丑数 Humble Numbers

https://www.luogu.org/problemnew/show/P2723

题解：

C++版本一

题解：STL+优化

/*
*@Author:   STZG
*@Language: C++
*/
#include <bits/stdc++.h>
#include<iostream>
#include<algorithm>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<string>
#include<vector>
#include<bitset>
#include<queue>
#include<deque>
#include<stack>
#include<cmath>
#include<list>
#include<map>
#include<set>
//#define DEBUG
#define RI register int
#define endl "\n"
using namespace std;
typedef long long ll;
//typedef __int128 lll;
const int N=100+10;
const int M=100000+10;
const int MOD=1e9+7;
const double PI = acos(-1.0);
const double EXP = 1E-8;
const int INF = 0x3f3f3f3f;
int t,n,m,k,p,l,r,u,v;
int ans,cnt,flag,temp,sum;
struct node{int v;int i;bool operator < (const node &S)const{return v>S.v;}
};
ll a[N];
priority_queue<node>heap;
char str;
int main()
{
#ifdef DEBUGfreopen("input.in", "r", stdin);//freopen("output.out", "w", stdout);
#endif//ios::sync_with_stdio(false);//cin.tie(0);//cout.tie(0);//scanf("%d",&t);//while(t--){scanf("%d%d",&k,&n);for(ll i=1;i<=k;i++){scanf("%lld",&a[i]);}heap.push({1,1});node humble;t=n;n++;while(n--){humble=heap.top();heap.pop();for(int i=humble.i;i<=k;i++){ll num=humble.v*a[i];if(num<=(1ll<<31)-1)heap.push({num,i});}}printf("%d\n",humble.v);//}#ifdef DEBUGprintf("Time cost : %lf s\n",(double)clock()/CLOCKS_PER_SEC);
#endif//cout << "Hello world!" << endl;return 0;
}

C++版本二

题解：贪心

#include<iostream>
#include<cmath>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;int i,j,n,m,k;
long long a[150],s[100011],f[100011];int main(){cin>>k>>n;for(i=1;i<=k;i++) cin>>a[i];f[0]=1;for(i=1;i<=n;i++){m=2147483647;for(int j=1;j<=k;j++){while(a[j]*f[s[j]]<=f[i-1]) s[j]++;if(a[j]*f[s[j]]<m) m=a[j]*f[s[j]];}f[i]=m;}cout<<f[n]<<endl;return 0;
}

C++版本三

题解：平衡树

#include <iostream>
#include <cstdio>using namespace std;const int S = 1 << 20;
char frd[S], *hed = frd + S;
const char *tal = hed;inline char nxtChar()
{if (hed == tal)fread(frd, 1, S, stdin), hed = frd;return *hed++;
}inline int get()
{char ch; int res = 0;while (!isdigit(ch = nxtChar()));res = ch ^ 48;while (isdigit(ch = nxtChar()))res = res * 10 + ch - 48;return res;
}typedef long long ll;
const int N = 11e4 + 5;
ll Int = 2147483647ll;
int fa[N], lc[N], rc[N], sze[N], val[N];
int T, n, k, rt, top, stk[N], a[N];inline void Push(int x) {sze[x] = sze[lc[x]] + sze[rc[x]] + 1;}inline void Rotate(int x)
{int y = fa[x], z = fa[y];int b = (lc[y] == x ? rc[x] : lc[x]);fa[y] = x; fa[x] = z;if (b) fa[b] = y;if (z) (lc[z] == y ? lc[z] : rc[z]) = x;if (lc[y] == x) rc[x] = y, lc[y] = b;else lc[x] = y, rc[y] = b;Push(y);
}inline bool Which(int x) {return lc[fa[x]] == x;}inline void Splay(int x, int tar)
{while (fa[x] != tar){if (fa[fa[x]] != tar)Which(fa[x]) == Which(x) ? Rotate(fa[x]) : Rotate(x);Rotate(x); }Push(x);if (!tar) rt = x;
}inline void Insert(int vi)
{int x = rt, y = 0, dir;while (x){y = x;if (val[x] == vi) return ;if (val[x] > vi) x = lc[x], dir = 0;else x = rc[x], dir = 1;  }int w = y; if (y) ++sze[y];while (fa[w]) ++sze[w = fa[w]];x = top ? stk[top--] : ++T;fa[x] = y; val[x] = vi; sze[x] = 1;if (y) (dir ? rc[y] : lc[y]) = x; Splay(x, 0);
}inline void Join(int x, int y)
{int w = y;while (lc[w]) w = lc[w];lc[fa[x] = w] = x; fa[rt = y] = 0;Splay(w, 0);
}inline void Delete(int x)
{Splay(x, 0);stk[++top] = x;int L = lc[x], R = rc[x];lc[x] = rc[x] = 0;if (!L || !R) fa[rt = L + R] = 0;else Join(L, R);
}inline int GetKth(int k)
{int x = rt;while (x){if (k <= sze[lc[x]])x = lc[x];else {k -= sze[lc[x]] + 1;if (!k) return x;x = rc[x];}}return 0;
}inline void Print(int x)
{if (!x) return ;Print(lc[x]); Print(rc[x]); stk[++top] = x; fa[x] = lc[x] = rc[x] = 0;
}inline int FindMin() {int x = rt; while (lc[x]) x = lc[x]; return x;}int main()
{k = get(); n = get(); int x, cnt = 0; ll y;for (int i = 1; i <= k; ++i) Insert(a[i] = get());while (++cnt <= n){y = val[x = FindMin()]; Delete(x);for (int i = 1; i <= k; ++i) if (y * a[i] < Int) Insert(y * a[i]);else break;if (sze[rt] + cnt >= n) {Int = val[x = GetKth(n - cnt)]; Splay(x, 0); Print(rc[x]); rc[x] = 0; Push(x);}}cout << y << endl;
}

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