Zju2112 Dynamic Rankings<\/p>\n
Time Limit:10000MS Memory Limit:165536K
Total Submit:18 Accepted:7
Case Time Limit:1000MS<\/p>\n
Description <\/strong><\/p>\n \u7ed9\u5b9a\u4e00\u4e2a\u542b\u6709n\u4e2a\u6570\u7684\u5e8f\u5217a[1],a[2],a[3]\u2026\u2026a[n]\uff0c\u7a0b\u5e8f\u5fc5\u987b\u56de\u7b54\u8fd9\u6837\u7684\u8be2\u95ee\uff1a\u5bf9\u4e8e\u7ed9\u5b9a\u7684i,j,k\uff0c\u5728 a[i],a[i+1],a[i+2]\u2026\u2026a[j]\u4e2d\u7b2ck\u5c0f\u7684\u6570\u662f\u591a\u5c11(1\u2264k\u2264j-i+1)\uff0c\u5e76\u4e14\uff0c\u4f60\u53ef\u4ee5\u6539\u53d8\u4e00\u4e9ba[i]\u7684\u503c\uff0c\u6539\u53d8\u540e\uff0c\u7a0b\u5e8f\u8fd8\u80fd\u9488\u5bf9 \u6539\u53d8\u540e\u7684a\u7ee7\u7eed\u56de\u7b54\u4e0a\u9762\u7684\u95ee\u9898\u3002 \u7b2c\u4e00\u884c\u6709\u4e24\u4e2a\u6b63\u6574\u6570n(1\u2264n\u226410000)\uff0cm(1\u2264m\u226410000)\u3002\u5206\u522b\u8868\u793a\u5e8f\u5217\u7684\u957f\u5ea6\u548c\u6307\u4ee4\u7684\u4e2a\u6570\u3002 Input <\/strong><\/p>\n \u5bf9\u4e8e\u6bcf\u4e00\u6b21\u8be2\u95ee\uff0c\u4f60\u90fd\u9700\u8981\u8f93\u51fa\u4ed6\u7684\u7b54\u6848\uff0c\u6bcf\u4e00\u4e2a\u8f93\u51fa\u5360\u5355\u72ec\u7684\u4e00\u884c\u3002 <\/p>\n Output <\/strong><\/p>\n<\/p>\n Sample Input <\/strong><\/p>\n 5 3 Sample Output <\/strong><\/p>\n 3 Hint <\/strong><\/p>\n 20%\u7684\u6570\u636e\u4e2d\uff0cm,n\u2264100; Source <\/strong><\/p>\n \u5404\u4f4d\u795e\u725b\u81f3\u5c113KB\u7684\u4ee3\u7801\u91cf\u8ba9\u6211\u5f88\u518f\u3002\u3002\u4e00\u822c\u6765\u8bf4\u662f\u8981\u6811\u5957\u6811\u7684\u628a\uff0c\u4f46\u6211\u611f\u89c9\u90a3\u6837\u5f88\u96be\u5199\uff0c\u7d22\u6027\u5199\u4e2a\u5757\u72b6\u6570\u7ec4\u7b97\u4e86\u3002\u3002\u7ed3\u679c\u53d1\u73b0\u901f\u5ea6\u975e\u5e38\u5feb\u518f\u3002\u3002\u3002 Zju2112 Dynamic Rankings Time Limit:10000MS Memory Limit:165536KTotal Submit:18 Accepted:7 Case Time Limit:1000MS Description \u7ed9\u5b9a\u4e00\u4e2a\u542b\u6709n\u4e2a\u6570\u7684\u5e8f\u5217a[1],a[2],a[3]\u2026\u2026a[n]\uff0c\u7a0b\u5e8f\u5fc5\u987b\u56de\u7b54\u8fd9\u6837\u7684\u8be2\u95ee\uff1a\u5bf9\u4e8e\u7ed9\u5b9a\u7684i,j,k\uff0c\u5728 a[i],a[i+1],a[i+2]\u2026\u2026a[j]\u4e2d\u7b2ck\u5c0f\u7684\u6570\u662f\u591a\u5c11(1\u2264k\u2264j-i+1)\uff0c\u5e76\u4e14\uff0c\u4f60\u53ef\u4ee5\u6539\u53d8\u4e00\u4e9ba[i]\u7684\u503c\uff0c\u6539\u53d8\u540e\uff0c\u7a0b\u5e8f\u8fd8\u80fd\u9488\u5bf9 \u6539\u53d8\u540e\u7684a\u7ee7\u7eed\u56de\u7b54\u4e0a\u9762\u7684\u95ee\u9898\u3002 \u4f60\u9700\u8981\u7f16\u4e00\u4e2a\u8fd9\u6837\u7684\u7a0b\u5e8f\uff0c\u4ece\u8f93\u5165\u6587\u4ef6\u4e2d\u8bfb\u5165\u5e8f\u5217a\uff0c\u7136\u540e\u8bfb\u5165\u4e00\u7cfb\u5217\u7684\u6307\u4ee4\uff0c\u5305\u62ec\u8be2\u95ee\u6307\u4ee4\u548c\u4fee\u6539\u6307\u4ee4\u3002\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u8be2\u95ee\u6307\u4ee4\uff0c\u4f60\u5fc5\u987b\u8f93\u51fa\u6b63\u786e\u7684\u56de\u7b54\u3002 \u7b2c\u4e00\u884c\u6709\u4e24\u4e2a\u6b63\u6574\u6570n(1\u2264n\u226410000)\uff0cm(1\u2264m\u226410000)\u3002\u5206\u522b\u8868\u793a\u5e8f\u5217\u7684\u957f\u5ea6\u548c\u6307\u4ee4\u7684\u4e2a\u6570\u3002 \u7b2c\u4e8c\u884c\u6709n\u4e2a\u6570\uff0c\u8868\u793aa[1],a[2]\u2026\u2026a[n]\uff0c\u8fd9\u4e9b\u6570\u90fd\u5c0f\u4e8e10^9\u3002 \u63a5\u4e0b\u6765\u7684m\u884c\u63cf\u8ff0\u6bcf\u6761\u6307\u4ee4\uff0c\u6bcf\u884c\u7684\u683c\u5f0f\u662f\u4e0b\u9762\u4e24\u79cd\u683c\u5f0f\u4e2d\u7684\u4e00\u79cd\u3002 Q i j k \u6216\u8005 C i t Q i j k \uff08i,j,k\u662f\u6570\u5b57\uff0c1\u2264i\u2264j\u2264n, 1\u2264k\u2264j-i+1\uff09\u8868\u793a\u8be2\u95ee\u6307\u4ee4\uff0c\u8be2\u95eea[i]\uff0ca[i+1]\u2026\u2026a[j]\u4e2d\u7b2ck\u5c0f\u7684\u6570\u3002C i t (1\u2264i\u2264n\uff0c0\u2264t\u226410^9)\u8868\u793a\u628aa[i]\u6539\u53d8\u6210\u4e3at\u3002 Input \u5bf9\u4e8e\u6bcf\u4e00\u6b21\u8be2\u95ee\uff0c\u4f60\u90fd\u9700\u8981\u8f93\u51fa\u4ed6\u7684\u7b54\u6848\uff0c\u6bcf\u4e00\u4e2a\u8f93\u51fa\u5360\u5355\u72ec\u7684\u4e00\u884c\u3002 Output Sample Input 5 33 2 1 4 7Q 1 4 3C 2 6Q 2 5 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[10],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts\/253"}],"collection":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=253"}],"version-history":[{"count":0,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts\/253\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=253"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=253"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=253"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u4f60\u9700\u8981\u7f16\u4e00\u4e2a\u8fd9\u6837\u7684\u7a0b\u5e8f\uff0c\u4ece\u8f93\u5165\u6587\u4ef6\u4e2d\u8bfb\u5165\u5e8f\u5217a\uff0c\u7136\u540e\u8bfb\u5165\u4e00\u7cfb\u5217\u7684\u6307\u4ee4\uff0c\u5305\u62ec\u8be2\u95ee\u6307\u4ee4\u548c\u4fee\u6539\u6307\u4ee4\u3002\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u8be2\u95ee\u6307\u4ee4\uff0c\u4f60\u5fc5\u987b\u8f93\u51fa\u6b63\u786e\u7684\u56de\u7b54\u3002 <\/p>\n
\u7b2c\u4e8c\u884c\u6709n\u4e2a\u6570\uff0c\u8868\u793aa[1],a[2]\u2026\u2026a[n]\uff0c\u8fd9\u4e9b\u6570\u90fd\u5c0f\u4e8e10^9\u3002
\u63a5\u4e0b\u6765\u7684m\u884c\u63cf\u8ff0\u6bcf\u6761\u6307\u4ee4\uff0c\u6bcf\u884c\u7684\u683c\u5f0f\u662f\u4e0b\u9762\u4e24\u79cd\u683c\u5f0f\u4e2d\u7684\u4e00\u79cd\u3002
Q i j k \u6216\u8005 C i t
Q i j k \uff08i,j,k\u662f\u6570\u5b57\uff0c1\u2264i\u2264j\u2264n, 1\u2264k\u2264j-i+1\uff09\u8868\u793a\u8be2\u95ee\u6307\u4ee4\uff0c\u8be2\u95eea[i]\uff0ca[i+1]\u2026\u2026a[j]\u4e2d\u7b2ck\u5c0f\u7684\u6570\u3002C i t (1\u2264i\u2264n\uff0c0\u2264t\u226410^9)\u8868\u793a\u628aa[i]\u6539\u53d8\u6210\u4e3at\u3002 <\/p>\n
