UVA - 1423 Guess （拓扑排序）

题意：已知矩阵S，求序列a。已知矩阵Sij = “ + ” if ai + . . . + aj > 0; Sij = “ − ” if ai + . . . + aj < 0; and Sij = “0” otherwise.

分析：

1、由Sij = ‘+’ 可知，ai + . . . + aj > 0，即sum[j] - sum[i - 1] > 0，即sum[j] > sum[i - 1]，即j优先级比i - 1高，由j向i - 1连一条有向边，i - 1入度+1。

2、按优先级由高到低，依次从10递减赋值，可知各前缀和的大小，由此得出序列a。

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<cctype>
#include<cmath>
#include<iostream>
#include<sstream>
#include<iterator>
#include<algorithm>
#include<string>
#include<vector>
#include<set>
#include<map>
#include<stack>
#include<deque>
#include<queue>
#include<list>
#define lowbit(x) (x & (-x))
const double eps = 1e-8;
inline int dcmp(double a, double b){
    if(fabs(a - b) < eps) return 0;
    return a > b ? 1 : -1;
}
typedef long long LL;
typedef unsigned long long ULL;
const int INT_INF = 0x3f3f3f3f;
const int INT_M_INF = 0x7f7f7f7f;
const LL LL_INF = 0x3f3f3f3f3f3f3f3f;
const LL LL_M_INF = 0x7f7f7f7f7f7f7f7f;
const int dr[] = {0, 0, -1, 1, -1, -1, 1, 1};
const int dc[] = {-1, 1, 0, 0, -1, 1, -1, 1};
const int MOD = 1e9 + 7;
const double pi = acos(-1.0);
const int MAXN = 10 + 10;
const int MAXT = 100 + 10;
using namespace std;
char s[MAXT];
int indegree[MAXN];
int pic[MAXN][MAXN];
int sum[MAXN];
bool vis[MAXN];
int ans[MAXN];
int n;
void topsort(){
    int num = 10, cnt = 0;
    while(cnt < n + 1){
        memset(vis, false, sizeof vis);
        for(int i = 0; i <= n; ++i){
            if(!indegree[i]){
                sum[i] = num;
                --indegree[i];
                vis[i] = true;
                ++cnt;
            }
        }
        for(int i = 0; i <= n; ++i){
            if(vis[i]){
                for(int j = 0; j <= n; ++j){
                    if(pic[i][j]){
                        --indegree[j];
                    }
                }
            }
        }
        --num;
    }
}
int main(){
    int T;
    scanf("%d", &T);
    while(T--){
        memset(indegree, 0, sizeof indegree);
        memset(pic, 0, sizeof pic);
        scanf("%d", &n);
        scanf("%s", s);
        int cnt = 0;
        for(int i = 1; i <= n; ++i){
            for(int j = i; j <= n; ++j){
                char c = s[cnt++];
                if(c == '+'){
                    pic[j][i - 1] = 1;
                    ++indegree[i - 1];
                }
                else if(c == '-'){
                    pic[i - 1][j] = 1;
                    ++indegree[j];
                }
            }
        }
        topsort();
        for(int i = 1; i <= n; ++i){
            if(i != 1) printf(" ");
            printf("%d", sum[i] - sum[i - 1]);
        }
        printf("\n");
    }
    return 0;
}