UVa 1377 - Ruler (BFS)

题意

给出一些数字,要求输出一些标记,根据这些标记可以得到上面的所有数字。

思路

一开始写了个贪心,后来发现不行。又写了个DFS,TLE了。最后还是看了帆神和柯神的题解。

这里好像有个YY的结论:最后所选的标号要么是给出的,要么是他们之间的差。

用BFS。不过好像所用的最长长度不能超过输入的最长,题目没说。感觉不太科学。

然后就是每走一步就加上每一个还没选到的值的和和差。我用了set判重。

代码

#include <cstdio>
#include <stack>
#include <set>
#include <iostream>
#include <string>
#include <vector>
#include <queue>
#include <functional>
#include <cstring>
#include <algorithm>
#include <cctype>
#include <ctime>
#include <string>
#include <map>
#include <iomanip>
#include <cmath>
#define LL long long
#define ULL unsigned long long
#define SZ(x) (int)x.size()
#define Lowbit(x) ((x) & (-x))
#define MP(a, b) make_pair(a, b)
#define MS(arr, num) memset(arr, num, sizeof(arr))
#define PB push_back
#define F first
#define S second
#define ROP freopen("input.txt", "r", stdin);
#define MID(a, b) (a + ((b - a) >> 1))
#define LC rt << 1, l, mid
#define RC rt << 1|1, mid + 1, r
#define LRT rt << 1
#define RRT rt << 1|1
#define BitCount(x) __builtin_popcount(x)
#define BitCountll(x) __builtin_popcountll(x)
#define LeftPos(x) 32 - __builtin_clz(x) - 1
#define LeftPosll(x) 64 - __builtin_clzll(x) - 1
const double PI = acos(-1.0);
const int INF = 0x3f3f3f3f;
using namespace std;
const double eps = 1e-6;
const int MAXN = 50 + 10;
const int MOD = 1000007;
typedef pair<int, int> pii;
typedef vector<int>::iterator viti;
typedef vector<pii>::iterator vitii;
 
struct STATE
{
    int ans;
    set<int> st;
}ans;
 
map<int, int> mp;
vector<int> num;
set<int> iniNum, vis;
int n;
 
void Init()
{
    mp.clear(); num.clear(); iniNum.clear(); vis.clear();
    for (int i = 0; i < n; i++)
    {
        int tmp;
        scanf("%d", &tmp);
        if (!iniNum.count(tmp))
        {
            num.push_back(tmp);
            iniNum.insert(tmp);
        }
    }
    sort(num.begin(), num.end());
    for (int i = 0; i < SZ(num); i++) mp[num[i]] = i;
    ans.ans = 0, ans.st.clear();
}  
 
STATE Add(int num, STATE cur)
{
    for (set<int>::iterator it = cur.st.begin(); it != cur.st.end(); it++)
    {
        int tmp = abs(*it - num);
        if (mp.count(tmp)) cur.ans |= (1 << mp[tmp]);
    }
    cur.st.insert(num);
    return cur;
}
 
void BFS()
{
    STATE cur;
    queue<STATE> qu;
    cur.ans = 0, cur.st.insert(0);
    qu.push(cur);
    int result = (1 << SZ(num)) - 1;
    while (!qu.empty())
    {
        cur = qu.front(); qu.pop();
        if (cur.ans == result)
        {
            if (SZ(ans.st) == 0) ans = cur;
            else
            {
                if (SZ(cur.st) > SZ(ans.st)) return;
                else if (SZ(ans.st) > SZ(cur.st)) ans = cur;
                else if (*ans.st.rbegin() > *cur.st.rbegin()) ans = cur;
            }
        }
        else
        {
            if (SZ(cur.st) > 7) continue;
            for (int i = 0; i < SZ(num); i++)
            {
                if (((1 << i) & cur.ans) == 0)
                {
                    for (set<int>::iterator it = cur.st.begin(); it != cur.st.end(); it++)
                    {
                        if (*it + num[i] <= *(--num.end()))
                        {
                            STATE tmp = Add(*it + num[i], cur);
                            if (!vis.count(tmp.ans)) qu.push(tmp);
                            vis.insert(tmp.ans);
                        }
                        if (*it > num[i])
                        {
                            STATE tmp = Add(*it - num[i], cur);
                            if (!vis.count(tmp.ans)) qu.push(tmp);
                            vis.insert(tmp.ans);
                        }
                    }
                     
                }
            }
        }
    }
}
 
int main()
{
    //ROP;
    int i, j, cases = 0;
    while (scanf("%d", &n), n)
    {
        Init();
        BFS();
        printf("Case %d:\n", ++cases);
        printf("%d\n", SZ(ans.st));
        set<int>::iterator it = ans.st.begin();
        for (; it != ans.st.end(); it++)
        {
            if (it == ans.st.begin()) printf("%d", *it);
            else printf(" %d", *it);
        }
        puts("");
    }
    return 0;
}

Powered by Jekyll and Theme by solid