两道题都需要进行双向SPFA,比范例复杂,代码也较长,其中第二题应该可以用DFS或者BFS做,如果用DFS可能需要的剪枝较多。
ZOJ3088-Easter Holydays
//利用SPFA找出下降最长路径和上升最短路径,输出最大的比值和回路路径 //Time:0Ms Memory:328K #include<iostream> #include<cstring> #include<cstdio> #include<algorithm> #include<queue> using namespace std; #define MAX 1005 #define INF 0x3f3f3f3f struct Edge { int u, w, next; Edge(){} Edge(int uu,int ww,int nn):u(uu),w(ww),next(nn){} }eu[MAX], ed[MAX]; //up-down int n, m, k; int hu[MAX], hd[MAX]; //邻接表头位置 int pu[MAX], pd[MAX]; //路径 int du[MAX], dd[MAX]; //最短路长 int tu[MAX], td[MAX]; //临时路径 bool v[MAX]; //上升最短路径 void spfa_u(int x) { memset(du, INF, sizeof(du)); memset(pu, -1, sizeof(pu)); memset(v, false, sizeof(v)); du[x] = 0; queue<int> q; q.push(x); pu[x] = x; while (!q.empty()) { int cur = q.front(); q.pop(); v[cur] = false; for (int i = hu[cur]; i != -1; i = eu[i].next) { int u = eu[i].u, w = eu[i].w; if (du[u] > du[cur] + w) { du[u] = du[cur] + w; pu[u] = cur; if (!v[u]) { v[u] = true; q.push(u); } } } } } //SPFA-下降最长路径 void spfa_d(int x) { memset(dd, -1, sizeof(dd)); memset(pd, -1, sizeof(pd)); memset(v, false, sizeof(v)); dd[x] = 0; queue<int> q; q.push(x); pd[x] = x; while (!q.empty()) { int cur = q.front(); q.pop(); v[cur] = false; for (int i = hd[cur]; i != -1; i = ed[i].next) { int u = ed[i].u, w = ed[i].w; if (dd[u] < dd[cur] + w) { dd[u] = dd[cur] + w; pd[u] = cur; if (!v[u]) { v[u] = true; q.push(u); } } } } } void path_u(int x) { if (tu[x] != x) path_u(tu[x]); printf("%d ", x); } void path_d(int x) { int i; for (i = td[x]; i != td[i]; i = td[i]) printf("%d ", i); printf("%d\n", i); } int main() { int T; scanf("%d", &T); while (T--) { memset(hu, -1, sizeof(hu)); memset(hd, -1, sizeof(hd)); scanf("%d%d%d", &n, &m, &k); int a, b, w; for (int i = 0; i < m; i++) { scanf("%d%d%d", &a, &b, &w); ed[i] = Edge(a, w, hd[b]); //反向建图 hd[b] = i; } for (int i = 0; i < k; i++) { scanf("%d%d%d", &a, &b, &w); eu[i] = Edge(b, w, hu[a]); //正向建图 hu[a] = i; } double rate = 0; int tmp = -1; for (int i = 1; i <= n; i++) { spfa_u(i); spfa_d(i); for (int j = 1; j <= n; j++) { if (i == j || du[j] == INF) continue; if (rate < 1.0 * dd[j] / du[j]) { rate = 1.0 * dd[j] / du[j]; tmp = j; memcpy(tu, pu, (n+1)*sizeof(int)); memcpy(td, pd, (n+1)*sizeof(int)); } } } path_u(tmp); path_d(tmp); printf("%.3f\n", rate); } return 0; }
ZOJ3103-Cliff Climbing
//需要理清题意,比较复杂,建立双向邻接表,并须计算双向最短路 //第一次边表设大了MLE了...考虑最大边数 < n*18个,因此设为MAX*18 //Time:190Ms Memory:1152K #include<iostream> #include<cstring> #include<cstdio> #include<algorithm> #include<queue> using namespace std; #define MAXW 32 #define MAXH 62 #define MAX MAXW*MAXH #define INF 0x3f3f3f3f #define IN_RANGE(x,y) (x >= 0 && x < H && y >= 0 && y < W) struct Edge { int u, w, next; Edge() {} Edge(int uu, int ww, int nn) :u(uu), w(ww), next(nn) {} }e[2][MAX*18]; //0:左脚点 1::右脚点 int W, H, n; int board[MAX]; int h[2][MAX], le[2]; int d[2][MAX]; //双向最短距离 bool v[MAX]; int mov0[9][2] = { { 0, 1 },{0, 2 },{0, 3 },{-1, 1 },{ -1, 2 },{ -2, 1 },{ 1, 1 },{ 1, 2 },{ 2, 1 } }; //左脚踩住,右脚移动位置 int mov1[9][2] = { { 0, -1},{0, -2},{0, -3},{-1, -1}, {-1, -2}, {-2, -1}, {1, -1}, {1, -2}, {2, -1} }; //右脚踩住,左脚移动位置 void spfa(int x) { memset(v, false, sizeof(v)); memset(d, INF, sizeof(d)); queue<int> q; q.push(x); d[0][x] = d[1][x] = 0; while (!q.empty()) { int cur = q.front(); q.pop(); v[cur] = false; for (int k = 0; k < 2; k++) //双向最短路 for (int i = h[k][cur]; i != -1; i = e[k][i].next) { int u = e[k][i].u; int w = e[k][i].w; if (d[!k][u] > d[k][cur] + w) //交叉影响 { d[!k][u] = d[k][cur] + w; if (!v[u]) { v[u] = true; q.push(u); } } } } } int main() { while (scanf("%d%d", &W, &H), W && H) { char s[3]; n = W*H; memset(h, -1, sizeof(h)); //一维序列表示各点 for (int i = 0; i < n; i++) { scanf("%s", s); if (s[0] == 'S' || s[0] == 'T') board[i] = 0; else if (s[0] == 'X') board[i] = INF; else board[i] = s[0] - '0'; } //构建邻接表 le[0] = le[1] = 0; for (int i = 0; i < n; i++) { if ((i < W && board[i] == 0) || board[i] == INF) continue; for (int j = 0; j < 9; j++) { int x = i / W, y = i % W; //计算行与列 int x0 = x + mov0[j][0], y0 = y + mov0[j][1]; int x1 = x + mov1[j][0], y1 = y + mov1[j][1]; int n0 = x0*W + y0, n1 = x1*W + y1; if (IN_RANGE(x0,y0) && board[n0] != INF) { e[0][le[0]] = Edge(n0, board[n0], h[0][i]); h[0][i] = le[0]++; } if (IN_RANGE(x1,y1) && board[n1] != INF) { e[1][le[1]] = Edge(n1, board[n1], h[1][i]); h[1][i] = le[1]++; } } } int Min = INF; for (int i = (H - 1) * W; i < n; i++) //枚举最后一行'S'进行SPFA if (board[i] == 0) { spfa(i); for (int j = 0; j < W; j++) //遍历第一行'T'的最短路长 if(board[j] == 0) Min = min(min(Min, d[0][j]), d[1][j]); } if (Min == INF) Min = -1; printf("%d\n", Min); } return 0; }