题意:对于一个序列,我们可以计算出一个符号矩阵,其中Sij为ai+...+aj的正负号,
现在给你一个矩阵的上三角,求一个满足的序列
思路:如果Sij>0的话,那么代表前缀和差Bj-Bi-1 >0 ,那么Bj > Bi-1,由此我们可以得到一系列的关系,利用toposort排序后,得到一个递增或者递减的序列,就可以求出来各个数了
#include <iostream> #include <cstdio> #include <cstring> #include <algorithm> #include <queue> using namespace std; const int MAXN = 20; int n,degree[MAXN]; int map[MAXN][MAXN],s[MAXN],ans[MAXN]; char text[1000]; void init(){ memset(map,0,sizeof(map)); memset(degree,0,sizeof(degree)); } void toposort(){ int count = 0,low = -10; while (count != n+1){ int tag[MAXN]; memset(tag,0,sizeof(tag)); for (int i = 0; i <= n; i++) if (degree[i] == 0){ s[i] = low; degree[i] = -1; tag[i] = 1; count++; } low++; for (int i = 0; i <= n; i++) if (tag[i]){ for (int j = 0; j <= n; j++) if (map[i][j]) degree[j]--; } } } int main(){ int t; scanf("%d",&t); while (t--){ scanf("%d%s",&n,text); init(); int cnt = 0; for (int i = 1; i <= n; i++) for (int j = i; j <= n; j++){ char a = text[cnt++]; if (a == '+'){ map[i-1][j] = 1; degree[j]++; } else if (a == '-'){ map[j][i-1] = 1; degree[i-1]++; } } toposort(); for (int i = 1; i <= n; i++) ans[i] = s[i] - s[i-1]; for (int i = 1; i < n; i++) printf("%d ",ans[i]); printf("%d\n",ans[n]); } return 0; }