{"id":72197,"date":"2026-02-05T07:17:04","date_gmt":"2026-02-04T23:17:04","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/72197.html"},"modified":"2026-02-05T07:17:04","modified_gmt":"2026-02-04T23:17:04","slug":"p8699-%e8%93%9d%e6%a1%a5%e6%9d%af-2019-%e5%9b%bd-b-%e6%8e%92%e5%88%97%e6%95%b0%e6%99%ae%e5%8f%8a","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/72197.html","title":{"rendered":"P8699 [\u84dd\u6865\u676f 2019 \u56fd B] \u6392\u5217\u6570|\u666e\u53ca+"},"content":{"rendered":"

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

\u6570\u8bba：\u8d28\u6570\u3001\u6700\u5927\u516c\u7ea6\u6570\u3001\u83f2\u8700\u5b9a\u7406<\/p>\n

P8699 [\u84dd\u6865\u676f 2019 \u56fd B] \u6392\u5217\u6570<\/h2>\n

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

\u5728\u4e00\u4e2a\u6392\u5217\u4e2d，\u4e00\u4e2a\u6298\u70b9\u662f\u6307\u6392\u5217\u4e2d\u7684\u4e00\u4e2a\u5143\u7d20，\u5b83\u540c\u65f6\u5c0f\u4e8e\u4e24\u8fb9\u7684\u5143\u7d20，\u6216\u8005\u540c\u65f6\u5927\u4e8e\u4e24\u8fb9\u7684\u5143\u7d20\u3002 \u5bf9\u4e8e\u4e00\u4e2a <\/p>\n

1<\/p>\n

\u223c<\/p>\n

n<\/p>\n

1 \u223c n<\/p>\n

<\/span><\/span>1<\/span><\/span>\u223c<\/span><\/span><\/span><\/span>n<\/span><\/span><\/span><\/span><\/span> \u7684\u6392\u5217，\u5982\u679c\u53ef\u4ee5\u5c06\u8fd9\u4e2a\u6392\u5217\u4e2d\u5305\u542b <\/p>\n

t<\/p>\n

t<\/p>\n

<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span> \u4e2a\u6298\u70b9，\u5219\u5b83\u79f0\u4e3a\u4e00\u4e2a <\/p>\n

t<\/p>\n

+<\/p>\n

1<\/p>\n

t + 1<\/p>\n

<\/span><\/span>t<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u5355\u8c03\u6392\u5217\u3002 \u4f8b\u5982，\u6392\u5217 <\/p>\n

(<\/p>\n

1<\/p>\n

,<\/p>\n

4<\/p>\n

,<\/p>\n

2<\/p>\n

,<\/p>\n

3<\/p>\n

)<\/p>\n

(1, 4, 2, 3)<\/p>\n

<\/span><\/span>(<\/span>1<\/span>,<\/span><\/span>4<\/span>,<\/span><\/span>2<\/span>,<\/span><\/span>3<\/span>)<\/span><\/span><\/span><\/span><\/span> \u662f\u4e00\u4e2a <\/p>\n

3<\/p>\n

3<\/p>\n

<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span> \u5355\u8c03\u6392\u5217，\u5176\u4e2d <\/p>\n

4<\/p>\n

4<\/p>\n

<\/span><\/span>4<\/span><\/span><\/span><\/span><\/span> \u548c <\/p>\n

2<\/p>\n

2<\/p>\n

<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u90fd\u662f\u6298\u70b9\u3002 \u7ed9\u5b9a <\/p>\n

n<\/p>\n

n<\/p>\n

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

k<\/p>\n

k<\/p>\n

<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>，\u8bf7\u95ee <\/p>\n

1<\/p>\n

\u223c<\/p>\n

n<\/p>\n

1 \u223c n<\/p>\n

<\/span><\/span>1<\/span><\/span>\u223c<\/span><\/span><\/span><\/span>n<\/span><\/span><\/span><\/span><\/span> \u7684\u6240\u6709\u6392\u5217\u4e2d\u6709\u591a\u5c11\u4e2a <\/p>\n

k<\/p>\n

k<\/p>\n

<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span> \u5355\u8c03\u6392\u5217？<\/p>\n

