[POJ 1639]
2016-02-22 17:46
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最大度限制生成树
#include <iostream> #include <map> #include <cstdio> #include <cstring> #include <algorithm> #define MAXN 105 #define MAXM 100005 #define INF 1000000000 using namespace std; struct node { int v, w, next; }edge[MAXM]; struct Edge { int u, v, w; Edge(){} Edge(int a, int b, int c){u = a; v = b; w = c;} void init(){w = 0;} bool operator >(const Edge &a) const{ return w > a.w; } }mx[MAXN];//用于存储每个点到park点的最大边 int n, m, k, sum;//sum为结果 int e, head[MAXN], vis[MAXN], dis[MAXN], use[MAXN][MAXN];//head用于邻接表 vis是标记数组 dis用于求最小生成树 //use用来标记两点之间是否有边 int blocks, size[MAXN], belong[MAXN], nearvex[MAXN];//blocks表示去除park后有几个连通块 size是每个连通块的个数 //belong表示该点属于哪个连通块 nearvex用于在生成树中记录边 int point[MAXN], link[MAXN]; //point表示每个连通块中与park点最近的点 link则是该点与park点的距离 map<string, int>mp; //用于映射名字 void init() { e = 0, n = 1; blocks = 0, sum = 0; memset(head, -1, sizeof(head)); memset(vis, 0, sizeof(vis)); memset(size, 0, sizeof(size)); memset(use, 0, sizeof(use)); for(int i = 1; i < MAXN; i++) mx[i].init(); memset(nearvex, 0, sizeof(nearvex)); mp.clear(); } void insert(int x, int y, int w) { edge[e].v = y; edge[e].w = w; edge[e].next = head[x]; head[x] = e++; } int getId(char s[]) { if(mp.find(s) == mp.end()) mp[s] = ++n; else return mp[s]; return n; } void dfs(int v) //该dfs将图分成了一些连通块 { vis[v] = 1; size[blocks]++; belong[v] = blocks; for(int i = head[v]; i != -1; i = edge[i].next) if(!vis[edge[i].v]) dfs(edge[i].v); } void prim(int cur) //对某个连通块求最小生成树 { for(int i = 1; i <= n; i++) dis[i] = INF; for(int i = 1; i <= n; i++) //设置块内某点为起点来求生成树 if(belong[i] == cur) { dis[i] = 0; break; } for(int i = 1; i <= size[cur]; i++) //循环次数为该块的顶点数,因为这与一般的求MST略微不同 { int mi = INF, pos = -1; for(int j = 1; j <= n; j++) if(nearvex[j] != -1 && mi > dis[j]) mi = dis[j], pos = j; if(pos != -1) { sum += mi; use[pos][nearvex[pos]] = use[nearvex[pos]][pos] = 1; //标记生成树中所用的边 nearvex[pos] = -1; for(int j = head[pos]; j != -1; j = edge[j].next) if(nearvex[edge[j].v] != -1 && dis[edge[j].v] > edge[j].w) { dis[edge[j].v] = edge[j].w; nearvex[edge[j].v] = pos; } } } } void getMax(int v, int fa, int w) //该函数用于更新新的生成树中点到park点的最大边 { nearvex[v] = fa; Edge t(v, fa, w); if(mx[fa] > t) mx[v] = mx[fa]; else mx[v] = t; for(int i = head[v]; i != -1; i = edge[i].next) if(use[v][edge[i].v] && edge[i].v != fa) getMax(edge[i].v, v, edge[i].w); //必须是生成树中的边并且不是回边才往下搜 } void GetMdegreeMST() { vis[1] = 1; for(int i = 2; i <= n; i++) //求连通块 if(!vis[i]) { blocks++; dfs(i); } nearvex[1] = -1; for(int i = 1; i <= blocks; i++) prim(i); for(int i = 1; i <= n; i++) link[i] = INF; for(int i = head[1]; i != -1; i = edge[i].next) //生成一棵m度的生成树 if(link[belong[edge[i].v]] > edge[i].w) { link[belong[edge[i].v]] = edge[i].w; point[belong[edge[i].v]] = edge[i].v; } for(int i = 1; i <= blocks; i++) //将park点与每个连通块中与其最近的点相连,并且标记边 { sum += link[i]; use[1][point[i]] = use[point[i]][1] = 1; } } void slove() { int degree = blocks; getMax(1, 0, 0); //首先从park点出发求一遍最大边 while(degree < k) //尝试迭代 k - degree次 { int maxval = 0, pos = 0, w; for(int i = head[1]; i != -1; i = edge[i].next) //用于找到差值最大的点 if(!use[1][edge[i].v] && mx[edge[i].v].w - edge[i].w > maxval) { maxval = mx[edge[i].v].w - edge[i].w, pos = edge[i].v; w = edge[i].w; } if(!pos) break; sum -= maxval;//更新答案 degree++; use[mx[pos].u][mx[pos].v] = use[mx[pos].v][mx[pos].u] = 0;//将最大边删除 use[1][pos] = use[pos][1] = 1; getMax(pos, 1, w);//更新最大边 } } int main() { char s1[55], s2[55]; int w; scanf("%d", &m); init(); mp["Park"] = 1; for(int i = 0; i < m; i++) { scanf("%s%s%d", s1, s2, &w); insert(getId(s1), getId(s2), w); insert(getId(s2), getId(s1), w); } scanf("%d", &k); GetMdegreeMST(); slove(); printf("Total miles driven: %d\n", sum); return 0; }
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