a<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2295<\/span><\/span><\/span><\/span>2<\/span><\/span>j<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u4f60\u53ef\u4ee5\u591a\u6b21\u53cd\u8f6c\u540c\u4e00\u4e2a\u4f4d\u3002\u5982\u679c\u6709\u591a\u4e2a\u4f7f\u603b\u548c\u6700\u5927\u5316\u7684\u89e3\u8f93\u51fa\u4efb\u610f\u4e00\u4e2a\u5373\u53ef\u3002<\/p>\n

\u8f93\u5165\u8f93\u51fa\u6837\u4f8b #1<\/h3>\n

\u8f93\u5165 #1<\/h4>\n

2 5 1
\n0 31<\/p>\n

\u8f93\u51fa #1<\/h4>\n

1 0<\/p>\n

\u8f93\u5165\u8f93\u51fa\u6837\u4f8b #2<\/h3>\n

\u8f93\u5165 #2<\/h4>\n

4 2 2
\n0 0 2 2<\/p>\n

\u8f93\u51fa #2<\/h4>\n

4 0
\n3 0<\/p>\n

\u8f93\u5165\u8f93\u51fa\u6837\u4f8b #3<\/h3>\n

\u8f93\u5165 #3<\/h4>\n

5 6 4
\n63 15 0 10 5<\/p>\n

\u8f93\u51fa #3<\/h4>\n

5 5
\n4 5
\n4 4
\n5 4<\/p>\n

P9277 [AGM 2023 \u8d44\u683c\u8d5b] \u53cd\u8f6c<\/h2>\n

\u4ece\u9ad8\u4f4d\u5f00\u59cb\u5904\u7406\u3002\u5982\u679c\u5904\u7406\u5b8c\u6240\u6709\u4f4d，\u8fd8\u6709\u5269\u4f59\u6b21\u6570\u3002\u5982\u679c\u662f\u5076\u6570，\u5bf9\u4efb\u610f\u6570\u4efb\u610f\u4f4d\u5904\u7406；\u5982\u679c\u5269\u4f59\u6b21\u6570\u662f\u5947\u6570，\u5219\u6700\u4f4e\u4f4d\u67d0\u4e2a\u6570\u7ffb\u8f6c\u4e00\u6b21， \u5176\u5b83\u6b21\u6570\u7ffb\u8f6c\u4efb\u610f\u6570\u4efb\u610f\u4f4d，\u5076\u6570\u6b21\u3002 \u5355\u72ec\u5904\u7406\u67d0\u4e00\u4f4d\u65f6，\u76f8\u5f53\u4e8eN\u54040\u30011\u3002\u5f02\u6216\u4e3a1\u7684\u6570\u5bf9\u6570\u4e3a：y1=(N-1)*N\/2 – \u5f02\u6216\u4e3a0\u7684\u6570\u91cf(y0)\u3002\u4ee41\u7684\u6570\u91cf\u4e3an1，\u5219\u5f02\u6216\u4e3a0\u7684\u6570\u91cf： y0= (n1-1)n1\/2 + (N – n1 -1 )(N-n1)\/2 \u53732y0 = n1n1-n1+NN-n1N-N-Nn1+n1n1+n1=2n1n1-2n1N+NN-N=-2n1(N-n1)+NN-N \u8981\u60f32y\u6700\u5c0f，\u5fc5\u987bn1(N-n1)\u6700\u5927\u3002\u5373\u5468\u957f\u4e00\u5b9a\u77e9\u5f62\u9762\u79ef\u6700\u5927\u3002\u9700\u8981n1\u548cN-n1\u6700\u63a5\u8fd1\u3002 v0\u548cv1\u8bb0\u5f55\u5404\u4f4d0\u548c1\u7684\u4e0b\u6807\u3002\u7a7a\u95f4\u590d\u6742\u5ea6：O(n) \u65f6\u95f4\u590d\u6742\u5ea6：O(nk)<\/p>\n

\u62c5\u5fc3\u8bc1\u660e\u9519\u8bef<\/h3>\n

\u6545\u66b4\u529b\u4e86 n <=10000\u3002\u6570\u636e\u8bc1\u660e\u6ca1\u6709\u9519\u8bef\u3002\u7ed3\u679c\u662f\u5c71\u9876\u6570\u7ec4\u3002<\/p>\n

for<\/span> (<\/span>int<\/span> i =<\/span> 1<\/span>;<\/span> i <=<\/span> 10000<\/span>;<\/span> i++<\/span>)<\/span> {<\/span>
\nvector<<\/span>long<\/span> long<\/span>><\/span> v;<\/span>
\nfor<\/span> (<\/span>long<\/span> long<\/span> j =<\/span> 0<\/span>;<\/span> j <=<\/span> i;<\/span> j++<\/span>)<\/span> {<\/span>
\nconst<\/span> long<\/span> long<\/span> k =<\/span> i –<\/span> j;<\/span>
\nconst<\/span> long<\/span> long<\/span> cur =<\/span> j *<\/span> (<\/span>j –<\/span> 1<\/span>)<\/span> \/<\/span> 2<\/span> +<\/span> k *<\/span> (<\/span>k –<\/span> 1<\/span>)<\/span> \/<\/span> 2<\/span>;<\/span>
\nv.<\/span>emplace_back<\/span>(<\/span>cur)<\/span>;<\/span>
\n}<\/span>
\nif<\/span> (<\/span>i &<\/span> 1<\/span>)<\/span> {<\/span>
\nfor<\/span> (<\/span>int<\/span> k =<\/span> 0<\/span>;<\/span> k +<\/span> 1<\/span> <=<\/span> i\/<\/span>2<\/span>;<\/span> k++<\/span>)<\/span> {<\/span>
\nassert<\/span>(<\/span>v[<\/span>k]<\/span> ><\/span> v[<\/span>k +<\/span> 1<\/span>]<\/span>)<\/span>;<\/span>
\n}<\/span>
\nassert<\/span>(<\/span>v[<\/span>i \/<\/span> 2<\/span>]<\/span> ==<\/span> v[<\/span>i \/<\/span> 2<\/span> +<\/span> 1<\/span>]<\/span>)<\/span>;<\/span>
\nfor<\/span> (<\/span>int<\/span> k =<\/span> i \/<\/span> 2<\/span> +<\/span> 1<\/span>;<\/span> k +<\/span> 1<\/span> <=<\/span> i;<\/span> k++<\/span>)<\/span> {<\/span>
\nassert<\/span>(<\/span>v[<\/span>k]<\/span> <<\/span> v[<\/span>k +<\/span> 1<\/span>]<\/span>)<\/span>;<\/span>
\n}<\/span>
\n}<\/span>
\nelse<\/span> {<\/span>
\nfor<\/span> (<\/span>int<\/span> k =<\/span> 0<\/span>;<\/span> k +<\/span> 1<\/span> <=<\/span> i \/<\/span> 2<\/span>;<\/span> k++<\/span>)<\/span> {<\/span>
\nassert<\/span>(<\/span>v[<\/span>k]<\/span> ><\/span> v[<\/span>k +<\/span> 1<\/span>]<\/span>)<\/span>;<\/span>
\n}<\/span><\/p>\n

for<\/span> (<\/span>int<\/span> k =<\/span> i \/<\/span> 2<\/span> ;<\/span> k +<\/span> 1<\/span> <=<\/span> i;<\/span> k++<\/span>)<\/span> {<\/span>
\nassert<\/span>(<\/span>v[<\/span>k]<\/span> <<\/span> v[<\/span>k +<\/span> 1<\/span>]<\/span>)<\/span>;<\/span>
\n}<\/span>
\n}<\/span><\/p>\n

}<\/span><\/p>\n

\u8fdb\u4e00\u6b65\u5206\u6790<\/h3>\n

\u5269\u4f59p\u662f\u5947\u6570\u3002 \u5982\u679cN\u662f\u5076\u6570，\u5404\u4f4d\u90fd\u662fN\/2\u4e2a0\u548cN\/2\u4e2a1\u3002\u7ffb\u8f6c\u6700\u4f4e\u4f4d\u548c\u53d8\u5c0f\u3002 \u5982\u679cN\u662f\u5947\u6570，N\/2\u4e2a0(1)\u6216N\/2+1\u4e2a1(0)\u3002\u53cd\u6b63N\/2+1\u4e2a\u7684，\u7ed3\u679c\u4e0d\u53d8\u3002 \u7ed3\u8bba：\u5269\u4f59\u6b21\u6570\u5168\u90e8\u7528\u6765\u7ffb\u8f6c\u6700\u4f4e\u4f4d\u591a\u7684\u6570\u3002\u5982\u679c0\u591a，\u7ffb\u8f6c0；1\u591a\u7ffb\u8f6c1\u3002\u76f8\u7b49\u7ffb\u8f6c0\u62161\u3002<\/p>\n

