UVALive - 4255-Guess（拓扑排序）

Problem UVALive - 4255-Guess

Time Limit: 3000 mSec

Problem Description

 

Input

The input consists of T test cases. The number of test cases T is given in the first line of the input. Each test case consists of two lines. The first line contains an integer n (1 ≤ n ≤ 10), where n is the length of a sequence of integers. The second line contains a string of n(n + 1)/2 characters such that the first n characters correspond to the first row of the sign matrix, the next n−1 characters to the second row, ..., and the last character to the n-th row.

Output

For each test case, output exactly one line containing a sequence of n integers which generates the sign matrix. If more than one sequence generates the sign matrix, you may output any one of them. Every integer in the sequence must be between −10 and 10, both inclusive.

 

Sample Input

3 4 -+0++++--+ 2 +++ 5 ++0+-+-+--+-+-

Sample Output

-2 5 -3 1

3 4

1 2 -3 4 -5

 

题解：这个题联想到拓扑排序不容易（做题太少），不过有了这个大方向之后就很好办了，关于赋值的问题，给最开始入度为0的点随便赋个值，之后每一层的点的是上一层的值减一，最后把sum[0]要化为0， 因此每个数都减去sum[0]即可。

 

#include <bits/stdc++.h>

using namespace std;

#define REP(i, n) for (int i = 1; i <= (n); i++)
#define sqr(x) ((x) * (x))

const int maxn = 50 + 10;
const int maxm = 30 + 10;
const int maxs = 10000 + 10;

typedef long long LL;
typedef pair<int, int> pii;
typedef pair<double, double> pdd;

const LL unit = 1LL;
const int INF = 0x3f3f3f3f;
const LL mod = 1000000007;
const double eps = 1e-14;
const double inf = 1e15;
const double pi = acos(-1.0);

int n, deg[maxn];
vector<int> G[maxn];
int ans[maxn];

void toposort()
{
    queue<int> que;
    for (int i = 0; i <= n; i++)
    {
        if (!deg[i])
        {
            que.push(i);
            ans[i] = 10;
        }
    }

    while (!que.empty())
    {
        int head = que.front();
        que.pop();
        for (auto v : G[head])
        {
            deg[v]--;
            if (!deg[v])
            {
                que.push(v);
                ans[v] = ans[head] - 1;
            }
        }
    }
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    freopen("input.txt", "r", stdin);
    //freopen("output.txt", "w", stdout);
    int T;
    cin >> T;
    while (T--)
    {
        cin >> n;
        for (int i = 0; i <= n; i++)
        {
            G[i].clear();
            deg[i] = ans[i] = 0;
        }
        string str;
        cin >> str;
        int pos = 0;
        for (int i = 1; i <= n; i++)
        {
            for (int j = i; j <= n; j++)
            {
                if (str[pos] == '+')
                {
                    G[j].push_back(i - 1);
                    deg[i - 1]++;
                }
                else if (str[pos] == '-')
                {
                    G[i - 1].push_back(j);
                    deg[j]++;
                }
                pos++;
            }
        }
        toposort();
        for (int i = 1; i <= n; i++)
        {
            ans[i] -= ans[0];
        }
        ans[0] = 0;
        for (int i = 1; i <= n; i++)
        {
            cout << ans[i] - ans[i - 1];
            if (i != n)
            {
                cout << " ";
            }
            else
            {
                cout << endl;
            }
        }
    }
    return 0;
}