POJ 1716 Integer Intervals (差分约束系统)

Description

An integer interval [a,b], a < b, is a set of all consecutive integers beginning with a and ending with b.
Write a program that: finds the minimal number of elements in a set containing at least two different integers from each interval.

Input

The first line of the input contains the number of intervals n, 1 <= n <= 10000. Each of the following n lines contains two integers a, b separated by a single space, 0 <= a < b <= 10000. They are the beginning and the end of an interval.

Output

Output the minimal number of elements in a set containing at least two different integers from each interval.

Sample Input

4
3 6
2 4
0 2
4 7

Sample Output

4

令d[k]为从区间[0, k]中选取的元素的个数，根据题意建立差分约束系统：d[bi+1]-d[ai]>=2, 0=<d[i+1]-d[i]<=1，然后用spfa求解。

#include <stdio.h>
#include <string.h>
#include <queue>
using namespace std;
#define MIN(a,b) ((a)<(b)?(a):(b))
#define MAX(a,b) ((a)>(b)?(a):(b))
#define N 10010
#define M 40010
#define INF 0x3fffffff
int n,s,t;
int d[N];
int inq[N];
int first[N],next[M],v[M],w[M];
int e;
void init()
{
    e=0;
    memset(first,-1,sizeof(first));
    s=N;
    t=-N;
}
void insert(int a,int b,int c)
{
    v[e]=b;
    w[e]=c;
    next[e]=first[a];
    first[a]=e++;
}
void spfa()
{
    queue<int> q;
    int a,b;
    memset(inq,0,sizeof(int)*(t+5));
    for(int i=s;i<=t;i++)   d[i]=INF;
    d[s]=0;
    inq[s]=1;
    q.push(s);
    while(!q.empty())
    {
        a=q.front(),q.pop();
        inq[a]=0;
        for(int i=first[a];i!=-1;i=next[i])
        {
            b=v[i];
            if(d[b]>d[a]+w[i])
            {
                d[b]=d[a]+w[i];
                if(inq[b]==0)   inq[b]=1,q.push(b);
            }
        }
    }
    printf("%d\n",-d[t]);
}
int main()
{
    int i,a,b;
    while(~scanf("%d",&n))
    {
        init();
        for(i=0;i<n;i++)
        {
            scanf("%d%d",&a,&b);
            s=MIN(s,a);
            t=MAX(t,b+1);
            insert(a,b+1,-2);
        }
        for(i=s;i<t;i++)    insert(i,i+1,0),insert(i+1,i,1);
        spfa();
    }
    return 0;
}