\u9519\u8bef\u4ee3\u7801<\/h3>\n

class<\/span> Solution<\/span> {<\/span>
\npublic<\/span>:<\/span>
\nvector<<\/span>pair<<\/span>int<\/span>,<\/span>int<\/span>>><\/span> Ans<\/span>(<\/span>const<\/span> int<\/span> N ,<\/span>const<\/span> int<\/span> K,<\/span>int<\/span> P,<\/span>const<\/span> vector<<\/span>int<\/span>><\/span>&<\/span> a)<\/span> {<\/span>
\nvector<<\/span>pair<<\/span>int<\/span>,<\/span> int<\/span>>><\/span> ans;<\/span>
\nfor<\/span> (<\/span>int<\/span> bit =<\/span> K –<\/span> 1<\/span>;<\/span> bit >=<\/span> 0<\/span>;<\/span> bit—<\/span>)<\/span> {<\/span>
\nvector<<\/span>int<\/span>><\/span> v0,<\/span> v1;<\/span>
\nauto<\/span> Do =<\/span> [<\/span>&<\/span>]<\/span>(<\/span>)<\/span> {<\/span>
\nP—<\/span>;<\/span>
\nif<\/span> (<\/span>v0.<\/span>size<\/span>(<\/span>)<\/span> <<\/span> v1.<\/span>size<\/span>(<\/span>)<\/span>)<\/span> {<\/span>
\nswap<\/span>(<\/span>v0,<\/span> v1)<\/span>;<\/span>
\n}<\/span>
\nans.<\/span>emplace_back<\/span>(<\/span>v0.<\/span>back<\/span>(<\/span>)<\/span>+<\/span>1<\/span>,<\/span> bit)<\/span>;<\/span>
\nv1.<\/span>emplace_back<\/span>(<\/span>v0.<\/span>back<\/span>(<\/span>)<\/span>)<\/span>;<\/span>
\nv0.<\/span>pop_back<\/span>(<\/span>)<\/span>;<\/span>
\n}<\/span>;<\/span>
\nfor<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> N;<\/span> i++<\/span>)<\/span> {<\/span>
\nif<\/span> (<\/span>(<\/span>1<\/span> <<<\/span> bit)<\/span> &<\/span> a[<\/span>i]<\/span>)<\/span> {<\/span>
\nv1.<\/span>emplace_back<\/span>(<\/span>i)<\/span>;<\/span>
\n}<\/span>
\nelse<\/span> {<\/span>
\nv0.<\/span>emplace_back<\/span>(<\/span>i)<\/span>;<\/span>
\n}<\/span>
\n}<\/span>
\nwhile<\/span> (<\/span>P &&<\/span> (<\/span>fabs<\/span>(<\/span>v0.<\/span>size<\/span>(<\/span>)<\/span> –<\/span> v1.<\/span>size<\/span>(<\/span>)<\/span>)<\/span> ><\/span> 1<\/span>)<\/span>)<\/span> {<\/span>
\nDo<\/span>(<\/span>)<\/span>;<\/span>
\n}<\/span>
\nwhile<\/span> (<\/span>P &&<\/span>(<\/span>0<\/span>==<\/span>bit)<\/span>)<\/span> {<\/span>
\nDo<\/span>(<\/span>)<\/span>;<\/span>
\n}<\/span>
\n}<\/span>
\nreturn<\/span> ans;<\/span>
\n}<\/span>
\n}<\/span>;<\/span><\/p>\n

\u9519\u8bef\u539f\u56e0：\u4e0d\u80fd\u4ece\u9ad8\u5230\u4f4e\u4f4d\u5904\u7406<\/h3>\n

\u7b2cbit\u4f4d\u6709c0\u4e2a0，c1\u4e2a1\u3002mi= min(c0,c1) ma=max(c0,c1)\u3002 \u5219\u6b64\u4f4d\u4e4b\u548c\u662f：<\/p>\n

c<\/p>\n

0<\/p>\n

\u2217<\/p>\n

c<\/p>\n

1<\/p>\n

\u2217<\/p>\n

(<\/p>\n

1<\/p>\n

L<\/p>\n

L<\/p>\n

<<\/p>\n

<<\/p>\n

b<\/p>\n

i<\/p>\n

t<\/p>\n

)<\/p>\n

c0*c1*(1LL<<bit)<\/p>\n

<\/span><\/span>c<\/span>0<\/span><\/span>\u2217<\/span><\/span><\/span><\/span>c<\/span>1<\/span><\/span>\u2217<\/span><\/span><\/span><\/span>(<\/span>1<\/span>LL<\/span><\/span><<<\/span><\/span><\/span><\/span>bi<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span>\u7cbe\u7b80 \u5982\u679cma-mi > 1，\u5219ma\u2013,mi++\u662f\u66f4\u4f18\u89e3\u3002\u589e\u52a0：<\/p>\n

f<\/p>\n

(<\/p>\n

m<\/p>\n

i<\/p>\n

)<\/p>\n

=<\/p>\n

(<\/p>\n

m<\/p>\n

i<\/p>\n

+<\/p>\n

1<\/p>\n

)<\/p>\n

\u00d7<\/p>\n

(<\/p>\n

m<\/p>\n

a<\/p>\n

\u2212<\/p>\n

1<\/p>\n

)<\/p>\n

\u2212<\/p>\n

m<\/p>\n

i<\/p>\n

\u00d7<\/p>\n

m<\/p>\n

a<\/p>\n

=<\/p>\n

m<\/p>\n

i<\/p>\n

\u00d7<\/p>\n

m<\/p>\n

a<\/p>\n

+<\/p>\n

m<\/p>\n

a<\/p>\n

\u2212<\/p>\n

m<\/p>\n

i<\/p>\n

\u2212<\/p>\n

1<\/p>\n

\u2212<\/p>\n

m<\/p>\n

i<\/p>\n

\u00d7<\/p>\n

m<\/p>\n

a<\/p>\n

=<\/p>\n

m<\/p>\n

a<\/p>\n

\u2212<\/p>\n

m<\/p>\n

i<\/p>\n

\u2212<\/p>\n

1<\/p>\n

=<\/p>\n

m<\/p>\n

a<\/p>\n

\u2212<\/p>\n

(<\/p>\n

N<\/p>\n

\u2212<\/p>\n

m<\/p>\n

a<\/p>\n

)<\/p>\n

\u2212<\/p>\n

1<\/p>\n

=<\/p>\n

2<\/p>\n

m<\/p>\n

a<\/p>\n

\u2212<\/p>\n

N<\/p>\n

\u2212<\/p>\n

1<\/p>\n

f(mi)=(mi+1)\\\\times(ma-1)- mi \\\\times ma=mi \\\\times ma +ma – mi-1- mi \\\\times ma =ma-mi-1=ma-(N-ma)-1=2ma-N-1<\/p>\n

<\/span><\/span>f<\/span>(<\/span>mi<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>mi<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span>)<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>(<\/span>ma<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>mi<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>ma<\/span><\/span>=<\/span><\/span><\/span><\/span>mi<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>ma<\/span><\/span>+<\/span><\/span><\/span><\/span>ma<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>mi<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>mi<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>ma<\/span><\/span>=<\/span><\/span><\/span><\/span>ma<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>mi<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span>=<\/span><\/span><\/span><\/span>ma<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>(<\/span>N<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>ma<\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span>ma<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>N<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u5c06\u5404\u4f4d\u7684f(mi)*(1LL<<bit)\u653e\u5230\u5927\u6839\u5806\u4e2d\u3002 vv0[bit] \u8bb0\u5f55\u7b2cbit\u4f4d\u662f0\u7684\u4e0b\u6807，vv1[bit] \u8bb0\u5f55\u7b2cbit\u4f4d\u662f1\u7684\u4e0b\u6807\u3002\u6bcf\u6b21Do\u51fd\u6570\u4e4b\u524d，\u5982\u679cvv0[bit].size() < vv1[bit].size() \u5219swap(vv[0],vv[1])\u3002<\/p>\n