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

\u8f93\u5165\u4e00\u884c\u5305\u542b\u4e24\u4e2a\u6574\u6570 <\/p>\n

n<\/p>\n

n<\/p>\n

<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>, <\/p>\n

k<\/p>\n

k<\/p>\n

<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

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

\u8f93\u51fa\u4e00\u4e2a\u6574\u6570，\u8868\u793a\u7b54\u6848\u3002\u7b54\u6848\u53ef\u80fd\u5f88\u5927，\u4f60\u53ef\u9700\u8981\u8f93\u51fa\u6ee1\u8db3\u6761\u4ef6\u7684\u6392\u5217 \u6570\u91cf\u9664\u4ee5 <\/p>\n

123456<\/p>\n

123456<\/p>\n

<\/span><\/span>123456<\/span><\/span><\/span><\/span><\/span> \u7684\u4f59\u6570\u5373\u53ef\u3002<\/p>\n

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

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

4 2<\/p>\n

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

12<\/p>\n

\u8bf4\u660e\/\u63d0\u793a<\/h3>\n

\u5bf9\u4e8e <\/p>\n

20<\/p>\n

%<\/p>\n

20 \\\\%<\/p>\n

<\/span><\/span>20%<\/span><\/span><\/span><\/span><\/span> \u7684\u8bc4\u6d4b\u7528\u4f8b, <\/p>\n

1<\/p>\n

\u2264<\/p>\n

k<\/p>\n

\u2264<\/p>\n

n<\/p>\n

\u2264<\/p>\n

10<\/p>\n

1 \\\\leq k \\\\leq n \\\\leq 10<\/p>\n

<\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>k<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>n<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>10<\/span><\/span><\/span><\/span><\/span>;<\/p>\n

\u5bf9\u4e8e <\/p>\n

40<\/p>\n

%<\/p>\n

40 \\\\%<\/p>\n

<\/span><\/span>40%<\/span><\/span><\/span><\/span><\/span> \u7684\u8bc4\u6d4b\u7528\u4f8b, <\/p>\n

1<\/p>\n

\u2264<\/p>\n

k<\/p>\n

\u2264<\/p>\n

n<\/p>\n

\u2264<\/p>\n

20<\/p>\n

1 \\\\leq k \\\\leq n \\\\leq 20<\/p>\n

<\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>k<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>n<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>20<\/span><\/span><\/span><\/span><\/span>; \u5bf9\u4e8e <\/p>\n

60<\/p>\n

%<\/p>\n

60 \\\\%<\/p>\n

<\/span><\/span>60%<\/span><\/span><\/span><\/span><\/span> \u7684\u8bc4\u6d4b\u7528\u4f8b, <\/p>\n

1<\/p>\n

\u2264<\/p>\n

k<\/p>\n

\u2264<\/p>\n

n<\/p>\n

\u2264<\/p>\n

100<\/p>\n

1 \\\\leq k \\\\leq n \\\\leq 100<\/p>\n

<\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>k<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>n<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>100<\/span><\/span><\/span><\/span><\/span>;<\/p>\n

\u5bf9\u4e8e\u6240\u6709\u8bc4\u6d4b\u7528\u4f8b， <\/p>\n

1<\/p>\n

\u2264<\/p>\n

k<\/p>\n

\u2264<\/p>\n

n<\/p>\n

\u2264<\/p>\n

500<\/p>\n

1 \\\\leq k \\\\leq n \\\\leq 500<\/p>\n

<\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>k<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>n<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>500<\/span><\/span><\/span><\/span><\/span> \u3002<\/p>\n

\u84dd\u6865\u676f 2019 \u5e74\u56fd\u8d5b B \u7ec4 G \u9898\u3002<\/p>\n

\u6570\u8bba<\/h2>\n

\u901a\u8fc7N\u6392\u5217\u6784\u5efaN+1\u6392\u5217<\/h3>\n

f(a,n)=b \u3002a\u662f\u957f\u5ea6\u4e3aN\u7684\u6392\u5217(\u4ee5\u4e0b\u7b80\u79f0N\u6392\u5217)，b\u662f\u957f\u5ea6\u4e3aN+1\u7684\u6392\u5217，<\/p>\n

n<\/p>\n

\u2208<\/p>\n

[<\/p>\n

0<\/p>\n

,<\/p>\n

N<\/p>\n

]<\/p>\n

n\\\\in[0,N]<\/p>\n

<\/span><\/span>n<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>[<\/span>0<\/span>,<\/span><\/span>N<\/span>]<\/span><\/span><\/span><\/span><\/span>\u8868\u793a\u5c06N+1\u63d2\u5165\u5230n\u5904\u3002\u4e0b\u9762\u6765\u8bc1\u660ef\u662f\u5355\u5c04\u51fd\u6570\u3002 \u4e00，<\/p>\n

