BestCoder Round #76 解题报告

DZY Loves Partition

【思路】

贪心

【代码】

 #include <iostream>
 using namespace std;

 typedef long long ll;
 const int mod=1e9+;

 ll n,k,a[];

 int main()
 {
     int T;
     cin>>T;
     while(T--) {
         cin>>n>>k;
         ll x=n/k;
         if(k*(k+)/>n)
             cout<<-<<endl;
         else {
             if(k%) {
                 for(int i=k/;i>;i--) a[i]=x-(k/-i+);
                 for(int i=k/+;i<=k;i++) a[i]=x+(i-k/-);
                 int m=n%k;
                 for(int i=k;m>;m--,i--) a[i]++;
             }
             else {
                 for(int i=k/;i>;i--) a[i]=x-(k/-i+);
                 for(int i=k/+;i<=k;i++) a[i]=x+(i-k/);
                 int m=n%k;
                 for(int i=k/;i&&m;i--,m--) a[i]++;
                 if(m>)
                     for(int i=k;i>k/&&m;i--,m--) a[i]++;
             }
             ll ans=a[];
             for(int i=;i<=k;i++) { ans*=a[i]; ans%=mod; }
             cout<<ans<<endl;
         }
     }
     return ;
 }

DZY Loves Math

【思路】

打表

打表ans[i,j]表示矩形i*250,j*250的答案，对于一次询问n，m，每次得到最大的ij使得i*250<n j*250<m，然后把剩下的算出来。

一本正经地说如何打表 =_=

【代码】

 #include<cstdio>
 #include<cstring>
 #define FOR(a,b,c) for(int a=b;a<=c;a++)
 using namespace std;

 typedef long long ll;
 const int N = +;

 ll gcd(ll a,ll b)
 {
     return b==? a:gcd(b,a%b);
 }

 int n,m;
 ll ans[][]={
     0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,0ll,1233565ll,4074650ll,8499351ll,14528348ll,22112783ll,31258028ll,42022235ll,54333886ll,68215245ll,83604852ll,100342301ll,119037956ll,139247081ll,160953944ll,184189845ll,208808216ll,235131699ll,263014890ll,292077145ll,322860316ll,354671659ll,387832730ll,423732485ll,461079108ll,499977159ll,540274672ll,581612419ll,625238784ll,670079719ll,716110832ll,763486909ll,811607982ll,862174745ll,914838526ll,968366587ll,1023771930ll,1079828725ll,1136843756ll,1196336605ll,1256381288ll,1317713203ll,1379320934ll,1439303311ll,1508074118ll,1578314363ll,1650013408ll,1723239749ll,1797767306ll,1874097743ll,1952029758ll,2031041435ll,2111879366ll,2193671779ll,2276770508ll,2362650307ll,2449778924ll,2538434079ll,2628251382ll,2718503929ll,2811912478ll,0ll,4074650ll,7236964ll,17864932ll,24259110ll,41201906ll,50876714ll,74003070ll,87203958ll,116277486ll,133058054ll,167233594ll,188423532ll,228708828ll,253627440ll,299146386ll,328164752ll,378484650ll,412390688ll,466667998ll,505578840ll,563009154ll,607236872ll,669206596ll,720509506ll,786706462ll,843095434ll,911849082ll,974794670ll,1047549924ll,1115737952ll,1190005868ll,1264697142ll,1339929572ll,1424756182ll,1501767640ll,1593854530ll,1671015968ll,1770440234ll,1847219398ll,1956837368ll,2030004380ll,2149961952ll,2210179474ll,2351928318ll,2422742568ll,2569912062ll,2644572028ll,2796409034ll,2875707214ll,3032824276ll,3116246290ll,3277281100ll,3365867606ll,3528716602ll,3625171034ll,3793290222ll,3894617276ll,4065679406ll,4171705146ll,4345313948ll,0ll,8499351ll,17864932ll,28939297ll,35610296ll,63494369ll,85831754ll,109824679ll,123325676ll,169090859ll,204928360ll,241168757ll,262620164ll,324371425ll,374868562ll,424523261ll,453828086ll,529403663ll,595220668ll,656839453ll,696000496ll,780108199ll,861608968ll,937418147ll,988996720ll,1083420733ll,1184485044ll,1271484839ll,1334685190ll,1436158113ll,1554905956ll,1654406813ll,1729396692ll,1829850397ll,1972075540ll,2084341879ll,2176688896ll,2275329913ll,2436571426ll,2561254695ll,2671159624ll,2756364197ll,2943146462ll,3068576207ll,3211034502ll,3282096321ll,3506136000ll,3659382531ll,3813622236ll,3893219363ll,4130850224ll,4298799179ll,4466017070ll,4554882051ll,4798687738ll,4986725705ll,5166874336ll,5268464759ll,5521869348ll,5723965803ll,5917068192ll,0ll,14528348ll,24259110ll,35610296ll,42740908ll,83198724ll,106324840ll,130613736ll,144392318ll,208411158ll,246107630ll,282609150ll,304327232ll,389027182ll,443487210ll,493446622ll,523107680ll,625330940ll,698187390ll,760051088ll,799452600ll,911465470ll,1005458366ll,1081519300ll,1133368358ll,1257134626ll,1376023992ll,1463256784ll,1526743394ll,1657930338ll,1800923756ll,1900708674ll,1975994418ll,2102503784ll,2279451312ll,2391966442ll,2484589240ll,2605384694ll,2812002824ll,2936912474ll,3047075826ll,3144811750ll,3392914280ll,3519004490ll,3661713362ll,3733029238ll,4035701846ll,4191330348ll,4345870056ll,4425754808ll,4745617662ll,4919142056ll,5086642584ll,5175820758ll,5502192048ll,5702220956ll,5882625548ll,5984482702ll,6321784548ll,6541312016ll,6734673648ll,0ll,22112783ll,41201906ll,63494369ll,83198724ll,124627673ll,148001904ll,172590113ll,186649202ll,270388205ll,330066628ll,389852943ll,436983512ll,525645975ll,580431294ll,630728761ll,660696414ll,790779983ll,898270176ll,995877233ll,1072806210ll,1196162587ll,1290464446ll,1366786217ll,1418950170ll,1572946999ll,1739028432ll,1874442949ll,1988534642ll,2143324915ll,2286618174ll,2386716025ll,2462300926ll,2615399437ll,2852089542ll,3025134285ll,3180239108ll,3344387577ll,3551282570ll,3676456871ll,3786935942ll,3897331653ll,4214759412ll,4408297083ll,4627164056ll,4776128211ll,5081171766ll,5237081669ll,5391918630ll,5472103957ll,5875453374ll,6135451835ll,6391298444ll,6569733045ll,6906700926ll,7107024291ll,7287720602ll,7389877471ll,7812095558ll,8129394837ll,8423805042ll,0ll,31258028ll,50876714ll,85831754ll,106324840ll,148001904ll,171941516ll,196800194ll,211178390ll,316141356ll,378292382ll,461234136ll,512332126ll,601308190ll,656377906ll,706965470ll,737384424ll,896594862ll,1012352332ll,1139932028ll,1227606726ll,1351240580ll,1445812392ll,1522386392ll,1574818868ll,1759960982ll,1945872960ll,2112208804ll,2249776166ll,2404851204ll,2548432030ll,2648801530ll,2724745138ll,2904940488ll,3179214498ll,3377831842ll,3575409640ll,3739783898ll,3946955526ll,4072397760ll,4183135406ll,4306486460ll,4688071714ll,4883043816ll,5180937700ll,5332576040ll,5637899048ll,5794159632ll,5949303390ll,6029824002ll,6518035676ll,6785109782ll,7126618080ll,7314732588ll,7651978856ll,7852565842ll,8033547024ll,8136029326ll,8644330156ll,8981157352ll,9360315550ll,0ll,42022235ll,74003070ll,109824679ll,130613736ll,172590113ll,196800194ll,222291013ll,236944836ll,364744127ll,451601168ll,538106187ll,589488592ll,678812019ll,734166008ll,785060803ll,815781018ll,1005556937ll,1158410560ll,1296089025ll,13840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 };