\u4ee3\u7801<\/h2>\n

\u6838\u5fc3\u4ee3\u7801<\/h3>\n

#<\/span>include<\/span> <iostream><\/span><\/span>
\n#<\/span>include<\/span> <sstream><\/span><\/span>
\n#<\/span>include<\/span> <vector><\/span><\/span>
\n#<\/span>include<\/span><map><\/span><\/span>
\n#<\/span>include<\/span><unordered_map><\/span><\/span>
\n#<\/span>include<\/span><set><\/span><\/span>
\n#<\/span>include<\/span><unordered_set><\/span><\/span>
\n#<\/span>include<\/span><string><\/span><\/span>
\n#<\/span>include<\/span><algorithm><\/span><\/span>
\n#<\/span>include<\/span><functional><\/span><\/span>
\n#<\/span>include<\/span><queue><\/span><\/span>
\n#<\/span>include<\/span> <stack><\/span><\/span>
\n#<\/span>include<\/span><iomanip><\/span><\/span>
\n#<\/span>include<\/span><numeric><\/span><\/span>
\n#<\/span>include<\/span> <math.h><\/span><\/span>
\n#<\/span>include<\/span> <climits><\/span><\/span>
\n#<\/span>include<\/span><assert.h><\/span><\/span>
\n#<\/span>include<\/span><cstring><\/span><\/span>
\n#<\/span>include<\/span><list><\/span><\/span>
\n#<\/span>include<\/span><array><\/span><\/span><\/p>\n

#<\/span>include<\/span> <bitset><\/span><\/span>
\nusing<\/span> namespace<\/span> std;<\/span><\/p>\n

template<\/span><<\/span>class<\/span> T1<\/span>,<\/span> class<\/span> T2<\/span>><\/span>
\nstd::<\/span>istream&<\/span> operator<\/span> >><\/span> (<\/span>std::<\/span>istream&<\/span> in,<\/span> pair<<\/span>T1,<\/span> T2><\/span>&<\/span> pr)<\/span> {<\/span>
\nin >><\/span> pr.<\/span>first >><\/span> pr.<\/span>second;<\/span>
\nreturn<\/span> in;<\/span>
\n}<\/span><\/p>\n

template<\/span><<\/span>class<\/span> T1<\/span>,<\/span> class<\/span> T2<\/span>,<\/span> class<\/span> T3<\/span> ><\/span>
\nstd::<\/span>istream&<\/span> operator<\/span> >><\/span> (<\/span>std::<\/span>istream&<\/span> in,<\/span> tuple<<\/span>T1,<\/span> T2,<\/span> T3><\/span>&<\/span> t)<\/span> {<\/span>
\nin >><\/span> get<\/span><<\/span>0<\/span>><\/span><\/span><\/span>(<\/span>t)<\/span> >><\/span> get<\/span><<\/span>1<\/span>><\/span><\/span><\/span>(<\/span>t)<\/span> >><\/span> get<\/span><<\/span>2<\/span>><\/span><\/span><\/span>(<\/span>t)<\/span>;<\/span>
\nreturn<\/span> in;<\/span>
\n}<\/span><\/p>\n

template<\/span><<\/span>class<\/span> T1<\/span>,<\/span> class<\/span> T2<\/span>,<\/span> class<\/span> T3<\/span>,<\/span> class<\/span> T4<\/span> ><\/span>
\nstd::<\/span>istream&<\/span> operator<\/span> >><\/span> (<\/span>std::<\/span>istream&<\/span> in,<\/span> tuple<<\/span>T1,<\/span> T2,<\/span> T3,<\/span> T4><\/span>&<\/span> t)<\/span> {<\/span>
\nin >><\/span> get<\/span><<\/span>0<\/span>><\/span><\/span><\/span>(<\/span>t)<\/span> >><\/span> get<\/span><<\/span>1<\/span>><\/span><\/span><\/span>(<\/span>t)<\/span> >><\/span> get<\/span><<\/span>2<\/span>><\/span><\/span><\/span>(<\/span>t)<\/span> >><\/span> get<\/span><<\/span>3<\/span>><\/span><\/span><\/span>(<\/span>t)<\/span>;<\/span>
\nreturn<\/span> in;<\/span>
\n}<\/span><\/p>\n

template<\/span><<\/span>class<\/span> T<\/span> =<\/span> int<\/span>><\/span>
\nvector<<\/span>T><\/span> Read<\/span>(<\/span>)<\/span> {<\/span>
\nint<\/span> n;<\/span>
\ncin >><\/span> n;<\/span>
\nvector<<\/span>T><\/span> ret<\/span>(<\/span>n)<\/span>;<\/span>
\nfor<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> i++<\/span>)<\/span> {<\/span>
\ncin >><\/span> ret[<\/span>i]<\/span>;<\/span>
\n}<\/span>
\nreturn<\/span> ret;<\/span>
\n}<\/span>
\ntemplate<\/span><<\/span>class<\/span> T<\/span> =<\/span> int<\/span>><\/span>
\nvector<<\/span>T><\/span> ReadNotNum<\/span>(<\/span>)<\/span> {<\/span>
\nvector<<\/span>T><\/span> ret;<\/span>
\nT tmp;<\/span>
\nwhile<\/span> (<\/span>cin >><\/span> tmp)<\/span> {<\/span>
\nret.<\/span>emplace_back<\/span>(<\/span>tmp)<\/span>;<\/span>
\nif<\/span> (<\/span>'\\\\n'<\/span> ==<\/span> cin.<\/span>get<\/span>(<\/span>)<\/span>)<\/span> {<\/span> break<\/span>;<\/span> }<\/span>
\n}<\/span>
\nreturn<\/span> ret;<\/span>
\n}<\/span><\/p>\n

template<\/span><<\/span>class<\/span> T<\/span> =<\/span> int<\/span>><\/span>
\nvector<<\/span>T><\/span> Read<\/span>(<\/span>int<\/span> n)<\/span> {<\/span>
\nvector<<\/span>T><\/span> ret<\/span>(<\/span>n)<\/span>;<\/span>
\nfor<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> i++<\/span>)<\/span> {<\/span>
\ncin >><\/span> ret[<\/span>i]<\/span>;<\/span>
\n}<\/span>
\nreturn<\/span> ret;<\/span>
\n}<\/span><\/p>\n

template<\/span><<\/span>int<\/span> N =<\/span> 1'000'000<\/span>><\/span>
\nclass<\/span> COutBuff<\/span>
\n{<\/span>
\npublic<\/span>:<\/span>
\nCOutBuff<\/span>(<\/span>)<\/span> {<\/span>
\nm_p =<\/span> puffer;<\/span>
\n}<\/span>
\ntemplate<\/span><<\/span>class<\/span> T<\/span>><\/span>
\nvoid<\/span> write<\/span>(<\/span>T x)<\/span> {<\/span>
\nint<\/span> num[<\/span>28<\/span>]<\/span>,<\/span> sp =<\/span> 0<\/span>;<\/span>
\nif<\/span> (<\/span>x <<\/span> 0<\/span>)<\/span>
\n*<\/span>m_p++<\/span> =<\/span> '-'<\/span>,<\/span> x =<\/span> –<\/span>x;<\/span><\/p>\n

if<\/span> (<\/span>!<\/span>x)<\/span>
\n*<\/span>m_p++<\/span> =<\/span> 48<\/span>;<\/span><\/p>\n

while<\/span> (<\/span>x)<\/span>
\nnum[<\/span>++<\/span>sp]<\/span> =<\/span> x %<\/span> 10<\/span>,<\/span> x \/=<\/span> 10<\/span>;<\/span><\/p>\n

while<\/span> (<\/span>sp)<\/span>
\n*<\/span>m_p++<\/span> =<\/span> num[<\/span>sp—<\/span>]<\/span> +<\/span> 48<\/span>;<\/span>
\nAuotToFile<\/span>(<\/span>)<\/span>;<\/span>
\n}<\/span>
\nvoid<\/span> writestr<\/span>(<\/span>const<\/span> char<\/span>*<\/span> sz)<\/span> {<\/span>
\nstrcpy<\/span>(<\/span>m_p,<\/span> sz)<\/span>;<\/span>
\nm_p +=<\/span> strlen<\/span>(<\/span>sz)<\/span>;<\/span>
\nAuotToFile<\/span>(<\/span>)<\/span>;<\/span>
\n}<\/span>
\ninline<\/span> void<\/span> write<\/span>(<\/span>char<\/span> ch)<\/span>
\n{<\/span>
\n*<\/span>m_p++<\/span> =<\/span> ch;<\/span>
\nAuotToFile<\/span>(<\/span>)<\/span>;<\/span>
\n}<\/span>
\ninline<\/span> void<\/span> ToFile<\/span>(<\/span>)<\/span> {<\/span>
\nfwrite<\/span>(<\/span>puffer,<\/span> 1<\/span>,<\/span> m_p –<\/span> puffer,<\/span> stdout<\/span>)<\/span>;<\/span>
\nm_p =<\/span> puffer;<\/span>
\n}<\/span>
\n~<\/span>COutBuff<\/span>(<\/span>)<\/span> {<\/span>
\nToFile<\/span>(<\/span>)<\/span>;<\/span>
\n}<\/span>
\nprivate<\/span>:<\/span>
\ninline<\/span> void<\/span> AuotToFile<\/span>(<\/span>)<\/span> {<\/span>
\nif<\/span> (<\/span>m_p –<\/span> puffer ><\/span> N –<\/span> 100<\/span>)<\/span> {<\/span>
\nToFile<\/span>(<\/span>)<\/span>;<\/span>
\n}<\/span>
\n}<\/span>
\nchar<\/span> puffer[<\/span>N]<\/span>,<\/span> *<\/span> m_p;<\/span>
\n}<\/span>;<\/span><\/p>\n