n<\/p>\n

1<\/p>\n

\u2260<\/p>\n

n<\/p>\n

2<\/p>\n

，\u5219<\/p>\n

f<\/p>\n

(<\/p>\n

a<\/p>\n

1<\/p>\n

,<\/p>\n

n<\/p>\n

1<\/p>\n

)<\/p>\n

\u2260<\/p>\n

f<\/p>\n

(<\/p>\n

a<\/p>\n

2<\/p>\n

,<\/p>\n

n<\/p>\n

2<\/p>\n

)<\/p>\n

n1 \\\\neq n2，\u5219f(a1,n1)\\\\neq f(a2,n2)<\/p>\n

<\/span><\/span>n<\/span>1<\/span><\/span><\/span>\ue020<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>n<\/span>2<\/span>，\u5219<\/span>f<\/span>(<\/span>a<\/span>1<\/span>,<\/span><\/span>n<\/span>1<\/span>)<\/span><\/span><\/span>\ue020<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>f<\/span>(<\/span>a<\/span>2<\/span>,<\/span><\/span>n<\/span>2<\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002\u56e0\u4e3a<\/p>\n

b<\/p>\n

1<\/p>\n

[<\/p>\n

n<\/p>\n

1<\/p>\n

]<\/p>\n

\u2260<\/p>\n

b<\/p>\n

2<\/p>\n

[<\/p>\n

n<\/p>\n

2<\/p>\n

]<\/p>\n

b1[n1]\\\\neq b2[n2]<\/p>\n

<\/span><\/span>b<\/span>1<\/span>[<\/span>n<\/span>1<\/span>]<\/span><\/span><\/span>\ue020<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>b<\/span>2<\/span>[<\/span>n<\/span>2<\/span>]<\/span><\/span><\/span><\/span><\/span>\u3002 \u4e8c，<\/p>\n

n<\/p>\n

1<\/p>\n

=<\/p>\n

=<\/p>\n

n<\/p>\n

2<\/p>\n

,<\/p>\n

a<\/p>\n

1<\/p>\n

\u2260<\/p>\n

a<\/p>\n

2<\/p>\n

\u2192<\/p>\n

\u4e00\u5b9a\u5b58\u5728<\/p>\n

a<\/p>\n

1<\/p>\n

[<\/p>\n

i<\/p>\n

1<\/p>\n

]<\/p>\n

\u2260<\/p>\n

a<\/p>\n

2<\/p>\n

[<\/p>\n

i<\/p>\n

1<\/p>\n

]<\/p>\n

\u5982\u679c<\/p>\n

n<\/p>\n

1<\/p>\n

><\/p>\n

i<\/p>\n

1<\/p>\n

，\u5219<\/p>\n

b<\/p>\n

1<\/p>\n

[<\/p>\n

i<\/p>\n

1<\/p>\n

]<\/p>\n

\u2260<\/p>\n

b<\/p>\n

1<\/p>\n

[<\/p>\n

i<\/p>\n

1<\/p>\n

]<\/p>\n

；\u5426\u5219<\/p>\n

b<\/p>\n

1<\/p>\n

[<\/p>\n

i<\/p>\n

1<\/p>\n

+<\/p>\n

1<\/p>\n

]<\/p>\n

\u2260<\/p>\n

b<\/p>\n

1<\/p>\n

[<\/p>\n

i<\/p>\n

1<\/p>\n

+<\/p>\n

1<\/p>\n

]<\/p>\n

n1 == n2,a1 \\\\neq a2 \\\\rightarrow \u4e00\u5b9a\u5b58\u5728a1[i1] \\\\neq a2[i1] \u5982\u679cn1 > i1，\u5219b1[i1] \\\\neq b1[i1]；\u5426\u5219b1[i1+1] \\\\neq b1[i1+1]<\/p>\n