 int main()
 {
     int T; scanf("%d",&T);
     while(T--) {
         scanf("%d%d",&n,&m);
         ll res=;
         FOR(i,,) FOR(j,,)
             if(i*>n&&j*>m) {
                 i--,j--;
                 res=ans[i][j];
                 FOR(x,,i*) FOR(y,j*+,m)
                     res+=gcd(x&y,x|y);
                 FOR(x,i*+,n) FOR(y,,m)
                     res+=gcd(x&y,x|y);
                 i=j=;
             }
         printf("%I64d\n",res);
     }
     return ;
 }

DZY Loves Connecting

【思路】

树形DP

设f[u]表示经过u的所有连续集的大小之和，cnt[u]表示经过u的所有连续集的个数。枚举u的每一个儿子，假设已经统计完前S-1个儿子，则有转移式：

f[u]=f[u]+f[u]*cnt[v]+f[v]*cnt[u]

cnt[u]=cnt[u]+cnt[u]*cnt[v]

感觉跟树分治的统计信息类似，大概就是因为信息可以直接由dp得出所以才采用的树DP而不是树分治。

【代码】

 #include<set>
 #include<cmath>
 #include<queue>
 #include<vector>
 #include<cstdio>
 #include<cstring>
 #include<iostream>
 #include<algorithm>
 //#pragma comment(linker, "/STACK:102400000,102400000")
 #define trav(u,i) for(int i=front[u];i;i=e[i].nxt)
 #define FOR(a,b,c) for(int a=(b);a<=(c);a++)
 using namespace std;

 typedef long long ll;
 const int N = 3e5+;
 const int M = N<<;
 const int MOD = 1e9+;

 ll read() {
     char c=getchar();
     ll f=,x=;
     while(!isdigit(c)) {
         if(c=='-') f=-; c=getchar();
     }
     while(isdigit(c))
         x=x*+c-'',c=getchar();
     return x*f;
 }
 struct Edge {
     int v,nxt;
     Edge(int v=,int nxt=):v(v),nxt(nxt){}
 }e[M];
 int en=,front[N];
 void adde(int u,int v)
 {
     e[++en]=Edge(v,front[u]); front[u]=en;
 }

