POJ 1201 Intervals 差分约束系统

/**
* @file main.cpp
* @brief 差分约束系统,基本不等式如下,求s

*      1. s[b] - s[a] >= c  直观理解是s[b] - s[a - 1] >= c,s[x]表示集合中选自[0,x]的数字总数,程序对下标做了处理
*      2. s[i] - s[i - 1] >= 0
*      3. s[i - 1] - s[i] >= -1
* 因此,由此可得松弛方法:
*      1. if (s[a] + c > s[b])
*          s[b] = s[a] + c
*      2. if (s[i - 1] + 0 > s[i])
*          s[i] = s[i - 1] + 0
*      3. if (s[i] + (-1) > s[i - 1])
*          s[i - 1] = s[i] + (-1)
* 因此,转换为最短路径的构图方式为:
*      1. <a, b>添加一条权为c的边
*      2. <i - 1, i>添加一条权为0的边
*      3. <i, i - 1>添加一条权为-1的边
*
* @author yekeren
* @version 1.0.0
* @date 2013-06-05
*/

#include <iostream>
#include <queue>

#define MAX_INT 0x7fffffff
#define LIMIT 51001

///(M)临接表
struct edge_t {
int e, c;
struct edge_t *next;
};
edge_t *g[LIMIT] = { NULL };
edge_t pool[LIMIT * 4];
int npool = 0;

/**
* @brief 临接表添加边
* @param s
* @param e
* @param c
*/
void add_edge(int s, int e, int c)
{
pool[npool].e = e;
pool[npool].c = c;
pool[npool].next = g[s];

g[s] = &pool[npool++];
}

/**
* @brief shortest path faster algorithm
* @param imin
* @param imax
* @return
*/
int spfa(int imin, int imax)
{
unsigned char visit[LIMIT] = { 0 };
std::queue<int> q;

int dist[LIMIT] = { 0 };
for (int i = imin; i <= imax; ++i) {
dist[i] = - MAX_INT;
}

dist[imin] = 0;
visit[imin] = 1;
q.push(imin);

while (!q.empty())
{
int u = q.front();
q.pop();
visit[u] = 0;

for (edge_t *p = g[u]; p != NULL; p = p->next)
{
int v = p->e;
int c = p->c;

if (dist[u] + c > dist[v])
{
dist[v] = dist[u] + c;
if (!visit[v])
{
visit[v] = 1;
q.push(v);
}
}
}
}
return dist[imax];
}

int main(int argc, char *argv[])
{
int n;
scanf("%d", &n);

int imin = MAX_INT;
int imax = 0;

for (int i = 0; i < n; ++i)
{
int a, b, c;

scanf("%d%d%d", &a, &b, &c);
++b;

add_edge(a, b, c);

if (a < imin) {
imin = a;
}
if (b > imax) {
imax = b;
}
}

for (int i = imin; i < imax; ++i)
{
add_edge(i, i + 1, 0);
add_edge(i + 1, i, -1);
}

printf("%d\n", spfa(imin, imax));
return 0;
}