<\/span><\/span>n<\/span>1<\/span><\/span>==<\/span><\/span><\/span><\/span>n<\/span>2<\/span>,<\/span><\/span>a<\/span>1<\/span><\/span><\/span>\ue020<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>a<\/span>2<\/span><\/span>\u2192<\/span><\/span><\/span><\/span>\u4e00\u5b9a\u5b58\u5728<\/span>a<\/span>1<\/span>[<\/span>i<\/span>1<\/span>]<\/span><\/span><\/span>\ue020<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>a<\/span>2<\/span>[<\/span>i<\/span>1<\/span>]<\/span>\u5982\u679c<\/span>n<\/span>1<\/span><\/span>><\/span><\/span><\/span><\/span>i<\/span>1<\/span>，\u5219<\/span>b<\/span>1<\/span>[<\/span>i<\/span>1<\/span>]<\/span><\/span><\/span>\ue020<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>b<\/span>1<\/span>[<\/span>i<\/span>1<\/span>]<\/span>；\u5426\u5219<\/span>b<\/span>1<\/span>[<\/span>i<\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span>]<\/span><\/span><\/span>\ue020<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>b<\/span>1<\/span>[<\/span>i<\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span>]<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u5355\u8c03\u533a\u95f4<\/h3>\n

\u4e00\u4e2a\u6392\u5217\u6709k\u4e2a\u6298\u70b9，\u4e0b\u6807\u5206\u522b\u4e3a<\/p>\n

i<\/p>\n

1<\/p>\n

,<\/p>\n

i<\/p>\n

2<\/p>\n

\u22ef<\/p>\n

i<\/p>\n

k<\/p>\n

\u2212<\/p>\n

1<\/p>\n

,<\/p>\n

i<\/p>\n

k<\/p>\n

i_1,i_2\\\\cdots i_k-1,i_k<\/p>\n

<\/span><\/span>i<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>i<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22ef<\/span><\/span>i<\/span><\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span>,<\/span><\/span>i<\/span><\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5219\u53ea\u6709\u4e24\u79cd\u60c5\u51b5\u3002\u60c5\u51b5\u4e00：<\/p>\n

a<\/p>\n

[<\/p>\n

0…<\/p>\n

i<\/p>\n

1<\/p>\n

]<\/p>\n

a<\/p>\n

[<\/p>\n

i<\/p>\n

2<\/p>\n

.<\/p>\n

.<\/p>\n

.<\/p>\n

i<\/p>\n

3<\/p>\n

]<\/p>\n

a<\/p>\n

[<\/p>\n

i<\/p>\n

4<\/p>\n

.<\/p>\n

.<\/p>\n

.<\/p>\n

i<\/p>\n

5<\/p>\n

]<\/p>\n

\u22ef<\/p>\n

a[0…i_1] a[i_2…i_3] a[i_4…i_5]\\\\cdots<\/p>\n

<\/span><\/span>a<\/span>[<\/span>0…<\/span>i<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span>a<\/span>[<\/span>i<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>…<\/span>i<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span>a<\/span>[<\/span>i<\/span><\/span>4<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>…<\/span>i<\/span><\/span>5<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span>\u22ef<\/span><\/span><\/span><\/span><\/span> \u5355\u8c03\u9012\u589e，\u5176\u5b83\u5355\u8c03\u9012\u51cf\u3002 \u60c5\u51b5\u4e8c：<\/p>\n

