BestCoder Round #76 解题报告

 

DZY Loves Partition 

【思路】

    贪心

【代码】

 

 1 #include <iostream>
 2 using namespace std;
 3 
 4 typedef long long ll;
 5 const int mod=1e9+7;
 6 
 7 ll n,k,a[200000];
 8 
 9 int main() 
10 {
11     int T;
12     cin>>T;
13     while(T--) {
14         cin>>n>>k;
15         ll x=n/k;
16         if(k*(k+1)/2>n)
17             cout<<-1<<endl;
18         else {
19             if(k%2) {
20                 for(int i=k/2;i>0;i--) a[i]=x-(k/2-i+1);
21                 for(int i=k/2+1;i<=k;i++) a[i]=x+(i-k/2-1);
22                 int m=n%k;
23                 for(int i=k;m>0;m--,i--) a[i]++;
24             }
25             else {
26                 for(int i=k/2;i>0;i--) a[i]=x-(k/2-i+1);
27                 for(int i=k/2+1;i<=k;i++) a[i]=x+(i-k/2);
28                 int m=n%k;
29                 for(int i=k/2;i&&m;i--,m--) a[i]++;
30                 if(m>0)
31                     for(int i=k;i>k/2&&m;i--,m--) a[i]++;
32             }
33             ll ans=a[1];
34             for(int i=2;i<=k;i++) { ans*=a[i]; ans%=mod; }
35             cout<<ans<<endl;
36         }
37     }
38     return 0;
39 }

View Code

 

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】

 

 1 #include<cstdio>
 2 #include<cstring>
 3 #define FOR(a,b,c) for(int a=b;a<=c;a++)
 4 using namespace std;
 5 
 6 typedef long long ll;
 7 const int N = 250+5;
 8 
 9 ll gcd(ll a,ll b) 
10 {
11     return b==0? a:gcd(b,a%b);
12 }
13 
14 int n,m;
15 ll ans[61][61]={
16     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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17 };
18 
19 int main()
20 {
21     int T; scanf("%d",&T);
22     while(T--) {
23         scanf("%d%d",&n,&m);
24         ll res=0;
25         FOR(i,1,61) FOR(j,1,61)
26             if(i*250>n&&j*250>m) {
27                 i--,j--;
28                 res=ans[i][j];
29                 FOR(x,1,i*250) FOR(y,j*250+1,m)
30                     res+=gcd(x&y,x|y);
31                 FOR(x,i*250+1,n) FOR(y,1,m)
32                     res+=gcd(x&y,x|y);
33                 i=j=62;
34             }
35         printf("%I64d\n",res);
36     }
37     return 0;
38 }

View Code

 

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】

 

 1 #include<set>
 2 #include<cmath>
 3 #include<queue>
 4 #include<vector>
 5 #include<cstdio>
 6 #include<cstring>
 7 #include<iostream>
 8 #include<algorithm>
 9 //#pragma comment(linker, "/STACK:102400000,102400000")
10 #define trav(u,i) for(int i=front[u];i;i=e[i].nxt)
11 #define FOR(a,b,c) for(int a=(b);a<=(c);a++)
12 using namespace std;
13 
14 typedef long long ll;
15 const int N = 3e5+10;
16 const int M = N<<1;
17 const int MOD = 1e9+7;
18 
19 ll read() {
20     char c=getchar();
21     ll f=1,x=0;
22     while(!isdigit(c)) {
23         if(c=='-') f=-1; c=getchar();
24     }
25     while(isdigit(c))
26         x=x*10+c-'0',c=getchar();
27     return x*f;
28 }
29 struct Edge {
30     int v,nxt;
31     Edge(int v=0,int nxt=0):v(v),nxt(nxt){}
32 }e[M];
33 int en=1,front[N];
34 void adde(int u,int v) 
35 {
36     e[++en]=Edge(v,front[u]); front[u]=en;
37 }
38 
39 int n;
40 ll f[N],cnt[N];
41 
42 void dp(int u,int fa)
43 {
44     cnt[u]=f[u]=1;
45     int v;
46     trav(u,i) if((v=e[i].v)!=fa) {
47         dp(v,u);
48         f[u]=(f[u]*(cnt[v]+1)%MOD+cnt[u]*f[v]%MOD)%MOD;
49         cnt[u]=cnt[u]*(cnt[v]+1)%MOD;
50     }
51 }
52 
53 int main()
54 {
55     int T=read();
56     while(T--) {
57         n=read();
58         en=1; memset(front,0,sizeof(front));
59         FOR(i,2,n) {
60             int v=read();
61             adde(i,v),adde(v,i);
62         }
63         ll ans=0;
64         dp(1,-1);
65         FOR(i,1,n) ans=(ans+f[i])%MOD;
66         printf("%I64d\n",ans); 
67     }
68     return 0;
69 }