3 2 1 4 7
Q 1 4 3
C 2 6
Q 2 5 3<\/p>\n
6<\/p>\n
40%\u7684\u6570\u636e\u4e2d\uff0cm,n\u22641000;
100%\u7684\u6570\u636e\u4e2d\uff0cm,n\u226410000\u3002 <\/p>\n
\u5bf9\u6bcf\u4e2a\u5757\u4fdd\u5b58\u6392\u5e8f\u7684\u7ed3\u679c\uff0c\u540c\u65f6\u4fdd\u5b58\u6574\u4f53\u6240\u6709\u7684\u6570\uff0c\u90a3\u4e48\u67e5\u8be2\u4e00\u4e2a\u6570\u5728\u4e00\u4e2a\u533a\u95f4\u4e2d\u6bd4\u5b83\u5c0f\u7684\u6570\u6570\u91cf\u662f
O(N^0.5LogN)\u7684\u3002\u3002\u518d\u52a0\u4e0a\u4e8c\u5206\u627e\u8fd9\u4e2a\u6570\uff0c\u5c31\u662fN^0.5*LogN^2\u4e86\u3002\u3002
\u8fd8\u6709\u4fee\u6539\u7684\u8bdd\u76f4\u63a5\u4fee\u6539\u4e00\u6392\u5e8f\u7684\u7ed3\u679c\uff08\u63d2\u5165\u6392\u5e8f\uff09\u548c\u6574\u4f53\u8fd9\u4e2a\u6570\uff0c\u662fO\uff08N^0.5\uff09\u7684\u3002\u3002\u4f46\u6211\u611f\u89c9\u67e5\u8be2\u90fd\u90a3\u4e48\u6162\u4e86\u4fee\u6539\u4e5f\u65e0\u6240\u8c13\u4e86\uff0c\u5c31\u66b4\u529bsort\u4e86\u518f\u3002\u3002\u3002\u7531\u4e8e\u8fd9\u91cc\u4e0d\u80fd\u641e\u51fa\u5f53\u524d\u6240\u6709\u6570\u7684\u6392\u5217\uff0c\u6240\u4ee5\u4e8c\u5206\u53ea\u80fd\u6309\u7167Log\uff0810^9\uff09=30\u6765\u641e\uff0c\u5b9e\u9645\u4e0a\u5982\u679c\u5148\u79bb\u7ebf\u4e00\u4e0b\u8bfb\u5165\u6240\u6709\u6570\u5c31\u53ef\u4ee5\u76f4\u63a5\u5728\u6240\u6709\u6570\u4e2d\u4e8c\u5206\uff0c\u90a3\u4e48\u5c31\u662fLog(20000)=15..\u5feb\u4e00\u500d\u3002\u3002\u4e0d\u8fc7\u6ca1\u5fc5\u8981\u3002\u3002\u3002
Code\uff1a
#include <vector>
#include <algorithm>
#include <utility>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#define rep(i,n) for(int i=0;i<n;i++)
#define For(i,l,r) for(int i=l;i<=r;i++)
#define pb push_back
const int inf=~0U>>1,maxn=10000,size=100;
int T[size][size],N[size]={},A[maxn],n,m,t,d=1<<6;
using namespace std;
void init()
{
scanf("%d%d",&n,&m);rep(i,n)scanf("%d",A+i),T[i\/size][N[i\/size]++]=A[i];
t=1+(n-1)\/size;rep(i,t)sort(T[i],T[i]+N[i]);
}
int get(int*A,int s,int x)
{
int i,l;
for(i=s,l=d;l;l>>=1)
if(i-l>=0&&A[i-l]>=x)i-=l;
return i;
}
int Count(int l,int r,int x)
{
int a=l\/size,b=r\/size,s=0;;
if(a==b){For(i,l,r)s+=A[i]<x;return s;}
For(i,l,(a+1)*size-1)s+=A[i]<x;
For(i,b*size,r)s+=A[i]<x;a++;b–;
For(i,a,b)s+=get(T[i],N[i],x);
return s;
}
int kth(int l,int r,int k)
{
#define C(x) (Count(l,r,x))
int i,d;
for(i=0,d=1<<30;d;d>>=1)
if(C(i+d)<k)i+=d;
return i;
}
void Change(int p,int x)
{
int a=p\/size;int t=A[p];A[p]=x;
t=lower_bound(T[a],T[a]+N[a],t)-T[a];
T[a][t]=x;sort(T[a],T[a]+N[a]);
}
int main()
{
\/\/freopen("in","r",stdin);
init();char c;int i,j,k;
while(m–)
{
scanf("n%c",&c);
if(c==’C’)scanf("%d%d",&i,&j),Change(i-1,j);
else scanf("%d%d%d",&i,&j,&k),printf("%dn",kth(i-1,j-1,k));
}
} <\/p>\n","protected":false},"excerpt":{"rendered":"