#583072 (C++14) No.1388 Less than K

• 問題: No.1388 Less than K
• ユーザー: 蜜蜂
• 提出日時: 2020-11-23 01:34:22
• 言語: C++14 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 1,003 ms / 3,000 ms
• コード長: 2,179 bytes
• コンパイル時間: 1,704 ms
• コンパイル使用メモリ: 173,036 KB
• 実行使用メモリ: 491,572 KB
• 最終ジャッジ日時: 2024-11-26 08:00:12
• 合計ジャッジ時間: 15,805 ms
• ジャッジサーバーID （参考情報）: judge5 / judge3

ファイルパターン	結果
sample	AC * 3
other	AC * 74

ソースコード

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#include<bits/stdc++.h>
using namespace std;
using ll = long long;
#define fi first
#define se second
constexpr ll mod=998244353;
const int MAX = 505000;
ll fac[MAX], finv[MAX], inv[MAX];
// テーブルを作る前処理
void COMinit(){
    fac[0]=fac[1]=1;
    finv[0]=finv[1]=1;
    inv[1]=1;
    for(int i=2;i<MAX;i++){
        fac[i]=fac[i-1]*i%mod;
        inv[i]=mod-inv[mod%i]*(mod/i)%mod;
        finv[i]=finv[i-1]*inv[i]%mod;
    }
}
// 二項係数計算
long long COM(int n,int k){
    if(n<k) return 0;
    if(n<0||k<0) return 0;
    return fac[n]*(finv[k]*finv[n-k]%mod)%mod;
}
void solve1(int h,int w,int k){
  int x=min(h,w);
  vector<vector<int>> dp(x+1,vector<int>(2*k+1,0));
  //dp[i][j] := move2 i times & distance j-k
  dp[0][k]=1;
  for(int i=0;i<=x;i++){
    for(int j=2*k;j>=0;j--){
      if(j-2>=0){
        dp[i][j-2]+=dp[i][j];
        if(dp[i][j-2]>mod){
          dp[i][j-2]-=mod;
        }
      }
    }    
    if(i!=x){
      for(int j=0;j<=k;j++){
        int r=k-j,s=k+j;
        if(r+2<=2*k){
          dp[i+1][r+2]+=dp[i][r];
          if(dp[i+1][r+2]>mod){
            dp[i+1][r+2]-=mod;
          }
        }
        if(r!=s){
          r=s;
          if(r+2<=2*k){
            dp[i+1][r+2]+=dp[i][r];
            if(dp[i+1][r+2]>mod){
              dp[i+1][r+2]-=mod;
            }
          }
        }
      }
    }    
  }
      
  ll ans=0;
  for(int i=0;i<=x;i++){
    ll way=dp[i][k];
    way*=(COM(h+w,h-i)*COM(w+i,w-i))%mod;
    way%=mod;
    ans+=way;
    ans%=mod;
  }
  cout<<ans<<endl;
}
void solve2(int h,int w,int k){
  int x=min(h,w);
  ll ans=0;
  for(int i=0;i<=x;i++){
    int kk=(k+2)/2;
    int a=1;
    ll way=COM(2*i,i);
    while(i-a*kk>=0){
      if(a%2==1){
        way-=2*COM(2*i,i-a*kk);
        way%=mod;
      }
      else{
        way+=2*COM(2*i,i-a*kk);
        way%=mod;
      }
      a++;
    }
    if(way<0){
      way+=mod*100;
      way%=mod;
    }
    way*=(COM(h+w,h-i)*COM(w+i,w-i))%mod;
    way%=mod;
    ans+=way;
    ans%=mod;
  }
  cout<<ans<<endl;
}
int main(){
  COMinit();
  int h,w,k;
  cin>>h>>w>>k;
  h--;
  w--;
  if(k<=300){
    solve1(h,w,k);
  }
  else{
    solve2(h,w,k);
  }
}
 
 
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