 int n;
 ll f[N],cnt[N];

 void dp(int u,int fa)
 {
     cnt[u]=f[u]=;
     int v;
     trav(u,i) if((v=e[i].v)!=fa) {
         dp(v,u);
         f[u]=(f[u]*(cnt[v]+)%MOD+cnt[u]*f[v]%MOD)%MOD;
         cnt[u]=cnt[u]*(cnt[v]+)%MOD;
     }
 }

 int main()
 {
     int T=read();
     while(T--) {
         n=read();
         en=; memset(front,,sizeof(front));
         FOR(i,,n) {
             int v=read();
             adde(i,v),adde(v,i);
         }
         ll ans=;
         dp(,-);
         FOR(i,,n) ans=(ans+f[i])%MOD;
         printf("%I64d\n",ans);
     }
     return ;
 }

DZY Loves Sorting

【思路】

二分+线段树

二分最终a[k]的值为mid，依次进行每一个操作，对于0号操作，统计区间[l,r]内比mid大的点数为x，将[l,r-x]设为0，[r-x+1,r]设为1，1号操作类似。然后用线段树提供区间赋值与区间查询的操作。

最终看a[k]==0?，如果成立则a[k]可能更小，因为

000[0]00111

01分界处为mid，[]为a[k]

太神辣，奇技淫巧系列+1

【代码】

 #include<set>
 #include<cmath>
 #include<queue>
 #include<vector>
 #include<cstdio>
 #include<cstring>
 #include<iostream>
 #include<algorithm>
 #define trav(u,i) for(int i=front[u];i;i=e[i].nxt)
 #define FOR(a,b,c) for(int a=(b);a<=(c);a++)
 using namespace std;

 typedef long long ll;
 const int N = 2e5+;

 ll read() {
     char c=getchar();
     ll f=,x=;
     while(!isdigit(c)) {
         if(c=='-') f=-; c=getchar();
     }
     while(isdigit(c))
         x=x*+c-'',c=getchar();
     return x*f;
 }

 struct Tnode {
     int l,r,s,tag;
 }T[N<<];
 void pushdown(int u) {
     if(T[u].tag!=-&&T[u].l!=T[u].r) {
         int lc=u<<,rc=lc|;
         T[lc].tag=T[rc].tag=T[u].tag;
         if(T[u].tag) {
             T[lc].s=T[lc].r-T[lc].l+;
             T[rc].s=T[rc].r-T[rc].l+;
         } else
             T[lc].s=T[rc].s=;
         T[u].tag=-;
     }
 }
 void maintain(int u) {
     T[u].s=T[u<<].s+T[u<<|].s;
 }
 void update(int u,int L,int R,int v) {
     pushdown(u);
     if(L<=T[u].l&&T[u].r<=R) {
         T[u].tag=v;
         if(v==) T[u].s=T[u].r-T[u].l+;
         else T[u].s=;
     } else {
         int mid=T[u].l+T[u].r>>;
         if(L<=mid) update(u<<,L,R,v);
         if(mid<R)  update(u<<|,L,R,v);
         maintain(u);
     }
 }
 int query(int u,int L,int R) {
     pushdown(u);
     if(L<=T[u].l&&T[u].r<=R) return T[u].s;
     else {
         int mid=T[u].l+T[u].r>>,ans=;;
         if(L<=mid) ans+=query(u<<,L,R);
         if(mid<R)  ans+=query(u<<|,L,R);
         return ans;
      }
 }

 struct Node {
     int op,l,r;
 }q[N];
 int n,m,K,a[N],M;

 void build(int u,int l,int r)
 {
     T[u].l=l,T[u].r=r; T[u].s=;
     T[u].tag=-;
     if(l==r) { T[u].s=a[l]>M; return ; }
     int mid=l+r>>;
     build(u<<,l,mid);
     build(u<<|,mid+,r);
     maintain(u);
 }
 int can()
 {
     build(,,n);
     FOR(i,,m) {
         if(q[i].op==) {
             int x=query(,q[i].l,q[i].r);
             update(,q[i].l,q[i].r,);
             if(x) update(,q[i].r-x+,q[i].r,);
         } else {
             int x=query(,q[i].l,q[i].r);
             update(,q[i].l,q[i].r,);
             if(x) update(,q[i].l,q[i].l+x-,);
         }
     }
     return query(,K,K)==;
 }

 int main()
 {
     int kase=read();
     while(kase--) {
         n=read(),m=read();
         int L=,R=,ans=;
         FOR(i,,n) a[i]=read(),R=max(R,a[i]);
         FOR(i,,m)
             q[i].op=read(),q[i].l=read(),q[i].r=read();
         K=read();
         while(L<=R) {
             M=L+R>>;
             if(can()) R=M-,ans=M; else L=M+;
         }
         printf("%d\n",ans);
     }
     return ;
 }