template<\/span><<\/span>int<\/span> N =<\/span> 1'000'000<\/span>><\/span>
\nclass<\/span> CInBuff<\/span>
\n{<\/span>
\npublic<\/span>:<\/span>
\ninline<\/span> CInBuff<\/span>(<\/span>)<\/span> {<\/span>}<\/span>
\ninline<\/span> CInBuff<<\/span>N><\/span>&<\/span> operator<\/span>>><\/span>(<\/span>char<\/span>&<\/span> ch)<\/span> {<\/span>
\nFileToBuf<\/span>(<\/span>)<\/span>;<\/span>
\nwhile<\/span> (<\/span>(<\/span>'\\\\r'<\/span> ==<\/span> *<\/span>S)<\/span> ||<\/span> (<\/span>'\\\\n'<\/span> ==<\/span> *<\/span>S)<\/span> ||<\/span> (<\/span>' '<\/span> ==<\/span> *<\/span>S)<\/span>)<\/span> {<\/span> S++<\/span>;<\/span> }<\/span>\/\/\u5ffd\u7565\u7a7a\u683c\u548c\u56de\u8f66<\/span>
\nch =<\/span> *<\/span>S++<\/span>;<\/span>
\nreturn<\/span> *<\/span>this<\/span>;<\/span>
\n}<\/span>
\ninline<\/span> CInBuff<<\/span>N><\/span>&<\/span> operator<\/span>>><\/span>(<\/span>int<\/span>&<\/span> val)<\/span> {<\/span>
\nFileToBuf<\/span>(<\/span>)<\/span>;<\/span>
\nint<\/span> x<\/span>(<\/span>0<\/span>)<\/span>,<\/span> f<\/span>(<\/span>0<\/span>)<\/span>;<\/span>
\nwhile<\/span> (<\/span>!<\/span>isdigit<\/span>(<\/span>*<\/span>S)<\/span>)<\/span>
\nf |=<\/span> (<\/span>*<\/span>S++<\/span> ==<\/span> '-'<\/span>)<\/span>;<\/span>
\nwhile<\/span> (<\/span>isdigit<\/span>(<\/span>*<\/span>S)<\/span>)<\/span>
\nx =<\/span> (<\/span>x <<<\/span> 1<\/span>)<\/span> +<\/span> (<\/span>x <<<\/span> 3<\/span>)<\/span> +<\/span> (<\/span>*<\/span>S++<\/span> ^<\/span> 48<\/span>)<\/span>;<\/span>
\nval =<\/span> f ?<\/span> –<\/span>x :<\/span> x;<\/span> S++<\/span>;<\/span>\/\/\u5ffd\u7565\u7a7a\u683c\u6362\u884c<\/span>
\nreturn<\/span> *<\/span>this<\/span>;<\/span>
\n}<\/span>
\ninline<\/span> CInBuff&<\/span> operator<\/span>>><\/span>(<\/span>long<\/span> long<\/span>&<\/span> val)<\/span> {<\/span>
\nFileToBuf<\/span>(<\/span>)<\/span>;<\/span>
\nlong<\/span> long<\/span> x<\/span>(<\/span>0<\/span>)<\/span>;<\/span> int<\/span> f<\/span>(<\/span>0<\/span>)<\/span>;<\/span>
\nwhile<\/span> (<\/span>!<\/span>isdigit<\/span>(<\/span>*<\/span>S)<\/span>)<\/span>
\nf |=<\/span> (<\/span>*<\/span>S++<\/span> ==<\/span> '-'<\/span>)<\/span>;<\/span>
\nwhile<\/span> (<\/span>isdigit<\/span>(<\/span>*<\/span>S)<\/span>)<\/span>
\nx =<\/span> (<\/span>x <<<\/span> 1<\/span>)<\/span> +<\/span> (<\/span>x <<<\/span> 3<\/span>)<\/span> +<\/span> (<\/span>*<\/span>S++<\/span> ^<\/span> 48<\/span>)<\/span>;<\/span>
\nval =<\/span> f ?<\/span> –<\/span>x :<\/span> x;<\/span> S++<\/span>;<\/span>\/\/\u5ffd\u7565\u7a7a\u683c\u6362\u884c<\/span>
\nreturn<\/span> *<\/span>this<\/span>;<\/span>
\n}<\/span>
\ntemplate<\/span><<\/span>class<\/span> T1<\/span>,<\/span> class<\/span> T2<\/span>><\/span>
\ninline<\/span> CInBuff&<\/span> operator<\/span>>><\/span>(<\/span>pair<<\/span>T1,<\/span> T2><\/span>&<\/span> val)<\/span> {<\/span>
\n*<\/span>this<\/span> >><\/span> val.<\/span>first >><\/span> val.<\/span>second;<\/span>
\nreturn<\/span> *<\/span>this<\/span>;<\/span>
\n}<\/span>
\ntemplate<\/span><<\/span>class<\/span> T1<\/span>,<\/span> class<\/span> T2<\/span>,<\/span> class<\/span> T3<\/span>><\/span>
\ninline<\/span> CInBuff&<\/span> operator<\/span>>><\/span>(<\/span>tuple<<\/span>T1,<\/span> T2,<\/span> T3><\/span>&<\/span> val)<\/span> {<\/span>
\n*<\/span>this<\/span> >><\/span> get<\/span><<\/span>0<\/span>><\/span><\/span><\/span>(<\/span>val)<\/span> >><\/span> get<\/span><<\/span>1<\/span>><\/span><\/span><\/span>(<\/span>val)<\/span> >><\/span> get<\/span><<\/span>2<\/span>><\/span><\/span><\/span>(<\/span>val)<\/span>;<\/span>
\nreturn<\/span> *<\/span>this<\/span>;<\/span>
\n}<\/span>
\ntemplate<\/span><<\/span>class<\/span> T1<\/span>,<\/span> class<\/span> T2<\/span>,<\/span> class<\/span> T3<\/span>,<\/span> class<\/span> T4<\/span>><\/span>
\ninline<\/span> CInBuff&<\/span> operator<\/span>>><\/span>(<\/span>tuple<<\/span>T1,<\/span> T2,<\/span> T3,<\/span> T4><\/span>&<\/span> val)<\/span> {<\/span>
\n*<\/span>this<\/span> >><\/span> get<\/span><<\/span>0<\/span>><\/span><\/span><\/span>(<\/span>val)<\/span> >><\/span> get<\/span><<\/span>1<\/span>><\/span><\/span><\/span>(<\/span>val)<\/span> >><\/span> get<\/span><<\/span>2<\/span>><\/span><\/span><\/span>(<\/span>val)<\/span> >><\/span> get<\/span><<\/span>3<\/span>><\/span><\/span><\/span>(<\/span>val)<\/span>;<\/span>
\nreturn<\/span> *<\/span>this<\/span>;<\/span>
\n}<\/span>
\ntemplate<\/span><<\/span>class<\/span> T<\/span> =<\/span> int<\/span>><\/span>
\ninline<\/span> CInBuff&<\/span> operator<\/span>>><\/span>(<\/span>vector<<\/span>T><\/span>&<\/span> val)<\/span> {<\/span>
\nint<\/span> n;<\/span>
\n*<\/span>this<\/span> >><\/span> n;<\/span>
\nval.<\/span>resize<\/span>(<\/span>n)<\/span>;<\/span>
\nfor<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> i++<\/span>)<\/span> {<\/span>
\n*<\/span>this<\/span> >><\/span> val[<\/span>i]<\/span>;<\/span>
\n}<\/span>
\nreturn<\/span> *<\/span>this<\/span>;<\/span>
\n}<\/span>
\ntemplate<\/span><<\/span>class<\/span> T<\/span> =<\/span> int<\/span>><\/span>
\nvector<<\/span>T><\/span> Read<\/span>(<\/span>int<\/span> n)<\/span> {<\/span>
\nvector<<\/span>T><\/span> ret<\/span>(<\/span>n)<\/span>;<\/span>
\nfor<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> i++<\/span>)<\/span> {<\/span>
\n*<\/span>this<\/span> >><\/span> ret[<\/span>i]<\/span>;<\/span>
\n}<\/span>
\nreturn<\/span> ret;<\/span>
\n}<\/span>
\ntemplate<\/span><<\/span>class<\/span> T<\/span> =<\/span> int<\/span>><\/span>
\nvector<<\/span>T><\/span> Read<\/span>(<\/span>)<\/span> {<\/span>
\nvector<<\/span>T><\/span> ret;<\/span>
\n*<\/span>this<\/span> >><\/span> ret;<\/span>
\nreturn<\/span> ret;<\/span>
\n}<\/span>
\nprivate<\/span>:<\/span>
\ninline<\/span> void<\/span> FileToBuf<\/span>(<\/span>)<\/span> {<\/span>
\nconst<\/span> int<\/span> canRead =<\/span> m_iWritePos –<\/span> (<\/span>S –<\/span> buffer)<\/span>;<\/span>
\nif<\/span> (<\/span>canRead >=<\/span> 100<\/span>)<\/span> {<\/span> return<\/span>;<\/span> }<\/span>
\nif<\/span> (<\/span>m_bFinish)<\/span> {<\/span> return<\/span>;<\/span> }<\/span>
\nfor<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> canRead;<\/span> i++<\/span>)<\/span>
\n{<\/span>
\nbuffer[<\/span>i]<\/span> =<\/span> S[<\/span>i]<\/span>;<\/span>\/\/memcpy\u51fa\u9519<\/span>
\n}<\/span>
\nm_iWritePos =<\/span> canRead;<\/span>
\nbuffer[<\/span>m_iWritePos]<\/span> =<\/span> 0<\/span>;<\/span>
\nS =<\/span> buffer;<\/span>
\nint<\/span> readCnt =<\/span> fread<\/span>(<\/span>buffer +<\/span> m_iWritePos,<\/span> 1<\/span>,<\/span> N –<\/span> m_iWritePos,<\/span> stdin<\/span>)<\/span>;<\/span>
\nif<\/span> (<\/span>readCnt <=<\/span> 0<\/span>)<\/span> {<\/span> m_bFinish =<\/span> true<\/span>;<\/span> return<\/span>;<\/span> }<\/span>
\nm_iWritePos +=<\/span> readCnt;<\/span>
\nbuffer[<\/span>m_iWritePos]<\/span> =<\/span> 0<\/span>;<\/span>
\nS =<\/span> buffer;<\/span>
\n}<\/span>
\nint<\/span> m_iWritePos =<\/span> 0<\/span>;<\/span> bool<\/span> m_bFinish =<\/span> false<\/span>;<\/span>
\nchar<\/span> buffer[<\/span>N +<\/span> 10<\/span>]<\/span>,<\/span> *<\/span> S =<\/span> buffer;<\/span>
\n}<\/span>;<\/span><\/p>\n