a<\/p>\n

[<\/p>\n

0…<\/p>\n

i<\/p>\n

1<\/p>\n

]<\/p>\n

a<\/p>\n

[<\/p>\n

i<\/p>\n

2<\/p>\n

.<\/p>\n

.<\/p>\n

.<\/p>\n

i<\/p>\n

3<\/p>\n

]<\/p>\n

a<\/p>\n

[<\/p>\n

i<\/p>\n

4<\/p>\n

.<\/p>\n

.<\/p>\n

.<\/p>\n

i<\/p>\n

5<\/p>\n

]<\/p>\n

\u22ef<\/p>\n

a[0…i_1] a[i_2…i_3] a[i_4…i_5]\\\\cdots<\/p>\n

<\/span><\/span>a<\/span>[<\/span>0…<\/span>i<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span>a<\/span>[<\/span>i<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>…<\/span>i<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span>a<\/span>[<\/span>i<\/span><\/span>4<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>…<\/span>i<\/span><\/span>5<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span>\u22ef<\/span><\/span><\/span><\/span><\/span> \u5355\u8c03\u9012\u51cf，\u5176\u5b83\u5355\u8c03\u9012\u589e\u3002 \u603b\u7ed3\u4e00：\u5171k+1\u4e2a\u5355\u8c03\u533a\u95f4，\u5947\u5076\u6027\u76f8\u540c\u7684\u533a\u95f4\u5355\u8c03\u6027\u76f8\u540c；\u5947\u5076\u6027\u4e0d\u540c\u7684\u533a\u95f4\u5355\u8c03\u6027\u4e0d\u540c\u3002 \u6027\u8d28\u4e00：\u4efb\u610f\u6392\u5217c[i]=N+1-a[i] (\u7b2ck\u5927\u7684\u6570\u53d8\u4f4ek\u5c0f)，\u5219a\u3001c\u7684\u5355\u8c03\u533a\u95f4\u6570\u91cf\u76f8\u7b49，\u5355\u8c03\u6027\u76f8\u53cd\u3002\u6211\u4eec\u6210ac\u4e3a\u4e00\u5bf9\u3002 \u5982\u679ca[i] < a[i+1]，\u5219\u662f\u589e\u52a0\u4e00\u6761\u53f3\u4e0a\u7684\u7ebf，\u5426\u5219\u53f3\u4e0b\u7684\u7ebf\u3002\u5219\u5bf9\u5e94\u4ee5\u4e0b\u4e24\u79cd\u60c5\u51b5： \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" dp[n][k]n\u6392\u5217\u5171\u6709k\u4e2a\u6298\u70b9\u7684\u65b9\u6848\u6570\u3002 \u60c5\u51b5\u4e00：\u5bf9\u4e8e\u4efb\u610fa，n = N\u3002\u5982\u679ca[N-1] < a[N-2]，\u5219b\u6bd4a\u591a\u4e00\u4e2a\u6298\u70b9N-1；\u5426\u5219\u6298\u70b9\u4e0d\u53d8\u3002 \u60c5\u51b5\u4e8c：n==0,\u5982\u679ca[0] < a[1]，\u6298\u70b9+1，\u5426\u5219\u6298\u70b9\u4e0d\u53d8\u3002 \u603b\u7ed3\u4e8c：\u5bf9\u6bcf\u5bf9\u65b9\u6848，\u60c5\u51b5\u4e00\u60c5\u51b5\u4e8c\u6298\u70b9\u4e0d\u53d8\u548c\u6298\u70b9\u52a0+1\u7684\u65b9\u6848\u6570\u4e00\u6837\u3002\u5373： dp[n+1][k] += dp[n][k] dp[n+1][k+1] += dp[n][k] \u60c5\u51b5\u4e09：\u9664\u53bb\u60c5\u51b5\u4e00\u4e8c，\u6211\u4eec\u53ef\u4ee5\u770b\u6210\u8fb9\u4e0a\u52a0\u4e00\u70b9\u3002\u4ee4\u5728\u8fb9i,i+1\u95f4\u63d2\u5165N+1\u3002 mi = min(a[i],a[i+1]) ma = max(a[i],a[i+1])\u3002 \u7531\u4e8emi\u5c0f\u4e8ema，\u6545mi\u4e0d\u4f1a\u662f\u5927\u6298\u70b9\u3002 \u5982\u679cmi\u662f\u5c0f\u6298\u70b9，\u5219N+1\u4ee3\u66ffa[ma]\u540e，\u4ecd\u7136\u662f\u5c0f\u6298\u70b9\u3002\u6545\u65e0\u9700\u8ba8\u8bbami\u3002 \u5982\u679cma\u662f\u5927\u6298\u70b9，\u5219\u63d2\u5165\u540e\u3002 ma\u4e0d\u518d\u662f\u5927\u6298\u70b9\u3002N+1\u53d8\u6210\u5927\u6298\u70b9\u3002\u4e00\u5bf9\u65b9\u6848，\u5171K\u4e2a\u5927\u6298\u70b9，\u51712k\u6761\u8fb9\u3002\u6545：dp[n][k] += dp[n][k] *k\u3002 \u5982\u679cma\u662fa[0]\u6216a[N-1]，\u63d2\u5165\u540e，ma\u4e0d\u662f\u6298\u70b9\u3002N+1\u662f\u6298\u70b9，\u6545\u6298\u70b9+1\u3002dp[n+1][k+1] += dp[n][k] \u5982\u679cma\u4e0d\u662fa[0]\u548ca[N-1]，\u63d2\u5165\u540e\u3002ma\u548cN+1\u90fd\u662f\u6298\u70b9，\u6298\u70b9+2\u3002 \u603b\u7ed3\u4e09：f\u51fd\u6570\u6267\u884c\u540e，\u6298\u70b9\u53ef\u80fd\u4e0d\u53d8，+1,+2\u3002 \u603b\u65b9\u6848\u6570：n+1 \u6298\u70b9\u4e0d\u53d8\u7684\u65b9\u6848\u6570：1+k \u6298\u70b9+1\u7684\u65b9\u6848\u6570：2 \u6298\u70b9+2\u7684\u65b9\u6848\u6570：<\/p>\n