View Code

 

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】

  1 #include<set>
  2 #include<cmath>
  3 #include<queue>
  4 #include<vector>
  5 #include<cstdio>
  6 #include<cstring>
  7 #include<iostream>
  8 #include<algorithm>
  9 #define trav(u,i) for(int i=front[u];i;i=e[i].nxt)
 10 #define FOR(a,b,c) for(int a=(b);a<=(c);a++)
 11 using namespace std;
 12 
 13 typedef long long ll;
 14 const int N = 2e5+10;
 15 
 16 ll read() {
 17     char c=getchar();
 18     ll f=1,x=0;
 19     while(!isdigit(c)) {
 20         if(c=='-') f=-1; c=getchar();
 21     }
 22     while(isdigit(c))
 23         x=x*10+c-'0',c=getchar();
 24     return x*f;
 25 }
 26 
 27 struct Tnode {
 28     int l,r,s,tag;
 29 }T[N<<2];
 30 void pushdown(int u) {
 31     if(T[u].tag!=-1&&T[u].l!=T[u].r) {
 32         int lc=u<<1,rc=lc|1;
 33         T[lc].tag=T[rc].tag=T[u].tag;
 34         if(T[u].tag) {
 35             T[lc].s=T[lc].r-T[lc].l+1;
 36             T[rc].s=T[rc].r-T[rc].l+1;
 37         } else
 38             T[lc].s=T[rc].s=0;
 39         T[u].tag=-1;
 40     }
 41 }
 42 void maintain(int u) {
 43     T[u].s=T[u<<1].s+T[u<<1|1].s;
 44 }
 45 void update(int u,int L,int R,int v) {
 46     pushdown(u);
 47     if(L<=T[u].l&&T[u].r<=R) {
 48         T[u].tag=v;
 49         if(v==1) T[u].s=T[u].r-T[u].l+1;
 50         else T[u].s=0;
 51     } else {
 52         int mid=T[u].l+T[u].r>>1;
 53         if(L<=mid) update(u<<1,L,R,v);
 54         if(mid<R)  update(u<<1|1,L,R,v);
 55         maintain(u);
 56     }
 57 }
 58 int query(int u,int L,int R) {
 59     pushdown(u);
 60     if(L<=T[u].l&&T[u].r<=R) return T[u].s;
 61     else {
 62         int mid=T[u].l+T[u].r>>1,ans=0;;
 63         if(L<=mid) ans+=query(u<<1,L,R);
 64         if(mid<R)  ans+=query(u<<1|1,L,R);
 65         return ans;
 66      }
 67 }
 68 
 69 struct Node {
 70     int op,l,r;
 71 }q[N];
 72 int n,m,K,a[N],M;
 73 
 74 void build(int u,int l,int r) 
 75 {
 76     T[u].l=l,T[u].r=r; T[u].s=0;
 77     T[u].tag=-1;
 78     if(l==r) { T[u].s=a[l]>M; return ; }
 79     int mid=l+r>>1;
 80     build(u<<1,l,mid);
 81     build(u<<1|1,mid+1,r);
 82     maintain(u);
 83 }
 84 int can() 
 85 {
 86     build(1,1,n);
 87     FOR(i,1,m) {
 88         if(q[i].op==0) {
 89             int x=query(1,q[i].l,q[i].r);
 90             update(1,q[i].l,q[i].r,0);
 91             if(x) update(1,q[i].r-x+1,q[i].r,1);
 92         } else {
 93             int x=query(1,q[i].l,q[i].r);
 94             update(1,q[i].l,q[i].r,0);
 95             if(x) update(1,q[i].l,q[i].l+x-1,1);
 96         }
 97     }
 98     return query(1,K,K)==0;
 99 }
100 
101 int main()
102 {
103     int kase=read();
104     while(kase--) {
105         n=read(),m=read();
106         int L=0,R=0,ans=0;
107         FOR(i,1,n) a[i]=read(),R=max(R,a[i]);
108         FOR(i,1,m)
109             q[i].op=read(),q[i].l=read(),q[i].r=read();
110         K=read();
111         while(L<=R) {
112             M=L+R>>1;
113             if(can()) R=M-1,ans=M; else L=M+1;
114         }
115         printf("%d\n",ans);
116     }
117     return 0;
118 }

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