题意:给定一个最大400*400的矩阵,每次操作可以将某一行或某一列乘上一个数,问能否通过这样的操作使得矩阵内的每个数都在[L,R]的区间内。
析:再把题意说明白一点就是是否存在ai,bj,使得l<=cij*(ai/bj)<=u (1<=i<=n,1<=j<=m)成立。
首先把cij先除到两边去,就变成了l‘<=ai/bj<=u‘,由于差分约束要是的减,怎么变成减法呢?取对数呗,两边取对数得到log(l‘)<=log(ai)-log(bj)<=log(u‘)。
然后把ai, bj看成是两个点,那两个是权值,就可以差分约束了,但是。。这个题太坑了,会TLE,必须要判断好结束条件,就是访问次数超过sqrt(m+n),
就结束,如果不开根号,就会一直TLE。。。。有没有天理了。。。。
析:
#pragma comment(linker, "/STACK:1024000000,1024000000") #include <cstdio> #include <string> #include <cstdlib> #include <cmath> #include <iostream> #include <cstring> #include <set> #include <queue> #include <algorithm> #include <vector> #include <map> #include <cctype> #include <stack> using namespace std ; typedef long long LL; typedef pair<int, int> P; const int INF = 0x3f3f3f3f; const double inf = 0x3f3f3f3f3f3f; const double PI = acos(-1.0); const double eps = 1e-10; const int maxn = 800 + 5; const int mod = 1e9 + 7; const char *mark = "+-*"; const int dr[] = {-1, 0, 1, 0}; const int dc[] = {0, 1, 0, -1}; int n, m; inline bool is_in(int r, int c){ return r >= 0 && r < n && c >= 0 && c < m; } int head[maxn], to[maxn*maxn/2], Next[maxn*maxn/2], cnt; double w[maxn*maxn/2], l, u, d[maxn]; void addedge(int u, int v, double c){ to[cnt] = v; w[cnt] = c; Next[cnt] = head[u]; head[u] = cnt++; } int vis[maxn], num[maxn]; bool spfa(){ memset(vis, 0, sizeof(vis)); memset(num, 0, sizeof(num)); fill(d, d+n+m+1, inf); queue<int> q; vis[0] = 1; d[0] = 0; num[0] = 1; q.push(0); int limit = sqrt(m+n+0.5);//不开根号,想AC?都到没有。 while(!q.empty()){ int u = q.front(); q.pop(); vis[u] = 0; for(int i = head[u]; i != -1; i = Next[i]){ int v = to[i]; double c = w[i]; if(!vis[v] && d[v] > d[u] + c){ if(++num[v] > limit) return false; d[v] = d[u] + c; q.push(v); vis[v] = 1; } } } return true; } int main(){ while(scanf("%d %d %lf %lf", &n, &m, &l, &u) == 4){ memset(head, -1, sizeof(head)); cnt = 0; double ll = log(l); double uu = log(u); for(int i = 0; i < n; ++i){ for(int j = 0; j < m; ++j){ double x; scanf("%lf", &x); x = log(x); addedge(i, j+n, x-ll); addedge(j+n, i, uu-x); } } if(spfa()) puts("YES"); else puts("NO"); } return 0; }
时间: 2024-11-07 14:12:33