class<\/span> Solution<\/span> {<\/span>
\npublic<\/span>:<\/span>
\nvector<<\/span>pair<<\/span>int<\/span>,<\/span> int<\/span>>><\/span> Ans<\/span>(<\/span>const<\/span> int<\/span> N,<\/span> const<\/span> int<\/span> K,<\/span> int<\/span> P,<\/span> const<\/span> vector<<\/span>int<\/span>><\/span>&<\/span> a)<\/span> {<\/span>
\nvector<<\/span>pair<<\/span>int<\/span>,<\/span> int<\/span>>><\/span> ans;<\/span>
\nvector<<\/span>vector<<\/span>int<\/span>>><\/span> vv0<\/span>(<\/span>K)<\/span>,<\/span> vv1<\/span>(<\/span>K)<\/span>;<\/span>
\npriority_queue<<\/span>pair<<\/span>long<\/span> long<\/span>,<\/span> int<\/span>>><\/span> maxHeap;<\/span>
\nfor<\/span> (<\/span>int<\/span> bit =<\/span> K –<\/span> 1<\/span>;<\/span> bit >=<\/span> 0<\/span>;<\/span> bit—<\/span>)<\/span> {<\/span>
\nfor<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> N;<\/span> i++<\/span>)<\/span> {<\/span>
\nif<\/span> (<\/span>(<\/span>1<\/span> <<<\/span> bit)<\/span> &<\/span> a[<\/span>i]<\/span>)<\/span> {<\/span>
\nvv1[<\/span>bit]<\/span>.<\/span>emplace_back<\/span>(<\/span>i)<\/span>;<\/span>
\n}<\/span>
\nelse<\/span> {<\/span>
\nvv0[<\/span>bit]<\/span>.<\/span>emplace_back<\/span>(<\/span>i)<\/span>;<\/span>
\n}<\/span>
\n}<\/span>
\nauto<\/span>&<\/span> v0 =<\/span> vv0[<\/span>bit]<\/span>;<\/span>
\nauto<\/span>&<\/span> v1 =<\/span> vv1[<\/span>bit]<\/span>;<\/span>
\nif<\/span> (<\/span>v0.<\/span>size<\/span>(<\/span>)<\/span> <<\/span> v1.<\/span>size<\/span>(<\/span>)<\/span>)<\/span> {<\/span>
\nswap<\/span>(<\/span>v0,<\/span> v1)<\/span>;<\/span>
\n}<\/span>
\nif<\/span> (<\/span>v0.<\/span>size<\/span>(<\/span>)<\/span> –<\/span> v1.<\/span>size<\/span>(<\/span>)<\/span> ><\/span> 1<\/span>)<\/span>
\n{<\/span>
\nmaxHeap.<\/span>emplace<\/span>(<\/span>(<\/span>1LL<\/span> <<<\/span> bit)<\/span> *<\/span> (<\/span>2<\/span> *<\/span> v0.<\/span>size<\/span>(<\/span>)<\/span> –<\/span> N –<\/span> 1<\/span>)<\/span>,<\/span> bit)<\/span>;<\/span>
\n}<\/span>
\n}<\/span>
\nauto<\/span> Do =<\/span> [<\/span>&<\/span>]<\/span>(<\/span>int<\/span> bit)<\/span> {<\/span>
\nP—<\/span>;<\/span>
\nauto<\/span>&<\/span> v0 =<\/span> vv0[<\/span>bit]<\/span>;<\/span>
\nauto<\/span>&<\/span> v1 =<\/span> vv1[<\/span>bit]<\/span>;<\/span>
\nif<\/span> (<\/span>v0.<\/span>size<\/span>(<\/span>)<\/span> <<\/span> v1.<\/span>size<\/span>(<\/span>)<\/span>)<\/span> {<\/span>
\nswap<\/span>(<\/span>v0,<\/span> v1)<\/span>;<\/span>
\n}<\/span>
\nans.<\/span>emplace_back<\/span>(<\/span>v0.<\/span>back<\/span>(<\/span>)<\/span> +<\/span> 1<\/span>,<\/span> bit)<\/span>;<\/span>
\nv1.<\/span>emplace_back<\/span>(<\/span>v0.<\/span>back<\/span>(<\/span>)<\/span>)<\/span>;<\/span>
\nv0.<\/span>pop_back<\/span>(<\/span>)<\/span>;<\/span>
\nif<\/span> (<\/span>v0.<\/span>size<\/span>(<\/span>)<\/span> –<\/span> v1.<\/span>size<\/span>(<\/span>)<\/span> ><\/span> 1<\/span>)<\/span>
\n{<\/span>
\nmaxHeap.<\/span>emplace<\/span>(<\/span>(<\/span>1LL<\/span> <<<\/span> bit)<\/span> *<\/span> (<\/span>2<\/span> *<\/span> v0.<\/span>size<\/span>(<\/span>)<\/span> –<\/span> N –<\/span> 1<\/span>)<\/span>,<\/span> bit)<\/span>;<\/span>
\n}<\/span>
\n}<\/span>;<\/span>
\nwhile<\/span> (<\/span>maxHeap.<\/span>size<\/span>(<\/span>)<\/span> &&<\/span> P)<\/span> {<\/span>
\nconst<\/span> auto<\/span> [<\/span>tmp,<\/span> bit]<\/span> =<\/span> maxHeap.<\/span>top<\/span>(<\/span>)<\/span>;<\/span>
\nmaxHeap.<\/span>pop<\/span>(<\/span>)<\/span>;<\/span>
\nDo<\/span>(<\/span>bit)<\/span>;<\/span>
\n}<\/span>
\nwhile<\/span> (<\/span>P)<\/span> {<\/span>
\nDo<\/span>(<\/span>0<\/span>)<\/span>;<\/span>
\n}<\/span>
\nreturn<\/span> ans;<\/span>
\n}<\/span>
\n}<\/span>;<\/span><\/p>\n

