BZOJ ~ 2662 ~ [BeiJing wc2012]冻结 （分层图最短路）

思路：分层图最短路，思路同：BZOJ ~ 2763，只不过层与层之间的花费不在是0，而是原来的一半。求的是1~N的最短路。

建图分层：#include<bits/stdc++.h>
using namespace std;
const int MAXN = 50 * 50 + 5;
const int INF = 0x3f3f3f3f;
struct Edge
{
int from, to, dist; //起点,终点,距离
Edge(int u, int v, int w):from(u), to(v), dist(w) {}
};

struct Dijkstra
{
int n, m; //结点数,边数(包括反向弧)
vector<Edge> edges; //边表。edges[e]和edges[e^1]互为反向弧
vector<int> G[MAXN]; //邻接表，G[i][j]表示结点i的第j条边在edges数组中的序号
int vis[MAXN]; //标记数组
int d[MAXN]; //s到各个点的最短路
int pre[MAXN]; //上一条弧

void init(int n)
{
this->n = n;
edges.clear();
for (int i = 0; i <= n; i++) G[i].clear();
}

void add_edge(int from, int to, int dist)
{
edges.push_back(Edge(from, to, dist));
m = edges.size();
G[from].push_back(m - 1);
}

struct HeapNode
{
int from, dist;
bool operator < (const HeapNode& rhs) const
{
return rhs.dist < dist;
}
HeapNode(int u, int w): from(u), dist(w) {}
};

void dijkstra(int s)
{
priority_queue<HeapNode> Q;
for (int i = 0; i <= n; i++) d[i] = INF;
memset(vis, 0, sizeof(vis));
d[s] = 0;
Q.push(HeapNode(s, 0));
while (!Q.empty())
{
HeapNode x = Q.top(); Q.pop();
int u = x.from;
if (vis[u]) continue;
vis[u] = true;
for (int i = 0; i < G[u].size(); i++)
{
Edge& e = edges[G[u][i]];
if (d[e.to] > d[u] + e.dist)
{
d[e.to] = d[u] + e.dist;
pre[e.to] = G[u][i];
Q.push(HeapNode(e.to, d[e.to]));
}
}
}
}
};

int n, m, k, s, t;
Dijkstra solve;
4000

int main()
{
while(~scanf("%d%d%d", &n, &m, &k))
{
solve.init(n * (k + 1));
while(m--)
{
int a, b, c;
scanf("%d%d%d", &a, &b, &c);
for (int i = 0; i <= k; i++)//k+1层图
{
//本层之间建图
solve.add_edge(a + i * n, b + i * n, c);
solve.add_edge(b + i * n, a + i * n, c);
//该层与下一层建图
if (i != k)//不是最后一层
{
solve.add_edge(a + i * n, b + (i + 1) * n, c / 2);
solve.add_edge(b + i * n, a + (i + 1) * n, c / 2);
}
}
}
solve.dijkstra(1);
int MIN = INF;
for (int i = 0; i <= k; i++)
{
MIN = min(MIN, solve.d[n + i * n]);
}
printf("%d\n", MIN);
}
return 0;
}
/*
4 4 1
1 2 4
4 2 6
1 3 8
3 4 8
*/

最短路计算时分层：#include<bits/stdc++.h>
using namespace std;
const int MAXN = 55;
const int MAXK = 55;
const int INF = 0x3f3f3f3f;
struct Edge
{
int from, to, dist; //起点,终点,距离
Edge(int u, int v, int w):from(u), to(v), dist(w) {}
};

struct Dijkstra
{
int n, m; //结点数,边数(包括反向弧)
vector<Edge> edges; //边表。edges[e]和edges[e^1]互为反向弧
vector<int> G[MAXN]; //邻接表，G[i][j]表示结点i的第j条边在edges数组中的序号
bool vis[MAXN][MAXK]; //标记数组
int d[MAXN][MAXK]; //s到各个点的最短路
int pre[MAXN]; //上一条弧

void init(int n)
{
this->n = n;
edges.clear();
for (int i = 0; i <= n; i++) G[i].clear();
}

void add_edge(int from, int to, int dist)
{
edges.push_back(Edge(from, to, dist));
m = edges.size();
G[from].push_back(m - 1);
}

struct HeapNode
{
int from, dist, cost;
bool operator < (const HeapNode& rhs) const
{
return rhs.dist < dist;
}
HeapNode(int u, int w, int c): from(u), dist(w), cost(c) {}
};

void dijkstra(int s, int k)
{
priority_queue<HeapNode> Q;
memset(d, 127, sizeof(d));//将d初始化为极大值
memset(vis, 0, sizeof(vis));
d[s][0] = 0;
Q.push(HeapNode(s, 0, 0));
while (!Q.empty())
{
HeapNode x = Q.top(); Q.pop();
int u = x.from, c = x.cost;
if (vis[u][c]) continue;
vis[u][c] = true;
//本层最短路更新
for (int i = 0; i < G[u].size(); i++)
{
Edge& e = edges[G[u][i]];
if (d[e.to][c] > d[u][c] + e.dist)
{
d[e.to][c] = d[u][c] + e.dist;
Q.push(HeapNode(e.to, d[e.to][c], c));
}
}
//本层到下一层最短路更新
if (c < k)//不是最后一层
{
for (int i = 0; i < G[u].size(); i++)
{
Edge& e = edges[G[u][i]];
if (d[e.to][c + 1] > d[u][c] + e.dist / 2)
{
d[e.to][c + 1] = d[u][c] + e.dist / 2;
Q.push(HeapNode(e.to, d[e.to][c + 1], c + 1));
}
}
}
}
}
};

int n, m, k, s, t;
Dijkstra solve;

int main()
{
while(~scanf("%d%d%d", &n, &m, &k))
{
solve.init(n);
while(m--)
{
int a, b, c;
scanf("%d%d%d", &a, &b, &c);
solve.add_edge(a, b, c);
solve.add_edge(b, a, c);
}
solve.dijkstra(1, k);
int MIN = INF;
for (int i = 0; i <= k; i++)
{
MIN = min(MIN, solve.d
[i]);
}
printf("%d\n", MIN);
}
return 0;
}
/*
4 4 1
1 2 4
4 2 6
1 3 8
3 4 8
*/