Go: package main

import (
	"bufio"
	"os"
	"strings"
	"strconv"
	"fmt"
)

var scanner = bufio.NewScanner(os.Stdin)

const INF = 0x7FFFFFFF

func main() {
	for scanner.Scan() {
		buf := strings.Split(scanner.Text(), " ")
		n, _ := strconv.Atoi(buf[0])
		m, _ := strconv.Atoi(buf[1])
		if n == 0 && m == 0 {
			break
		}
		chair := make([]string, n+1)
		for i := range chair {
			chair[i] = "#"
		}
		chair[n] = "Sentinel"
		for i := 0; i < m; i++ {
			scanner.Scan()
			switch who := scanner.Text(); who {
			case "A": // 左から眺めて行って空いている席があったら即座に座る
				for j := 0; j < n; j++ {
					if chair[j] == "#" {
						chair[j] = "A"
						break
					}
				}
				// log.Println(chair)
				break // 次の人を読み込む
			case "B":
				flag := true
				// 右端からAの隣でない席を探していく
				for j := n-1; j > -1; j-- {
					if chair[j] == "#" && (j == 0 || chair[j-1] != "A") && chair[j+1] != "A" {
						flag = false
						chair[j] = "B"
						break
					}
				}
				// Aの隣しか空いていないので一番左端の空いている席に座る
				if flag {
					for j := 0; j < n; j++ {
						if chair[j] == "#" {
							chair[j] = "B"
							break
						}
					}
				}
				// log.Println(chair)
				break // 次の人を読み込む
			case "C":
				if i == 0 {
					chair[n/2] = "C" // 先客が誰もいないときは真ん中の椅子に座る
				} else {
					for j := 0; j < n; j++ { // 左から舐めて
						if chair[j] != "#" { // その席が空いていなくて
							if chair[j+1] == "#" { // 右隣が空いているなら座る
								chair[j+1] = "C"
								break
							} else if j != 0 && chair[j-1] == "#" { // 右隣が空いていないので左隣に座る
								chair[j-1] = "C"
								break
							}
						}
					}
				}
				// log.Println(chair)
				break // 次の人を読み込む
			case "D":
				distanceTable := make([]int ,n)
				for j := range distanceTable {
					distanceTable[j] = INF
				}
				for j:= 0; j < n; j++ {
					if chair[j] != "#" {
						for k := 0; k < n; k++ {
							distanceTable[k] = min(distanceTable[k], abs(j-k))
						}
					}
				}
				// log.Println("distanceTAble:", distanceTable)
				at := 0
				distance := 0
				for j := 0; j < n; j++ {
					if distance < distanceTable[j] {
						at = j
						distance = distanceTable[j]
					}
				}
				chair[at] = "D"
				// log.Println(chair)
				break // 次の人を読み込む
			}
		}
		fmt.Println(strings.Join(chair[:len(chair)-1], ""))
	}
}

func min(a, b int) int {
	if a > b {
		return b
	}
	return a
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

C++: #include<iostream>
#define MAX_N 110
using namespace std;

char dx[MAX_N];
bool firstflag;
void reset();
void typeA(int n);
void typeB(int n);
void typeC(int n);
void typeD(int n);

int main(){
    int n, m;
    while(cin >>n >>m){
        if(n == 0 && m == 0) break;
        reset();
        firstflag = true;
        for(int i = 0; i < m; i++){
            char input;
            cin >>input;
            if(input == 'A') typeA(n);
            if(input == 'B') typeB(n);
            if(input == 'C') typeC(n);
            if(input == 'D') typeD(n);
            if(i == 0) firstflag = false;
            for(int i = n - 1; i >= 0; i--){
                cout <<dx[i];
            }
            cout <<endl;
        }
    }
    return 0;
}

void reset(){
    for(int i = 0; i < MAX_N; i++){
        dx[i] = '#';
    }
}

void typeA(int n){
    for(int i = n - 1; i >= 0; i--){
        if(dx[i] == '#'){
            dx[i] = 'A';
            break;
        }
    }
}