(<\/p>\n

n<\/p>\n

+<\/p>\n

1<\/p>\n

)<\/p>\n

\u2212<\/p>\n

(<\/p>\n

1<\/p>\n

+<\/p>\n

k<\/p>\n

)<\/p>\n

\u2212<\/p>\n

2<\/p>\n

=<\/p>\n

n<\/p>\n

\u2212<\/p>\n

k<\/p>\n

\u2212<\/p>\n

2<\/p>\n

(n+1)-(1+k)-2=n-k-2<\/p>\n

<\/span><\/span>(<\/span>n<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>(<\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>k<\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>2<\/span><\/span>=<\/span><\/span><\/span><\/span>n<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>k<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/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

template<\/span><<\/span>long<\/span> long<\/span> MOD =<\/span> 1000000007<\/span>,<\/span> class<\/span> T1<\/span> =<\/span> int<\/span>,<\/span> class<\/span> T2<\/span> =<\/span> long<\/span> long<\/span>><\/span>
\nclass<\/span> C1097Int<\/span>
\n{<\/span>
\npublic<\/span>:<\/span>
\nC1097Int<\/span>(<\/span>T1 iData =<\/span> 0<\/span>)<\/span> :<\/span>m_iData<\/span>(<\/span>iData%<\/span> MOD)<\/span>
\n{<\/span><\/p>\n

}<\/span>
\nC1097Int<\/span>(<\/span>T2 llData)<\/span> :<\/span>m_iData<\/span>(<\/span>llData%<\/span> MOD)<\/span> {<\/span><\/p>\n

