Submission #132066

#	Time	Username	Problem	Language	Result	Execution time	Memory
132066		dragonslayerit	Fish (IOI08_fish)	C++14	100 / 100	1289 ms	61336 KiB

fish

#include <cstdio>
#include <algorithm>
#include <vector>

//Strategy:
//Sort fishes by size
//Relabel gems by last appearance (e.g. gem of largest fish is 0)
//count multisets of gems => count multisets of fish such that if a fish is chosen, all smaller fish with same gem are chosen
//For the actual subset of fish, some gem will be chosen to be "boosted" to the largest fish with that gem.
//Iterate over last fish in multiset (pre-boosting) and count number of valid subsets
//A multiset is bad iff no gem in the prefix is present and the largest fish's gem cannot be boosted.

int N,MOD;

int cps[500005];
int cps_size=0;

int freq[500005];
int freq2[500005];
int last[500005];

int half[500005];
int prev[500005];

struct Fish{
  int size,gem;
  bool operator<(Fish f)const{
    return size<f.size;
  }
}fishes[500005];

struct Op{
  int sgn;
  int l,r,x;
  Op(int sgn,int l,int r,int x):sgn(sgn),l(l),r(r),x(x){
  }
};

std::vector<Op> ops[500005];

int st[1000010];

void pull(int i){
  st[i]=1LL*st[i<<1]*st[i<<1|1]%MOD;
}

void update(int i){
  for(st[i+=N]++;i>1;i>>=1){
    pull(i>>1);
  }
}

int query(int a,int b){
  int res=1;
  for(a+=N,b+=N;a<b;a>>=1,b>>=1){
    if(a&1) res=1LL*res*st[a++]%MOD;
    if(b&1) res=1LL*res*st[--b]%MOD;
  }
  return res;
}

int main(){
  int K;
  scanf("%d %d",&N,&K);
  scanf("%d",&MOD);
  for(int i=0;i<N;i++){
    scanf("%d %d",&fishes[i].size,&fishes[i].gem);
    fishes[i].gem--;
  }
  std::sort(fishes,fishes+N);
  //Relabel gems by last appearance
  std::fill(cps,cps+K,-1);
  for(int i=N-1;i>=0;i--){
    if(cps[fishes[i].gem]==-1){
      cps[fishes[i].gem]=cps_size++;
    }
  }
  for(int i=0;i<N;i++){
    fishes[i].gem=cps[fishes[i].gem];
  }
  for(int k=0;k<K;k++){
    last[k]=-1;
  }
  for(int i=0;i<N;i++){
    prev[i]=last[fishes[i].gem];
    last[fishes[i].gem]=i;
  }
  for(int k=0;k<K;k++){
    int low=-1,high=N;
    while(high-low>1){
      int mid=(low+high)/2;
      if(fishes[mid].size*2<=fishes[last[k]].size){
	low=mid;
      }else{
	high=mid;
      }
    }
    half[k]=high;
    //half[k] is index of first fish larger than fishes[last[k]].size/2
  }
  
  int prefix=K-1;//largest gem # that can be "boosted"
  for(int i=0;i<N;i++){
    //Counting configurations where fishes[i].gem occurs exactly freq[fishes[i].gem] times
    while(prefix>=0&&fishes[last[prefix]].size<2*fishes[i].size) prefix--;
    //Subtract multisets where none in prefix exist to be boosted
    ops[i+1].emplace_back(-1,prefix+1,K,fishes[i].gem);
    //Add back multisets where none in prefix exist to be boosted but fishes[i] can be boosted
    //Must be able to take all of fishes[i].gem before i
    if(prev[i]==-1||fishes[prev[i]].size*2<=fishes[last[fishes[i].gem]].size){
      //Cannot have fish whose size <=1/2*size of last fish with fishes[i].gem
      ops[std::min(i,half[fishes[i].gem])].emplace_back(1,prefix+1,K,fishes[i].gem);
    }
  }
  //Count all
  ops[N].emplace_back(1,0,K,-1);
  //init st
  std::fill(st,st+N*2,1);
  //-1 for empty set
  int ans=-1;
  for(int i=0;i<=N;i++){
    for(Op op:ops[i]){
      int product=1;
      /*
      for(int k=op.l;k<op.r;k++){
	if(k==op.x) continue;
	product=1LL*product*(freq[k]+1)%MOD;
      }
      */
      if(op.x>=op.l&&op.x<op.r){
	product=1LL*query(op.l,op.x)*query(op.x+1,op.r)%MOD;
      }else{
	product=1LL*query(op.l,op.r);
      }
      ans=(ans+op.sgn*product)%MOD;
    }
    if(i==N) break;
    freq[fishes[i].gem]++;
    update(fishes[i].gem);
  }
  printf("%d\n",(ans+MOD)%MOD);
  return 0;
}

Compilation message (stderr)

fish.cpp: In function 'int main()':
fish.cpp:64:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%d %d",&N,&K);
   ~~~~~^~~~~~~~~~~~~~~
fish.cpp:65:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%d",&MOD);
   ~~~~~^~~~~~~~~~~
fish.cpp:67:10: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%d %d",&fishes[i].size,&fishes[i].gem);
     ~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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