Integer Intervals [poj-1716] [differential constraint]

Posted by thenature4u on Fri, 18 Oct 2019 17:39:51 +0200

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If there is a hole, I didn't expect it at first!

There are n intervals. We can put some points in [0, 10000]. Then, we ask that there are at least 2 points in each of the N intervals we give, so how many points should we put at least?

It can be thought that we can still see the difference between the sum of prefixes to represent a certain interval [l, r] can be seen as sum(r) - sum(l-1). Then, we only need to find the minimum value of sum (up).

But there is a hole in the difference constraint. If we change the initial value of dis[i] to 0 in spfa(), we will be wa! Because in this way, the later updated ones will not enter the queue. Unless we go directly from 0 to all the points with a weight of 0, we will actually be WA, which is related to the operation of SPFA () to determine the size.

Therefore, we need to make dis [i] < 0 at the beginning, just "< 0" is enough, and the specific amount is arbitrary.

#include <iostream>
#include <cstdio>
#include <cmath>
#include <string>
#include <cstring>
#include <algorithm>
#include <limits>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#define lowbit(x) ( x&(-x) )
#define pi 3.141592653589793
#define e 2.718281828459045
#define efs 1e-6
#define INF 0x3f3f3f3f
#define HalF (l + r)>>1
#define lsn rt<<1
#define rsn rt<<1|1
#define Lson lsn, l, mid
#define Rson rsn, mid+1, r
#define QL Lson, ql, qr
#define QR Rson, ql, qr
#define myself rt, l, r
#define MAX_3(a, b, c) max(max(a, b), c)
using namespace std;
typedef unsigned long long ull;
typedef long long ll;
const int maxN = 1e4 + 7, maxE = 5e4 + 7;
int N, M, cnt, head[maxN], dist[maxN], used[maxN], _UP;
struct node
{
    int val, id;
}a[maxN];
inline bool cmp(node e1, node e2) { return e1.val < e2.val; }
struct Eddge
{
    int nex, to, val;
    Eddge(int a=-1, int b=0, int c=0):nex(a), to(b), val(c) {}
}edge[maxE];
inline void addEddge(int u, int v, int w)
{
    edge[cnt] = Eddge(head[u], v, w);
    head[u] = cnt++;
}
queue<int> Q;
bool inque[maxN];
inline int spfa(int st = 0, int ed = _UP)
{
    while(!Q.empty()) Q.pop();
    for(int i=0; i<=_UP; i++) { dist[i] = -INF; inque[i] = false; }
    Q.push(st); inque[st] = true; dist[st] = 0;
    while(!Q.empty())
    {
        int u = Q.front(); Q.pop(); inque[u] = false;
        for(int i=head[u], v, w; ~i; i=edge[i].nex)
        {
            v = edge[i].to; w = edge[i].val;
            if(dist[v] < dist[u] + w)
            {
                dist[v] = dist[u] + w;
                if(!inque[v])
                {
                    inque[v] = true;
                    Q.push(v);
                }
            }
        }
    }
    return dist[ed];
}
inline void init()
{
    cnt = 0;    _UP = 0;
    memset(head, -1, sizeof(head));
}
char op[5];
int main()
{
    while(scanf("%d", &N) != EOF)
    {
        init();
        for(int i=1, u, v; i<=N; i++)
        {
            scanf("%d%d", &u, &v);
            v++;
            addEddge(u, v, 2);
            _UP = max(_UP, v);
        }
        for(int i=1; i<=_UP; i++)
        {
            addEddge(i-1, i, 0);
            addEddge(i, i-1, -1);
        }
        printf("%d\n", spfa());
    }
    return 0;
}