int<\/span> main<\/span>(<\/span>)<\/span> {<\/span>
\n#<\/span>ifdef<\/span> _DEBUG<\/span><\/span>
\nfreopen<\/span>(<\/span>"a.in"<\/span>,<\/span> "r"<\/span>,<\/span> stdin<\/span>)<\/span>;<\/span>
\n#<\/span>endif<\/span> \/\/ DEBUG<\/span><\/span>
\nios::<\/span>sync_with_stdio<\/span>(<\/span>0<\/span>)<\/span>;<\/span> cin.<\/span>tie<\/span>(<\/span>nullptr<\/span>)<\/span>;<\/span>
\nCInBuff<<\/span>><\/span> in;<\/span> COutBuff<<\/span>10'000'000<\/span>><\/span> ob;<\/span>
\nint<\/span> N,<\/span>K,<\/span>P;<\/span>
\nin >><\/span> N >><\/span> K >><\/span> P ;<\/span>
\nauto<\/span> a =<\/span> in.<\/span>Read<\/span><<\/span>int<\/span>><\/span><\/span><\/span>(<\/span>N)<\/span>;<\/span><\/p>\n

#<\/span>ifdef<\/span> _DEBUG<\/span><\/span>
\nprintf<\/span>(<\/span>"N=%d,K=%d,P=%d"<\/span>,<\/span> N,<\/span>K,<\/span>P)<\/span>;<\/span>
\nOut<\/span>(<\/span>a,<\/span> ",a="<\/span>)<\/span>;<\/span>
\n\/\/Out(ab, ",ab=");<\/span>
\n\/\/Out(B, "B=");<\/span>
\n\/\/Out(que, "que=");<\/span>
\n\/\/Out(B, "B=");<\/span>
\n#<\/span>endif<\/span> \/\/ DEBUG<\/span><\/span>
\nauto<\/span> res =<\/span> Solution<\/span>(<\/span>)<\/span>.<\/span>Ans<\/span>(<\/span>N,<\/span>K,<\/span>P,<\/span>a)<\/span>;<\/span>
\nfor<\/span> (<\/span>const<\/span> auto<\/span>&<\/span> [<\/span>i,<\/span> j]<\/span> :<\/span> res)<\/span> {<\/span>
\ncout <<<\/span> i <<<\/span> " "<\/span> <<<\/span> j <<<\/span> "\\\\n"<\/span>;<\/span>
\n}<\/span>
\nreturn<\/span> 0<\/span>;<\/span>
\n}<\/span>;<\/span><\/p>\n

\u5355\u5143\u6d4b\u8bd5<\/h3>\n

int<\/span> N,<\/span> K,<\/span>P;<\/span>
\nvector<<\/span>int<\/span>><\/span> a;<\/span>
\nvoid<\/span> Check<\/span>(<\/span>const<\/span> vector<<\/span>int<\/span>><\/span>&<\/span> a,<\/span> const<\/span> vector<<\/span>pair<<\/span>int<\/span>,<\/span>int<\/span>>><\/span>&<\/span> act,<\/span> vector<<\/span>pair<<\/span>int<\/span>,<\/span> int<\/span>>><\/span>&<\/span> res)<\/span> {<\/span>
\nAssertEx<\/span>(<\/span>Cal<\/span>(<\/span>a,<\/span> act)<\/span>,<\/span> Cal<\/span>(<\/span>a,<\/span> res)<\/span>)<\/span>;<\/span>
\n}<\/span>
\nlong<\/span> long<\/span> Cal<\/span>(<\/span> vector<<\/span>int<\/span>><\/span> a,<\/span>const<\/span> vector<<\/span>pair<<\/span>int<\/span>,<\/span> int<\/span>>><\/span>&<\/span> res)<\/span> {<\/span>
\nfor<\/span> (<\/span>const<\/span> auto<\/span>&<\/span> [<\/span>i,<\/span> j]<\/span> :<\/span> res)<\/span> {<\/span>
\na[<\/span>i –<\/span> 1<\/span>]<\/span> ^=<\/span> (<\/span>1<\/span> <<<\/span> j)<\/span>;<\/span>
\n}<\/span>
\nlong<\/span> long<\/span> ans =<\/span> 0<\/span>;<\/span>
\nfor<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> a.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> i++<\/span>)<\/span> {<\/span>
\nfor<\/span> (<\/span>int<\/span> j =<\/span> i +<\/span> 1<\/span>;<\/span> j <<\/span> a.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> j++<\/span>)<\/span> {<\/span>
\nans +=<\/span> a[<\/span>i]<\/span> ^<\/span> a[<\/span>j]<\/span>;<\/span>
\n}<\/span>
\n}<\/span>
\nreturn<\/span> ans;<\/span>
\n}<\/span>
\nTEST_METHOD<\/span>(<\/span>TestMethod01)<\/span>
\n{<\/span>
\na =<\/span> {<\/span> 0<\/span>,<\/span>31<\/span> }<\/span>;<\/span>
\nauto<\/span> res =<\/span> Solution<\/span>(<\/span>)<\/span>.<\/span>Ans<\/span>(<\/span>2<\/span>,<\/span>5<\/span>,<\/span>1<\/span>,<\/span>a)<\/span>;<\/span>
\nCheck<\/span>(<\/span>a,<\/span>{<\/span> {<\/span> 1<\/span>,<\/span>0<\/span> }<\/span> }<\/span>,<\/span> res)<\/span>;<\/span>
\n}<\/span>
\nTEST_METHOD<\/span>(<\/span>TestMethod02)<\/span>
\n{<\/span>
\na =<\/span> {<\/span> 0<\/span>,<\/span>0<\/span>,<\/span>2<\/span>,<\/span>2<\/span> }<\/span>;<\/span>
\nauto<\/span> res =<\/span> Solution<\/span>(<\/span>)<\/span>.<\/span>Ans<\/span>(<\/span>4<\/span>,<\/span>2<\/span>,<\/span>2<\/span>,<\/span>a)<\/span>;<\/span>
\nCheck<\/span>(<\/span>a,<\/span>{<\/span> {<\/span> 4<\/span>,<\/span>0<\/span> }<\/span>,<\/span>{<\/span>3<\/span>,<\/span>0<\/span>}<\/span> }<\/span>,<\/span> res)<\/span>;<\/span>
\n}<\/span>
\nTEST_METHOD<\/span>(<\/span>TestMethod03)<\/span>
\n{<\/span>
\nN =<\/span> 5<\/span>,<\/span> K =<\/span> 6<\/span>,<\/span> P =<\/span> 4<\/span>,<\/span> a =<\/span> {<\/span> 63<\/span>,<\/span>15<\/span>,<\/span>0<\/span>,<\/span>10<\/span>,<\/span>5<\/span> }<\/span>;<\/span>
\nauto<\/span> res =<\/span> Solution<\/span>(<\/span>)<\/span>.<\/span>Ans<\/span>(<\/span>N,<\/span>K,<\/span>P,<\/span> a)<\/span>;<\/span>
\nCheck<\/span>(<\/span>a,<\/span> {<\/span> {<\/span> 5<\/span>,<\/span>5<\/span> }<\/span>,<\/span>{<\/span>5<\/span>,<\/span>4<\/span>}<\/span>,<\/span>{<\/span>4<\/span>,<\/span>3<\/span>}<\/span>,<\/span>{<\/span>4<\/span>,<\/span>3<\/span>}<\/span> }<\/span>,<\/span> res)<\/span>;<\/span>
\n}<\/span>
\nTEST_METHOD<\/span>(<\/span>TestMethod04)<\/span>
\n{<\/span>
\nN =<\/span> 2<\/span>,<\/span> K =<\/span> 2<\/span>,<\/span> P =<\/span> 3<\/span>,<\/span> a =<\/span> {<\/span> 1<\/span>,<\/span>2<\/span> }<\/span>;<\/span>
\nauto<\/span> res =<\/span> Solution<\/span>(<\/span>)<\/span>.<\/span>Ans<\/span>(<\/span>N,<\/span> K,<\/span> P,<\/span> a)<\/span>;<\/span>
\nAssertV<\/span>(<\/span>{<\/span> {<\/span> 2<\/span>,<\/span>0<\/span> }<\/span>,<\/span>{<\/span>2<\/span>,<\/span>0<\/span>}<\/span>,<\/span>{<\/span>1<\/span>,<\/span>0<\/span>}<\/span> }<\/span>,<\/span> res)<\/span>;<\/span>
\n}<\/span>
\nTEST_METHOD<\/span>(<\/span>TestMethod05)<\/span>
\n{<\/span>
\nN =<\/span> 2<\/span>,<\/span> K =<\/span> 2<\/span>,<\/span> P =<\/span> 4<\/span>,<\/span> a =<\/span> {<\/span> 1<\/span>,<\/span>2<\/span> }<\/span>;<\/span>
\nauto<\/span> res =<\/span> Solution<\/span>(<\/span>)<\/span>.<\/span>Ans<\/span>(<\/span>N,<\/span> K,<\/span> P,<\/span> a)<\/span>;<\/span>
\nCheck<\/span>(<\/span>a,<\/span> {<\/span> }<\/span>,<\/span> res)<\/span>;<\/span>
\n}<\/span>
\nTEST_METHOD<\/span>(<\/span>TestMethod06)<\/span>
\n{<\/span>
\nN =<\/span> 3<\/span>,<\/span> K =<\/span> 3<\/span>,<\/span> P =<\/span> 4<\/span>,<\/span> a =<\/span> {<\/span> 1<\/span>,<\/span>2<\/span>,<\/span>4<\/span> }<\/span>;<\/span>
\nauto<\/span> res =<\/span> Solution<\/span>(<\/span>)<\/span>.<\/span>Ans<\/span>(<\/span>N,<\/span> K,<\/span> P,<\/span> a)<\/span>;<\/span>
\nCheck<\/span>(<\/span>a,<\/span> {<\/span> }<\/span>,<\/span> res)<\/span>;<\/span>
\n}<\/span>
\nTEST_METHOD<\/span>(<\/span>TestMethod07)<\/span>
\n{<\/span>
\nN =<\/span> 3<\/span>,<\/span> K =<\/span> 3<\/span>,<\/span> P =<\/span> 1<\/span>,<\/span> a =<\/span> {<\/span> 1<\/span>,<\/span>2<\/span>,<\/span>4<\/span> }<\/span>;<\/span>
\nauto<\/span> res =<\/span> Solution<\/span>(<\/span>)<\/span>.<\/span>Ans<\/span>(<\/span>N,<\/span> K,<\/span> P,<\/span> a)<\/span>;<\/span>
\nCheck<\/span>(<\/span>a,<\/span> {<\/span> {<\/span>2<\/span>,<\/span>0<\/span>}<\/span> }<\/span>,<\/span> res)<\/span>;<\/span>
\n}<\/span>
\nTEST_METHOD<\/span>(<\/span>TestMethod08)<\/span>
\n{<\/span>
\nN =<\/span> 6<\/span>,<\/span> K =<\/span> 2<\/span>,<\/span> P =<\/span> 1<\/span>,<\/span> a =<\/span> {<\/span> 2<\/span>,<\/span>2<\/span>,<\/span>0<\/span>,<\/span>0<\/span>,<\/span>0<\/span>,<\/span>0<\/span> }<\/span>;<\/span>
\nauto<\/span> res =<\/span> Solution<\/span>(<\/span>)<\/span>.<\/span>Ans<\/span>(<\/span>N,<\/span> K,<\/span> P,<\/span> a)<\/span>;<\/span>
\nCheck<\/span>(<\/span>a,<\/span> {<\/span> {<\/span>1<\/span>,<\/span>0<\/span>}<\/span> }<\/span>,<\/span> res)<\/span>;<\/span>
\n}<\/span><\/p>\n