void typeB(int n){
    bool okflag = false;
    for(int i = 0; i < n; i++){
        if(dx[i] == '#'){
            if(i == 0){
                if(dx[i + 1] != 'A'){
                    dx[i] = 'B';
                    okflag = true;
                }
            } else if(i == n - 1){
                if(dx[i - 1] != 'A'){
                    dx[i] = 'B';
                    okflag = true;
                }
            } else{
                if(dx[i + 1] != 'A' && dx[i - 1] != 'A'){
                    dx[i] = 'B';
                    okflag = true;
                }
            }
        }
        if(okflag) break;
    }
    if(!okflag){
        for(int i = n - 1; i >= 0; i--){
            if(dx[i] == '#'){
                dx[i] = 'B';
                break;
            }
        }
    }
}

void typeC(int n){
    if(firstflag){
        if(n % 2 == 0){
            dx[n - (n / 2 + 1)] = 'C';
        } else{
            dx[n - ((n + 1) / 2)] = 'C';
        }
    } else{
        bool okflag = false;
        for(int i = n - 1; i >= 0; i--){
            if(i != 0){
                if(dx[i] !='#' && dx[i - 1] == '#'){
                    dx[i - 1] = 'C';
                    okflag = true;
                }
                if(okflag) break;
            }
            if(i != n - 1){
                if(dx[i] != '#' && dx[i + 1] == '#'){
                    dx[i + 1] = 'C';
                    okflag = true;
                }
                if(okflag) break;
            }
        }
    }
}

void typeD(int n){
    if(firstflag){
        dx[n - 1] = 'D';
    } else{
        int max = 0, maxi = 0, now = 0, f = 0;
        for(int i = 0; i < n; i++){
            if(dx[i] == '#'){
                now++;
            } else{
                if(f == 0) f++;
                else if(f == 1) f++;
                if(max <= now){
                    max = now;
                    maxi = i;
                }
                now = 0;
            }
        }
        //cout <<"max = " <<max <<"maxi = " <<maxi <<"f = " <<f <<endl;
        if(max <= now){
            //cout <<"!" <<endl;
            dx[n -  1] = 'D';
        } else if(f == 1){
            dx[0] = 'D';
        } else{
            int tmp = maxi - (max / 2);
            if(max % 2 == 1) tmp--;
            dx[tmp] = 'D';
        }
    }
}

C++: #include<iostream>
using namespace std;

int main(){

  int n,m;
  int j;
  char chair[100];
  char p;
  int left,max,m_left;

  while(1){

    cin >> n >> m;
    if(n==0 && m==0)
      break;

    for(int i=0; i<n; i++)
      chair[i]='#';


    for(int i=0; i<m; i++){

    cin >> p;

    if(p=='A'){
      j=0;
      while(chair[j]!='#')
	j++;

      chair[j]='A';
    }///////////////////////A

    else if(p=='B'){
      j=n-1;
      while(1){
	if(chair[j]=='#'){
	  if(j==n-1 && chair[j-1]!='A')
	    break;

	  else if(j>0 && chair[j+1]!='A' && chair[j-1]!='A')
	    break;

	  else if(chair[j+1]!='A')
	    break;
	  
	  else if(j==0){
	    j=-1;
	    break;
	  }
	}
	j--;
      }

      if(j!=-1)
	chair[j]='B';

      else{
	j=0;
	while(chair[j]!='#')
	  j++;

	chair[j]='B';
      }

    }////////////////////////B


    else if(p=='C'){
      j=0;
      while(1){
	if(chair[j]!='#'){
	  if(chair[j+1]=='#'&&j!=n-1){
	    j++;
	    break;
	  }
	  else if(j!=0 && chair[j-1]=='#'){
	    j--;
	    break;
	  }
	}

	if(j==n-1){
	  j=-1;
	  break;
	}

	j++;
      }

      if(j==-1){
	if(n%2==1)
	  j=(n+1)/2-1;
	else
	  j=n/2;
      }

      chair[j] = 'C';
    }///////////////////////C


    else{
      left=0; max=1; m_left=0;
      j=1;
      while(j<=n-1){
	if(chair[j]!='#'){
	  left=j;

	  j++;
	}

	if(max < j-left){
	  max = j-left;
	  m_left = left;
	}

	j++;
      }

      if(max <= 2){
	j=0;
	while(j<n && chair[j] != '#')
	  j++;
      }

      else if(max == n-1)
	j=0;

      else{
	if(j==n)
	  j--;
	else if(j==0)
	  continue;
	else if(max%2==1)
	  j=m_left+max/2 +1;
	else
	  j=m_left+max/2;
      }


      chair[j]='D';

    }///////////////////////D

    }


    for(int i=0; i<n; i++)
      cout << chair[i];


    cout << endl;

  }


  return 0;

}