目录
- [1 介绍](#1 介绍)
- [2 训练](#2 训练)
1 介绍
本专题用来记录使用最小生成树算法(prim或kruskal)解决的扩展题目。
2 训练
题目1 :1146新的开始
C++代码如下,
cpp
#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
const int N = 310, INF = 0x3f3f3f3f3;
int n, m;
int g[N][N];
int d[N];
bool st[N];
void prim() {
memset(d, 0x3f, sizeof d);
int res = 0;
for (int i = 0; i < n + 1; ++i) {
int t = -1;
for (int j = 0; j <= n; ++j) {
if (!st[j] && (t == -1 || d[t] > d[j])) {
t = j;
}
}
st[t] = true;
if (i) res += d[t];
for (int j = 0; j <= n; ++j) {
if (d[j] > g[t][j]) {
d[j] = g[t][j];
}
}
}
cout << res << endl;
return;
}
int main() {
cin >> n;
memset(g, 0, sizeof g);
for (int i = 1; i <= n; ++i) {
int t;
cin >> t;
g[0][i] = t;
g[i][0] = t;
}
for (int i = 1; i <= n; ++i) {
for (int j = 1; j <= n; ++j) {
cin >> g[i][j];
}
}
prim();
return 0;
}
题目2 :1145北极通讯网络
C++代码如下,
cpp
#include <iostream>
#include <cstring>
#include <algorithm>
#include <vector>
#include <cmath>
using namespace std;
typedef pair<int, int> PII;
const int N = 510, M = N * N;
int n, k;
vector<PII> points;
int p[N];
struct Edge {
int a, b;
double w;
bool operator< (const Edge &W) const {
return w < W.w;
}
}edges[M];
int find(int x) {
if (p[x] != x) p[x] = find(p[x]);
return p[x];
}
double compute_dis(int i, int j) {
int x1 = points[i].first, y1 = points[i].second;
int x2 = points[j].first, y2 = points[j].second;
double d = double(x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
d = sqrt(d);
return d;
}
int main() {
cin >> n >> k;
for (int i = 0; i < n; ++i) {
int x, y;
cin >> x >> y;
points.emplace_back(x,y);
}
for (int i = 0; i < n; ++i) p[i] = i;
int m = 0;
for (int i = 0; i < n; ++i) {
for (int j = i + 1; j < n; ++j) {
double w = compute_dis(i, j);
edges[m] = {i, j, w};
m += 1;
}
}
sort(edges, edges + m);
double res = 0.0;
int cnt = n; //连通块的个数
for (int i = 0; i < m; ++i) {
int a = edges[i].a, b = edges[i].b;
double w = edges[i].w;
a = find(a);
b = find(b);
if (cnt == k) {
break;
}
if (a != b) {
p[a] = b;
cnt--;
res = w;
}
}
printf("%.2lf\n", res);
return 0;
}
题目3 :346走廊泼水节
C++代码如下,
cpp
#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
const int N = 6010;
int n, m;
int p[N], ms[N];
struct Edge {
int a, b, w;
bool operator< (const Edge &W) const {
return w < W.w;
}
}edges[N];
int find(int x) {
if (p[x] != x) p[x] = find(p[x]);
return p[x];
}
int main() {
int T;
cin >> T;
while (T--) {
cin >> n;
for (int i = 0; i < n - 1; ++i) {
cin >> edges[i].a >> edges[i].b >> edges[i].w;
}
for (int i = 1; i <= n; ++i) p[i] = i, ms[i] = 1;
sort(edges, edges + n - 1);
int res = 0;
for (int i = 0; i < n - 1; ++i) {
int a = edges[i].a, b = edges[i].b, w = edges[i].w;
a = find(a);
b = find(b);
if (a != b) {
res += (ms[a] * ms[b] - 1) * (w + 1);
p[a] = b;
ms[b] += ms[a];
}
}
cout << res << endl;
}
return 0;
}
题目4 :1148秘密的牛奶运输
C++代码如下,
cpp
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
typedef long long LL;
const int N = 510, M = 10010;
int n, m;
struct Edge {
int a, b, w;
bool f;
bool operator< (const Edge &W) const {
return w < W.w;
}
}edges[M];
int p[N];
int dist1[N][N], dist2[N][N];
int h[N], e[N * 2], w[N * 2], ne[N * 2], idx;
void add(int a, int b, int c) {
e[idx] = b, w[idx] = c, ne[idx] = h[a], h[a] = idx++;
}
int find(int x) {
if (p[x] != x) p[x] = find(p[x]);
return p[x];
}
void dfs(int u, int fa, int maxd1, int maxd2, int d1[], int d2[]) {
d1[u] = maxd1, d2[u] = maxd2;
for (int i = h[u]; ~i; i = ne[i]) {
int j = e[i];
if (j != fa) {
int td1 = maxd1, td2 = maxd2;
if (w[i] > td1) td2 = td1, td1 = w[i];
else if (w[i] < td1 && w[i] > td2) td2 = w[i];
dfs(j, u, td1, td2, d1, d2);
}
}
return;
}
int main() {
scanf("%d%d", &n, &m);
memset(h, -1, sizeof h);
for (int i = 0; i < m; ++i) {
int a, b, w;
scanf("%d%d%d", &a, &b, &w);
edges[i] = {a, b, w};
}
sort(edges, edges + m);
for (int i = 1; i <= n; ++i) p[i] = i;
LL sum = 0;
for (int i = 0; i < m; ++i) {
int a = edges[i].a, b = edges[i].b, w = edges[i].w;
int pa = find(a), pb = find(b);
if (pa != pb) {
p[pa] = pb;
sum += w;
add(a, b, w), add(b, a, w);
edges[i].f = true;
}
}
for (int i = 1; i <= n; ++i) dfs(i, -1, -1e9, -1e9, dist1[i], dist2[i]);
LL res = 1e18;
for (int i = 0; i < m; ++i) {
if (!edges[i].f) {
int a = edges[i].a, b = edges[i].b, w = edges[i].w;
LL t;
if (w > dist1[a][b]) {
t = sum + w - dist1[a][b];
} else if (w > dist2[a][b]) {
t = sum + w - dist2[a][b];
}
res= min(res, t);
}
}
printf("%lld\n", res);
return 0;
}