\u6269\u5c55\u9605\u8bfb<\/h2>\n\n\u6211\u60f3\u5bf9\u5927\u5bb6\u8bf4\u7684\u8bdd<\/tr>\n\n\n\n\n\n\n\n\n
\u5de5\u4f5c\u4e2d\u9047\u5230\u7684\u95ee\u9898，\u53ef\u4ee5\u6309\u7c7b\u522b\u67e5\u9605\u9119\u4eba\u7684\u7b97\u6cd5\u6587\u7ae0，\u8bf7\u70b9\u51fb\u300a\u7b97\u6cd5\u4e0e\u6570\u636e\u6c47\u603b\u300b\u3002<\/td>\n<\/tr>\n
\u5b66\u4e60\u7b97\u6cd5：\u6309\u7ae0\u8282\u5b66\u4e60\u300a\u559c\u7f3a\u5168\u4e66\u7b97\u6cd5\u518c\u300b，\u5927\u91cf\u7684\u9898\u76ee\u548c\u6d4b\u8bd5\u7528\u4f8b，\u6253\u5305\u4e0b\u8f7d\u3002\u91cd\u89c6\u64cd\u4f5c<\/td>\n<\/tr>\n
\u6709\u6548\u5b66\u4e60：\u660e\u786e\u7684\u76ee\u6807 \u53ca\u65f6\u7684\u53cd\u9988 \u62c9\u4f38\u533a（\u96be\u5ea6\u5408\u9002） \u4e13\u6ce8<\/td>\n<\/tr>\n
\u95fb\u7f3a\u9677\u5219\u559c(\u559c\u7f3a)\u662f\u4e00\u4e2a\u7f8e\u597d\u7684\u613f\u671b，\u65e9\u53d1\u73b0\u95ee\u9898，\u65e9\u4fee\u6539\u95ee\u9898，\u7ed9\u8001\u677f\u8282\u7ea6\u94b1\u3002<\/td>\n<\/tr>\n
\u5b50\u58a8\u5b50\u8a00\u4e4b：\u4e8b\u65e0\u7ec8\u59cb，\u65e0\u52a1\u591a\u4e1a\u3002\u4e5f\u5c31\u662f\u6211\u4eec\u5e38\u8bf4\u7684\u4e13\u4e1a\u7684\u4eba\u505a\u4e13\u4e1a\u7684\u4e8b\u3002<\/td>\n<\/tr>\n
\u5982\u679c\u7a0b\u5e8f\u662f\u4e00\u6761\u9f99，\u90a3\u7b97\u6cd5\u5c31\u662f\u4ed6\u7684\u662f\u775b<\/td>\n<\/tr>\n
\u5931\u8d25+\u53cd\u601d=\u6210\u529f \u6210\u529f+\u53cd\u601d=\u6210\u529f<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u89c6\u9891\u8bfe\u7a0b<\/h3>\n

\u5148\u5b66\u7b80\u5355\u7684\u8bfe\u7a0b，\u8bf7\u79fb\u6b65CSDN\u5b66\u9662，\u542c\u767d\u94f6\u8bb2\u5e08（\u4e5f\u5c31\u662f\u9119\u4eba）\u7684\u8bb2\u89e3\u3002 https:\/\/edu.csdn.net\/course\/detail\/38771 \u5982\u4f55\u4f60\u60f3\u5feb\u901f\u5f62\u6210\u6218\u6597\u4e86，\u4e3a\u8001\u677f\u5206\u5fe7，\u8bf7\u5b66\u4e60C#\u5165\u804c\u57f9\u8bad\u3001C++\u5165\u804c\u57f9\u8bad\u7b49\u8bfe\u7a0b https:\/\/edu.csdn.net\/lecturer\/6176<\/p>\n

\u6d4b\u8bd5\u73af\u5883<\/h3>\n

\u64cd\u4f5c\u7cfb\u7edf：win7 \u5f00\u53d1\u73af\u5883： VS2019 C++17 \u6216\u8005 \u64cd\u4f5c\u7cfb\u7edf：win10 \u5f00\u53d1\u73af\u5883： VS2022 C++17 \u5982\u65e0\u7279\u6b8a\u8bf4\u660e，\u672c\u7b97\u6cd5\u7528**C++**\u5b9e\u73b0\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

