7-1 旅游规划
#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;
typedef pair<int,int> PII;
const int N = 510;
int g[N][N];
int n,m,s,d;
int dist[N];
int w[N],t[N][N];
bool st[N];
void dijkstra(){
memset(dist, 0x3f, sizeof dist);
dist[s] = 0;
for(int i=0;i<n;i++){int k = -1;for(int j = 0;j<n;j++)if(!st[j] && (k == -1 || dist[k] > dist[j]))k = j;st[k] = true;for(int j=0;j<n;j++){if(!st[j] && dist[j] > dist[k] + g[k][j]){dist[j] = dist[k] + g[k][j];w[j] = w[k] + t[k][j];//随时更新金额}else if(!st[j] && dist[j] == dist[k] + g[k][j] && w[j] > w[k] + t[k][j])w[j] = w[k] + t[k][j];}
}
}
int main(){
scanf("%d%d%d%d",&n,&m,&s,&d);
memset(g, 0x3f, sizeof g);
memset(t, 0x3f, sizeof t);
for(int i=1;i<=m;i++){int a,b,c,f;scanf("%d%d%d%d",&a,&b,&c,&f);g[a][b] = c;g[b][a] = c;t[a][b] = f;t[b][a] = f;
}
//for(int i=0;i<n;i++) w[i] = t[s][i];
dijkstra();
printf("%d %d\n",dist[d],w[d]);
return 0;
}
7-2 大众情人
#include<iostream>
#include<vector>
using namespace std;
const int N = 510;
int g[N][N],sex[N],d[N];
int main()
{
int n;scanf("%d",&n);
for(int i=1;i<=n;i++)for(int j=1;j<=n;j++)if(i==j) g[i][j]=0;else g[i][j]=1e9;for(int i=1;i<=n;i++)
{char op;int k;scanf(" %c %d",&op,&k);if(op=='F') sex[i]=1;//女生 else sex[i]=2;//男生 for(int j=1;j<=k;j++){int a,b;scanf("%d:%d",&a,&b);g[i][a]=b;}
}
for(int k=1;k<=n;k++)for(int i=1;i<=n;i++)for(int j=1;j<=n;j++)g[i][j]=min(g[i][j],g[i][k]+g[k][j]);for(int i=1;i<=n;i++)for(int j=1;j<=n;j++)if(sex[i]!=sex[j])d[i]=max(d[i],g[j][i]);int d1=1e9,d2=1e9;//d1,表示男对女的距离 d2,表示女对男的距离
for(int i=1;i<=n;i++)
{if(sex[i]==2) d1=min(d1,d[i]);//找男对女的最小距离 ,即男性的"大众情人" else d2=min(d2,d[i]);//找女对男的最小距离 ,即女性的 "大众情人"
}vector<int> a,b;
for(int i=1;i<=n;i++)//女性的"大众情人"
{if(sex[i]==2) continue;if(d[i]==d2) a.push_back(i);
} for(int i=1;i<=n;i++)//男性的"大众情人"
{if(sex[i]==1) continue;if(d[i]==d1) b.push_back(i);
}printf("%d",a[0]);
for(int i=1;i<(int)a.size();i++) printf(" %d",a[i]); puts("");printf("%d",b[0]);
for(int i=1;i<(int)b.size();i++)printf(" %d",b[i]);return 0;
}
7-3 寻宝图
#include <iostream>
using namespace std;
const int MAXN=100005;
string a[MAXN];
//这里不定义二维数组以防止数组过大
int n,m;
int flag=0;
int px[]={1,0,-1,0},py[]={0,1,0,-1};
//格子控制左上右下移动
//dfs递归
void dfs(int i,int j)
{
if(i<0||i>=n||j<0||j>=m||a[i][j]=='0')return;
//该点不是1，或者i，j超出边界
if(a[i][j]>'1')flag=1;//是宝藏
a[i][j]='0';
//置该点为0
for(int k=0;k<4;k++)dfs(i+px[k],j+py[k]);
//向各个方向延申
}
int main()
{
int c=0,cnt=0;
cin>>n>>m;
for(int i=0;i<n;i++)
{cin>>a[i];
}
for(int i=0;i<n;i++){for(int j=0;j<m;j++){if(a[i][j]>'0'){c=c+1;flag=0;dfs(i,j);if(flag)cnt++;}}
}
cout<<c<<" "<<cnt<<endl;
}
7-4 最小生成树-Prim算法（从任意顶点开始）
#include<bits/stdc++.h>
using namespace std;
int inf=0x3f3f3f3f;
int graph[10000][10000]={0};
int lowcost[10000]={0};//点集
