数据结构 - 树（基础）

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1、无根树转有根树

#include <cstdio>#include <cstring>#include <iostream>#include <algorithm>#define LL long long#define INF 0x7fffffff#include <vector>using namespace std;const int maxn = 1000005;int p[maxn];int n;int root;vector<int> G[maxn];void read_tree() {//输入整棵树 int u, v;scanf("%d", &n);for(int i = 0; i < n - 1; i++) {scanf("%d %d", &u, &v);G[u].push_back(v);G[v].push_back(u);}}void dfs(int u, int fa) {//递归转化以u为根的子树，u的父亲为fa int d = G[u].size();for(int i = 0; i < d; i++) {//结点u的相邻点个数 int v = G[u][i];//结点u的第i个相邻点v if(v != fa) dfs(v, p[v] = u); //把v的父亲设为u，然后递归转化以v为根的子树 }}int main() {//freopen("in.txt", "r", stdin);read_tree();scanf("%d", &root);p[root] = -1;dfs(root, -1);for(int i = 0; i < n; i++) {printf("%d ", p[i]);}return 0;}

2、表达式树

#include <cstdio>#include <cstring>#include <iostream>#include <algorithm>#define LL long long#define INF 0x7fffffffusing namespace std;char str[10005]; const int maxn = 1000;int lch[maxn], rch[maxn];//每个结点的左右儿子编号和字符 char op[maxn];int nc;//结点数 int build_tree(char * s, int x, int y) {int i, c1 = -1, c2 = -1, p = 0;int u;if(y - x == 1) {//仅一个字符，建立单独结点 u = ++nc;lch[u] = rch[u] = 0;op[u] = s[x];return u;} for(int i = x; i < y; i++) {switch(s[i]) {case '(': p++; break;case ')': p--; break;case '+': case '-': if(!p) c1 = i; break;case '*': case '/': if(!p) c2 = i; break;}}if(c1 < 0) c1 = c2;if(c2 < 0) return build_tree(s, x + 1, y - 1);u = ++nc;lch[u] = build_tree(s, x, c1);rch[u] = build_tree(s, c1 + 1, y);op[u] = s[c1];return u;}int main() {while(scanf("%s", str) != EOF) {nc = 0;int len = strlen(str);op[0] = build_tree(str, 0, len);for(int i = 1; i <= nc; i++) {printf("%c ", op[i]);}}return 0;}

3、最小生成树（MST，kruskal）

#include <cstdio>#include <cstring>#include <iostream>#include <algorithm>#define LL long long#define INF 0x7fffffffusing namespace std;struct edge {int a, b, w;}e[10005];int pa[1000005];int n, m;int cmp(edge a, edge b) {//间接排序函数 return a.w < b.w;}int find(int x) {//并查集查找 return x == pa[x] ? x : pa[x] = find(pa[x]);}int join(edge e) {//并查集联合 int x = find(e.a), y = find(e.b);if(x != y) {pa[x] = y;return e.w;}return 0;}int kruskal() {//kruskal算法求MST int ans = 0;for(int i = 0; i < n; i++) pa[i] = i;//初始化并查集 sort(e, e + m, cmp);//给边排序 for(int i = 0; i < n; i++) ans += join(e[i]);return ans;}int main() {while(scanf("%d %d", &n, &m) != EOF) {//n个点，m条边 for(int i = 0; i < m; i++) {scanf("%d %d %d", &e[i].a, &e[i].b, &e[i].w);} printf("%d\n", kruskal());}return 0;}

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