}<\/span>
\nC1097Int operator<\/span>+<\/span>(<\/span>const<\/span> C1097Int&<\/span> o)<\/span>const<\/span>
\n{<\/span>
\nreturn<\/span> C1097Int<\/span>(<\/span>(<\/span>(<\/span>T2)<\/span>m_iData +<\/span> o.<\/span>m_iData)<\/span> %<\/span> MOD)<\/span>;<\/span>
\n}<\/span>
\nC1097Int&<\/span> operator<\/span>+=<\/span>(<\/span>const<\/span> C1097Int&<\/span> o)<\/span>
\n{<\/span>
\nm_iData =<\/span> (<\/span>(<\/span>T2)<\/span>m_iData +<\/span> o.<\/span>m_iData)<\/span> %<\/span> MOD;<\/span>
\nreturn<\/span> *<\/span>this<\/span>;<\/span>
\n}<\/span>
\nC1097Int&<\/span> operator<\/span>-=<\/span>(<\/span>const<\/span> C1097Int&<\/span> o)<\/span>
\n{<\/span>
\nm_iData =<\/span> (<\/span>(<\/span>T2)<\/span>MOD +<\/span> m_iData –<\/span> o.<\/span>m_iData)<\/span> %<\/span> MOD;<\/span>
\nreturn<\/span> *<\/span>this<\/span>;<\/span>
\n}<\/span>
\nC1097Int operator<\/span>–<\/span>(<\/span>const<\/span> C1097Int&<\/span> o)<\/span>const<\/span>
\n{<\/span>
\nreturn<\/span> C1097Int<\/span>(<\/span>(<\/span>(<\/span>T2)<\/span>MOD +<\/span> m_iData –<\/span> o.<\/span>m_iData)<\/span> %<\/span> MOD)<\/span>;<\/span>
\n}<\/span>
\nC1097Int operator<\/span>*<\/span>(<\/span>const<\/span> C1097Int&<\/span> o)<\/span>const<\/span>
\n{<\/span>
\nreturn<\/span>(<\/span>(<\/span>T2)<\/span>m_iData *<\/span> o.<\/span>m_iData)<\/span> %<\/span> MOD;<\/span>
\n}<\/span>
\nC1097Int&<\/span> operator<\/span>*=<\/span>(<\/span>const<\/span> C1097Int&<\/span> o)<\/span>
\n{<\/span>
\nm_iData =<\/span> (<\/span>(<\/span>T2)<\/span>m_iData *<\/span> o.<\/span>m_iData)<\/span> %<\/span> MOD;<\/span>
\nreturn<\/span> *<\/span>this<\/span>;<\/span>
\n}<\/span>
\nC1097Int operator<\/span>\/<\/span>(<\/span>const<\/span> C1097Int&<\/span> o)<\/span>const<\/span>
\n{<\/span>
\nreturn<\/span> *<\/span>this<\/span> *<\/span> o.<\/span>PowNegative1<\/span>(<\/span>)<\/span>;<\/span>
\n}<\/span>
\nC1097Int&<\/span> operator<\/span>\/=<\/span>(<\/span>const<\/span> C1097Int&<\/span> o)<\/span>
\n{<\/span>
\n*<\/span>this<\/span> *=<\/span> o.<\/span>PowNegative1<\/span>(<\/span>)<\/span>;<\/span>
\nreturn<\/span> *<\/span>this<\/span>;<\/span>
\n}<\/span>
\nbool<\/span> operator<\/span>==<\/span>(<\/span>const<\/span> C1097Int&<\/span> o)<\/span>const<\/span>
\n{<\/span>
\nreturn<\/span> m_iData ==<\/span> o.<\/span>m_iData;<\/span>
\n}<\/span>
\nbool<\/span> operator<\/span><<\/span>(<\/span>const<\/span> C1097Int&<\/span> o)<\/span>const<\/span>
\n{<\/span>
\nreturn<\/span> m_iData <<\/span> o.<\/span>m_iData;<\/span>
\n}<\/span>
\nC1097Int pow<\/span>(<\/span>T2 n)<\/span>const<\/span>
\n{<\/span>
\nC1097Int iRet =<\/span> (<\/span>T1)<\/span>1<\/span>,<\/span> iCur =<\/span> *<\/span>this<\/span>;<\/span>
\nwhile<\/span> (<\/span>n)<\/span>
\n{<\/span>
\nif<\/span> (<\/span>n &<\/span> 1<\/span>)<\/span>
\n{<\/span>
\niRet *=<\/span> iCur;<\/span>
\n}<\/span>
\niCur *=<\/span> iCur;<\/span>
\nn >>=<\/span> 1<\/span>;<\/span>
\n}<\/span>
\nreturn<\/span> iRet;<\/span>
\n}<\/span>
\nC1097Int PowNegative1<\/span>(<\/span>)<\/span>const<\/span>
\n{<\/span>
\nreturn<\/span> pow<\/span>(<\/span>MOD –<\/span> 2<\/span>)<\/span>;<\/span>
\n}<\/span>
\nT1 ToInt<\/span>(<\/span>)<\/span>const<\/span>
\n{<\/span>
\nreturn<\/span> (<\/span>(<\/span>T2)<\/span>m_iData +<\/span> MOD)<\/span> %<\/span> MOD;<\/span>
\n}<\/span>
\nprivate<\/span>:<\/span>
\nT1 m_iData =<\/span> 0<\/span>;<\/span>;<\/span>
\n}<\/span>;<\/span><\/p>\n

