POJ1201 Intervals[差分约束系统]
Intervals
Time Limit: 2000MS | Memory Limit: 65536K | |
Total Submissions: 26028 | Accepted: 9952 |
Description
You are given n closed, integer intervals [ai, bi] and n integers c1, ..., cn.
Write a program that:
reads the number of intervals, their end points and integers c1, ..., cn from the standard input,
computes the minimal size of a set Z of integers which has at least ci common elements with interval [ai, bi], for each i=1,2,...,n,
writes the answer to the standard output.
Write a program that:
reads the number of intervals, their end points and integers c1, ..., cn from the standard input,
computes the minimal size of a set Z of integers which has at least ci common elements with interval [ai, bi], for each i=1,2,...,n,
writes the answer to the standard output.
Input
The first line of the input contains an integer n (1 <= n <= 50000) -- the number of intervals. The following n lines describe the intervals. The (i+1)-th line of the input contains three integers ai, bi and ci separated by single spaces and such that 0 <= ai <= bi <= 50000 and 1 <= ci <= bi - ai+1.
Output
The output contains exactly one integer equal to the minimal size of set Z sharing at least ci elements with interval [ai, bi], for each i=1,2,...,n.
Sample Input
5 3 7 3 8 10 3 6 8 1 1 3 1 10 11 1
Sample Output
6
Source
题意:有n个区间,每个区间有3个值,ai,bi,ci代表,在区间[ai,bi]上至少要选择ci个整数点,ci可以在区间内任意取不重复的点
现在要满足所有区间的自身条件,问最少选多少个点
一段区间,想到前缀和处理选的个数
每个前缀和建一个点
s[b]-s[a-1]>=c
同时要满足前缀和的性质,即:
s[i]-s[i-1]>=0
s[i]-s[i-1]<=1
最小值,按>=建图跑最长路
注意区间范围0..n,读入时改成了1...n+1(n)
但是0节点也是(前缀和!)
#include <iostream> #include <cstdio> #include <algorithm> #include <cstring> using namespace std; typedef long long ll; const int N=5e4+5,M=15e4+5,INF=1e9; inline int read(){ char c=getchar();int x=0,f=1; while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();} while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();} return x*f; } int n,m,a,b,c; struct edge{ int v,ne; double w; }e[M]; int h[N],cnt=0; inline void ins(int u,int v,int w){ cnt++; e[cnt].v=v;e[cnt].w=w;e[cnt].ne=h[u];h[u]=cnt; } int q[N],head,tail,inq[N],num[N],d[N]; inline void lop(int &x){if(x==N) x=1;else if(x==0) x=N-1;} bool spfa(){ head=tail=1; memset(inq,0,sizeof(inq)); memset(num,0,sizeof(num)); for(int i=0;i<=n;i++) q[tail++]=i,inq[i]=1,d[i]=0; while(head!=tail){ int u=q[head++];inq[u]=0;lop(head); for(int i=h[u];i;i=e[i].ne){ int v=e[i].v,w=e[i].w; if(d[v]<d[u]+w){ d[v]=d[u]+w; if(!inq[v]){ inq[v]=1; if(++num[v]>n) return true; if(d[v]>d[q[head]]) head--,lop(head),q[head]=v; else q[tail++]=v,lop(tail); } } } } return false; } int main(){ m=read(); for(int i=1;i<=m;i++){ a=read()+1;b=read()+1;c=read();n=max(n,b); ins(a-1,b,c); } for(int i=1;i<=n;i++) ins(i-1,i,0),ins(i,i-1,-1); spfa(); printf("%d",d[n]); }
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