\u672c\u6587\u6d89\u53ca\u77e5\u8bc6\u70b9
\n\u4f4d\u8fd0\u7b97\u3001\u72b6\u6001\u538b\u7f29\u3001\u679a\u4e3e\u5b50\u96c6\u6c47\u603b
\nP9277 [AGM 2023 \u8d44\u683c\u8d5b] \u53cd\u8f6c
\n\u9898\u76ee\u63cf\u8ff0
\n\u7ed9\u5b9a\u957f\u5ea6\u4e3a NNN \u7684\u5e8f\u5217 aaa \u6ee1\u8db3\u6bcf\u4e2a\u6570\u90fd\u5c0f\u4e8e 2K2^K2K\u3002\u4f60\u9700\u8981\u6267\u884c\u6070\u597d PPP \u6b21\u64cd\u4f5c，\u6bcf\u6b21\u64cd\u4f5c\u662f\u628a\u5176\u4e2d\u4e00\u4e2a\u6570\u7684\u67d0\u4e00\u4e2a\u4e8c\u8fdb\u5236\u4f4d\u53cd\u8f6c\u3002\u6700\u7ec8\u4f60\u9700\u8981\u4f7f\u5f97 \u2211i\u2211jai\u2295aj(i<j)\\\\sum_i\\\\sum_j a_i\\\\oplus a_j(i<j)i\u2211\u200bj\u2211\u200bai\u200b\u2295aj\u200b(i<j)
\n\u6700\u5927，\u5176\u4e2d \u2295\\\\oplus\u2295 \u4e3a\u6309\u4f4d\u5f02\u6216\u8fd0\u7b97\u3002<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[8152,8151,55,427],"topic":[],"class_list":["post-76037","post","type-post","status-publish","format-standard","hentry","category-server","tag-8152","tag-8151","tag-c","tag-427"],"yoast_head":"\n\u3010\u62c6\u4f4d\u6cd5\u3011P9277 [AGM 2023 \u8d44\u683c\u8d5b] \u53cd\u8f6c|\u666e\u53ca+ - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/76037.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u3010\u62c6\u4f4d\u6cd5\u3011P9277 [AGM 2023 \u8d44\u683c\u8d5b] \u53cd\u8f6c|\u666e\u53ca+ - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u672c\u6587\u6d89\u53ca\u77e5\u8bc6\u70b9 \u4f4d\u8fd0\u7b97\u3001\u72b6\u6001\u538b\u7f29\u3001\u679a\u4e3e\u5b50\u96c6\u6c47\u603b P9277 [AGM 2023 \u8d44\u683c\u8d5b] \u53cd\u8f6c \u9898\u76ee\u63cf\u8ff0 \u7ed9\u5b9a\u957f\u5ea6\u4e3a NNN \u7684\u5e8f\u5217 aaa \u6ee1\u8db3\u6bcf\u4e2a\u6570\u90fd\u5c0f\u4e8e 2K2^K2K\u3002\u4f60\u9700\u8981\u6267\u884c\u6070\u597d PPP \u6b21\u64cd\u4f5c，\u6bcf\u6b21\u64cd\u4f5c\u662f\u628a\u5176\u4e2d\u4e00\u4e2a\u6570\u7684\u67d0\u4e00\u4e2a\u4e8c\u8fdb\u5236\u4f4d\u53cd\u8f6c\u3002\u6700\u7ec8\u4f60\u9700\u8981\u4f7f\u5f97 \u2211i\u2211jai\u2295aj(i<j)\\sum_i\\sum_j a_i\\oplus a_j(i<j)i\u2211\u200bj\u2211\u200bai\u200b\u2295aj\u200b(i<j) \u6700\u5927，\u5176\u4e2d \u2295\\oplus\u2295 \u4e3a\u6309\u4f4d\u5f02\u6216\u8fd0\u7b97\u3002\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/76037.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2026-02-13T13:05:24+00:00\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"10 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/76037.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/76037.html\",\"name\":\"\u3010\u62c6\u4f4d\u6cd5\u3011P9277 [AGM 2023 \u8d44\u683c\u8d5b] \u53cd\u8f6c|\u666e\u53ca+ - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"isPartOf\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\"},\"datePublished\":\"2026-02-13T13:05:24+00:00\",\"dateModified\":\"2026-02-13T13:05:24+00:00\",\"author\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\"},\"breadcrumb\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/76037.html#breadcrumb\"},\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.wsisp.com\/helps\/76037.html\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/76037.html#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u9996\u9875\",\"item\":\"https:\/\/www.wsisp.com\/helps\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u3010\u62c6\u4f4d\u6cd5\u3011P9277 [AGM 2023 \u8d44\u683c\u8d5b] \u53cd\u8f6c|\u666e\u53ca+\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\",\"url\":\"https:\/\/www.wsisp.com\/helps\/\",\"name\":\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"description\":\"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"zh-Hans\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\",\"name\":\"admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-Hans\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"contentUrl\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"caption\":\"admin\"},\"sameAs\":[\"http:\/\/wp.wsisp.com\"],\"url\":\"https:\/\/www.wsisp.com\/helps\/author\/admin\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u3010\u62c6\u4f4d\u6cd5\u3011P9277 [AGM 2023 \u8d44\u683c\u8d5b] \u53cd\u8f6c|\u666e\u53ca+ - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.wsisp.com\/helps\/76037.html","og_locale":"zh_CN","og_type":"article","og_title":"\u3010\u62c6\u4f4d\u6cd5\u3011P9277 [AGM 2023 \u8d44\u683c\u8d5b] \u53cd\u8f6c|\u666e\u53ca+ - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","og_description":"\u672c\u6587\u6d89\u53ca\u77e5\u8bc6\u70b9 \u4f4d\u8fd0\u7b97\u3001\u72b6\u6001\u538b\u7f29\u3001\u679a\u4e3e\u5b50\u96c6\u6c47\u603b P9277 [AGM 2023 \u8d44\u683c\u8d5b] \u53cd\u8f6c \u9898\u76ee\u63cf\u8ff0 \u7ed9\u5b9a\u957f\u5ea6\u4e3a NNN \u7684\u5e8f\u5217 aaa \u6ee1\u8db3\u6bcf\u4e2a\u6570\u90fd\u5c0f\u4e8e 2K2^K2K\u3002\u4f60\u9700\u8981\u6267\u884c\u6070\u597d PPP \u6b21\u64cd\u4f5c，\u6bcf\u6b21\u64cd\u4f5c\u662f\u628a\u5176\u4e2d\u4e00\u4e2a\u6570\u7684\u67d0\u4e00\u4e2a\u4e8c\u8fdb\u5236\u4f4d\u53cd\u8f6c\u3002\u6700\u7ec8\u4f60\u9700\u8981\u4f7f\u5f97 \u2211i\u2211jai\u2295aj(i<j)\\sum_i\\sum_j a_i\\oplus a_j(i<j)i\u2211\u200bj\u2211\u200bai\u200b\u2295aj\u200b(i<j) \u6700\u5927，\u5176\u4e2d \u2295\\oplus\u2295 \u4e3a\u6309\u4f4d\u5f02\u6216\u8fd0\u7b97\u3002","og_url":"https:\/\/www.wsisp.com\/helps\/76037.html","og_site_name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","article_published_time":"2026-02-13T13:05:24+00:00","author":"admin","twitter_card":"summary_large_image","twitter_misc":{"\u4f5c\u8005":"admin","\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4":"10 \u5206"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.wsisp.com\/helps\/76037.html","url":"https:\/\/www.wsisp.com\/helps\/76037.html","name":"\u3010\u62c6\u4f4d\u6cd5\u3011P9277 [AGM 2023 \u8d44\u683c\u8d5b] \u53cd\u8f6c|\u666e\u53ca+ - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","isPartOf":{"@id":"https:\/\/www.wsisp.com\/helps\/#website"},"datePublished":"2026-02-13T13:05:24+00:00","dateModified":"2026-02-13T13:05:24+00:00","author":{"@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41"},"breadcrumb":{"@id":"https:\/\/www.wsisp.com\/helps\/76037.html#breadcrumb"},"inLanguage":"zh-Hans","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.wsisp.com\/helps\/76037.html"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.wsisp.com\/helps\/76037.html#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u9996\u9875","item":"https:\/\/www.wsisp.com\/helps"},{"@type":"ListItem","position":2,"name":"\u3010\u62c6\u4f4d\u6cd5\u3011P9277 [AGM 2023 \u8d44\u683c\u8d5b] \u53cd\u8f6c|\u666e\u53ca+"}]},{"@type":"WebSite","@id":"https:\/\/www.wsisp.com\/helps\/#website","url":"https:\/\/www.wsisp.com\/helps\/","name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","description":"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"zh-Hans"},{"@type":"Person","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41","name":"admin","image":{"@type":"ImageObject","inLanguage":"zh-Hans","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/","url":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","contentUrl":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","caption":"admin"},"sameAs":["http:\/\/wp.wsisp.com"],"url":"https:\/\/www.wsisp.com\/helps\/author\/admin"}]}},"_links":{"self":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/76037","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/comments?post=76037"}],"version-history":[{"count":0,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/76037\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/media?parent=76037"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/categories?post=76037"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/tags?post=76037"},{"taxonomy":"topic","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/topic?post=76037"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}