class<\/span> Solution<\/span> {<\/span>
\npublic<\/span>:<\/span>
\nint<\/span> Ans<\/span>(<\/span>const<\/span> int<\/span> N,<\/span> const<\/span> int<\/span> K)<\/span> {<\/span>
\nif<\/span> (<\/span>1<\/span> ==<\/span> N)<\/span> {<\/span> return<\/span> 1<\/span> ==<\/span> K;<\/span> }<\/span>
\ntypedef<\/span> C1097Int<<\/span>123456<\/span>><\/span> BI;<\/span>
\nvector<<\/span>BI><\/span> pre =<\/span> {<\/span> 2<\/span>,<\/span>0<\/span>,<\/span>0<\/span> }<\/span>;<\/span>
\nfor<\/span> (<\/span>int<\/span> n =<\/span> 2<\/span>;<\/span> n <<\/span> N;<\/span> n++<\/span>)<\/span> {<\/span>
\nvector<<\/span>BI><\/span> cur<\/span>(<\/span>n +<\/span> 2<\/span>)<\/span>;<\/span>
\nfor<\/span> (<\/span>int<\/span> k =<\/span> 0<\/span>;<\/span> k <<\/span> pre.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> k++<\/span>)<\/span> {<\/span>
\ncur[<\/span>k]<\/span> +=<\/span> pre[<\/span>k]<\/span> *<\/span> (<\/span>1<\/span> +<\/span> k)<\/span>;<\/span>
\ncur[<\/span>k +<\/span> 1<\/span>]<\/span> +=<\/span> pre[<\/span>k]<\/span> *<\/span> 2<\/span>;<\/span>
\nif<\/span> (<\/span>n –<\/span> k –<\/span> 2<\/span> ><\/span> 0<\/span>)<\/span>
\n{<\/span>
\ncur[<\/span>k +<\/span> 2<\/span>]<\/span> +=<\/span> pre[<\/span>k]<\/span> *<\/span> (<\/span>n –<\/span> k –<\/span> 2<\/span>)<\/span>;<\/span>
\n}<\/span>
\n}<\/span>
\npre.<\/span>swap<\/span>(<\/span>cur)<\/span>;<\/span>
\n}<\/span>
\nreturn<\/span> pre[<\/span>K –<\/span> 1<\/span>]<\/span>.<\/span>ToInt<\/span>(<\/span>)<\/span>;<\/span>
\n}<\/span><\/p>\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>
\n\/\/CInBuff<> in; COutBuff<10'000'000> ob;<\/span><\/p>\n

int<\/span> N,<\/span>K;<\/span>
\ncin >><\/span> N >><\/span> K;<\/span>
\n#<\/span>ifdef<\/span> _DEBUG<\/span><\/span>
\n\/\/printf("N=%d,K=%d", N,M);<\/span>
\n\/\/Out(grid, ",gird=");<\/span>
\n\/\/Out(rr, ",rr=");<\/span>
\n \/\/Out(ab, ",ab=");<\/span>
\n \/\/Out(par, "par=");<\/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>;<\/span>
\ncout <<<\/span> res <<<\/span> "\\\\n"<\/span>;<\/span>
\nreturn<\/span> 0<\/span>;<\/span>
\n}<\/span>;<\/span><\/p>\n

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

TEST_METHOD<\/span>(<\/span>TestMethod11)<\/span>
\n{<\/span>
\nauto<\/span> res =<\/span> Solution<\/span>(<\/span>)<\/span>.<\/span>Ans<\/span>(<\/span>4<\/span>,<\/span>2<\/span>)<\/span>;<\/span>
\nAssertEx<\/span>(<\/span>12<\/span>,<\/span> res)<\/span>;<\/span>
\n}<\/span>
\nTEST_METHOD<\/span>(<\/span>TestMethod12)<\/span>
\n{<\/span>
\nauto<\/span> res =<\/span> Solution<\/span>(<\/span>)<\/span>.<\/span>Ans<\/span>(<\/span>2<\/span>,<\/span> 1<\/span>)<\/span>;<\/span>
\nAssertEx<\/span>(<\/span>2<\/span>,<\/span> res)<\/span>;<\/span>
\n}<\/span>
\nTEST_METHOD<\/span>(<\/span>TestMethod13)<\/span>
\n{<\/span>
\nauto<\/span> res =<\/span> Solution<\/span>(<\/span>)<\/span>.<\/span>Ans<\/span>(<\/span>1<\/span>,<\/span> 1<\/span>)<\/span>;<\/span>
\nAssertEx<\/span>(<\/span>1<\/span>,<\/span> res)<\/span>;<\/span>
\n}<\/span>
\nTEST_METHOD<\/span>(<\/span>TestMethod14)<\/span>
\n{<\/span>
\nauto<\/span> res =<\/span> Solution<\/span>(<\/span>)<\/span>.<\/span>Ans<\/span>(<\/span>1<\/span>,<\/span> 2<\/span>)<\/span>;<\/span>
\nAssertEx<\/span>(<\/span>0<\/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\u6570\u8bba：\u8d28\u6570\u3001\u6700\u5927\u516c\u7ea6\u6570\u3001\u83f2\u8700\u5b9a\u7406
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