假回溯-uva140带宽

Posted 2021-01-29 doubest

题目链接：https://vjudge.net/problem/UVA-140

题解：这道题利用全排函数即可解决，但是这道题技巧性强，稍微不注意就会超时，一开始没有想起全排函数，自己写回溯全排超时了，主要问题出在：1、递归过程中疯狂判断最小带宽，循环太多了。2、处理原字符串的方法太LOW了。在借鉴了紫书思路的之后写出了AC代码如下：

AC代码：

 

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<vector>
#define MAXN 30
using namespace std;
typedef long long ll;

vector<int> u;
vector<int> v;

int main(void){
    char s[1000];
    while(scanf("%s",s) == 1 && s[0] != ‘#‘){
        u.clear();
        v.clear();
        int len = strlen(s);
        int p = 0,q = 0;
        int n = 0;
        int id[256];
        char letter[MAXN];
        for(char i = ‘A‘;i<=‘Z‘;i++){
            if(strchr(s,i) != NULL){
                id[i] = n++;
                letter[id[i]] = i;
            }
        }
        for(;;){
            if(p<len && q < len){
                while(1){
                    if(s[p] == ‘:‘){
                        break;
                    }
                    p++;
                    if(p == len){
                        break;
                    }
                }
                while(1){
                    if(s[q] == ‘;‘){
                        break;
                    }
                    q++;
                    if(q == len){
                        break;
                    }
                }
                for(int i = p+1;i<q;i++){
                    u.push_back(id[s[p - 1]]);
                    v.push_back(id[s[i]]);
                }
            }
            else
                break;
            p++;q++;
        }
        int P[MAXN],BESTP[MAXN];
        int pos[MAXN];
        int best = n;
        for(int i = 0;i<n;i++){
            P[i] = i;
        }
        do{
            for(int i = 0;i<n;i++){
                pos[P[i]] = i;
            }
            int bandwith = 0;
            for(int i = 0;i<u.size();i++){
                bandwith = max(bandwith,abs(pos[u[i]]-pos[v[i]]));
            }
            if(bandwith < best){
                best = bandwith;
                memcpy(BESTP,P,sizeof(P));
            }
        }while(next_permutation(P,P+n));
        for(int i = 0; i < n; i++) printf("%c ", letter[BESTP[i]]);
        printf("-> %d
", best);
    }
    return 0;
}

 

超时代码：

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>
#include<string>
#include<cmath>
#define MAXN 30
using namespace std;
typedef long long ll;
int mmin;
int maxalp;
int nowMin;
int graph[MAXN][MAXN];
int nowbox[MAXN];
int ansbox[MAXN];
void findNiceList(int cur){
    if(cur - 1 == maxalp){
        int ok = 1;
        int nowbig;
        int big1;
        int big = 0;
        for(int i =0;i<cur;i++){
            big1 = 0;
            if(!ok){
                break;
            }
            int nowchar =  nowbox[i];
            for(int j = 0;j<=maxalp;j++){
                if(graph[nowchar][j] == 1){
                    nowbig = abs((find(nowbox,nowbox+cur,j) - nowbox) - i);
                    if(nowbig > big1){
                        big1 = nowbig;
                    }
                    if(big1 >= mmin){
                        ok = 0;
                        break;
                    }
                }
            }
            if(big1 > big){
                big = big1;
            }
        }
        nowMin = big;
        if(nowMin < mmin && ok){
            for(int i = 0;i<=maxalp;i++){
                ansbox[i] = nowbox[i];
                mmin = nowMin;
            }
        }
    }
    else{
        for(int i = 0;i<=maxalp;i++){
            int ok = 1;
            for(int j = 0;j<cur;j++){
                if(nowbox[j] == i){
                    ok = 0;
                    break;
                }
            }
            if(ok){
                nowbox[cur] =  i;
                findNiceList(cur+1);
            }
        }
    }
}

/*void graphprint(void){
    for(int i = 0;i<=maxalp;i++){
        printf("%c:",‘A‘+i);
        for(int j = 0; j<MAXN;j++){
            if(graph[i][j] == 1){
                printf("%c ",j+‘A‘);
            }
        }
        printf("
");
    }
}*/

int main(void){
    string inistr;
    const string endstr = "#";
    while((cin >> inistr) && inistr != endstr){
        memset(graph,-1,sizeof(graph));
        int len = inistr.size();
        maxalp = -1;
        mmin = 99;
        nowMin = 0;
        for(int i = 0;i < len;i++){
            if(inistr[i] <= ‘Z‘ && inistr[i] >=‘A‘){
                if(inistr[i] - ‘A‘ > maxalp){
                    maxalp = inistr[i] - ‘A‘;
                }
            }
            if(i+1 == len || inistr[i+1] == ‘;‘){
                int okindex;
                for(int m = i - 1;m>=0;m--){
                    if(inistr[m] == ‘:‘){
                        okindex = m;
                        break;
                    }
                }
                for(int m = okindex + 1;m<=i;m++){
                    graph[inistr[okindex - 1] - ‘A‘][inistr[m] - ‘A‘] = 1;
                    graph[inistr[m] - ‘A‘][inistr[okindex - 1] - ‘A‘] = 1;
                }
            }
        }
        findNiceList(0);
        for(int i = 0;i<=maxalp;i++){
            printf("%c ",ansbox[i] + ‘A‘);
        }
        printf("-> ");
        printf("%d
",mmin);
    }
    return 0;
}