CodeForces - 794C:Naming Company（博弈&简单贪心）

Posted 2021-01-01 hua-dong

Oleg the client and Igor the analyst are good friends. However, sometimes they argue over little things. Recently, they started a new company, but they are having trouble finding a name for the company.

To settle this problem, they‘ve decided to play a game. The company name will consist of n letters. Oleg and Igor each have a set of n letters (which might contain multiple copies of the same letter, the sets can be different). Initially, the company name is denoted by n question marks. Oleg and Igor takes turns to play the game, Oleg moves first. In each turn, a player can choose one of the letters c in his set and replace any of the question marks with c. Then, a copy of the letter c is removed from his set. The game ends when all the question marks has been replaced by some letter.

For example, suppose Oleg has the set of letters {i, o, i} and Igor has the set of letters {i, m, o}. One possible game is as follows :

Initially, the company name is ???.

Oleg replaces the second question mark with ‘i‘. The company name becomes ?i?. The set of letters Oleg have now is {i, o}.

Igor replaces the third question mark with ‘o‘. The company name becomes ?io. The set of letters Igor have now is {i, m}.

Finally, Oleg replaces the first question mark with ‘o‘. The company name becomes oio. The set of letters Oleg have now is {i}.

In the end, the company name is oio.

Oleg wants the company name to be as lexicographically small as possible while Igor wants the company name to be as lexicographically large as possible. What will be the company name if Oleg and Igor always play optimally?

A string s = s₁s₂...s_m is called lexicographically smaller than a string t = t₁t₂...t_m(where s ≠ t) if s_i < t_i where i is the smallest index such that s_i ≠ t_i. (so s_j = t_jfor all j < i)

Input

The first line of input contains a string s of length n (1 ≤ n ≤ 3·10⁵). All characters of the string are lowercase English letters. This string denotes the set of letters Oleg has initially.

The second line of input contains a string t of length n. All characters of the string are lowercase English letters. This string denotes the set of letters Igor has initially.

Output

The output should contain a string of n lowercase English letters, denoting the company name if Oleg and Igor plays optimally.

Examples

Input

tinkoff
zscoder

Output

fzfsirk

Input

xxxxxx
xxxxxx

Output

xxxxxx

Input

ioi
imo

Output

ioi

题意：A，B都有N个字符，A和B轮流贡献一个字符，A想组成的字典序越小，B想组成的字典序越大。

思路：A肯定是贡献出最小的(N+1)/2个字符，B贡献出最大的N/2个字符。 错误思路是A从小到大贡献字符，B从大到小贡献字符，但是会出现错误，

比如A=cbxy，B=aaaa，错误解=baca，正解=abac。正确的贪心策略应该是：对A，如果最小值小于B的最大值，那么把最小值填到前面，否则把最大值填到最后。B同理。

#include<bits/stdc++.h>
using namespace std;
const int maxn=1000010;
char a[maxn],b[maxn],ans[maxn];
int main()
{
    int N,L,R,h1,t1,h2,t2;
    scanf("%s%s",a+1,b+1); N=strlen(a+1);
    sort(a+1,a+N+1); sort(b+1,b+N+1);
    L=1; R=N; h1=1; t1=(N+1)/2; h2=N; t2=N-N/2+1;
    while(L<=R){
        if(a[h1]<b[h2]) ans[L++]=a[h1++];
        else ans[R--]=a[t1--];
        if(L>R) break;
        if(b[h2]>a[h1]) ans[L++]=b[h2--];
        else ans[R--]=b[t2++];
    }
    for(int i=1;i<=N;i++) printf("%c",ans[i]);
    return 0;
}