int tree[10000]={0};
int m,n,ls;
void prim(int s)
{for(int i=1;i<=n;i++){if(i==s)lowcost[i]=0;elselowcost[i]=graph[s][i];tree[i]=s;//初始化，所有的边都待选}int minn,pos;for(int i=1;i<n;i++)//循环了n-1次，因为n个点，n-1个边{minn=inf;for(int j=1;j<=n;j++){if(lowcost[j]!=0&&lowcost[j]<minn){minn=lowcost[j];pos=j;}//这个找的就是点集周围的最小边}cout<<(tree[pos]<pos?tree[pos]:pos)<<","<<(tree[pos]>pos?tree[pos]:pos)<<","<<graph[tree[pos]][pos]<<endl;//每找到一个边就输出一个边if(minn==inf)break;lowcost[pos]=0;//加入！！for(int j=1;j<=n;j++){if(lowcost[j]!=0&&graph[pos][j]<lowcost[j])//因为没在点集里，s到j比较大，pos到j小，就更新一下{lowcost[j]=graph[pos][j];//其实就是点集到j最短的距离tree[j]=pos;//加入到tree的待选，下次循环会选出来合适的，到时候这里的j会是合适的pos，这里的pos对应上一次合适的值。}}}
}
int main()
{cin>>n>>m>>ls;for(int i=1;i<=n;i++)for(int j=1;j<=n;j++)graph[i][j]=inf;for(int i=0;i<m;i++){int a,b;cin>>a>>b;cin>>graph[a][b];graph[b][a]=graph[a][b];}prim(ls);
}
7-5 h0359. 并查集
#include <iostream>
#include <vector>using namespace std;vector<int> parent;int find(int x) {if (parent[x] == x) {return x;} else {return parent[x] = find(parent[x]);}
}void merge(int a, int b) {int rootA = find(a);int rootB = find(b);if (rootA != rootB) {parent[rootB] = rootA;}
}int main() {int n, m;cin >> n >> m;// 初始化并查集parent.resize(n + 1);for (int i = 1; i <= n; ++i) {parent[i] = i;}char op;int a, b;for (int i = 0; i < m; ++i) {cin >> op >> a >> b;if (op == 'M') {merge(a, b);} else if (op == 'Q') {if (find(a) == find(b)) {cout << "Yes" << endl;} else {cout << "No" << endl;}}}return 0;
}
7-6 h0360. 并查集2
#include <iostream>using namespace std;const int N = 100010;
int n, m;
int p[N], cnt[N];int find(int x) {if(p[x] != x) p[x] = find(p[x]);return p[x];
}int main()
{scanf("%d%d", &n, &m);for(int i = 1; i <= n; i ++ ) p[i] = i, cnt[i] = 1;while(m -- ) {char op[3];int a, b;scanf("%s", op);if(op[0] == 'C') {scanf("%d%d", &a, &b);if(find(a) == find(b)) continue;cnt[find(b)] += cnt[find(a)];p[find(a)] = find(b);} else if(op[1] == '1') {scanf("%d%d", &a, &b);if(find(a) == find(b)) printf("Yes\n");else printf("No\n");} else {scanf("%d", &a);printf("%d\n", cnt[find(a)]);}}return 0;}
7-7 h0361. 并查集3
#include<iostream>
#include<cstdio>using namespace std;
int pre[50003],rel[50003];int f(int x){if(x==pre[x])return x;int tmp=pre[x];pre[x]=f(pre[x]);rel[x]=(rel[x]+rel[tmp])%3;return pre[x];
}int link(int x,int y,int flag){int root1=f(x),root2=f(y);if(root1==root2){//表示已经合并啦if(flag!=(3-rel[x]+rel[y])%3)return 0;else return 1;}pre[root2]=root1;rel[root2]=(rel[x]+flag+3-rel[y])%3;return 1;
}int main(){int n,k,flag,x,y;scanf("%d%d",&n,&k);int ans=0;for(int i=1;i<=n;i++){pre[i]=i;rel[i]=0;}while(k--){scanf("%d%d%d",&flag,&x,&y);if(x>n||y>n){ans++;continue;}if(flag==2&&x==y){ans++;continue;}if(!link(x,y,flag-1))ans++;}printf("%d\n",ans);
}
7-8 吉利矩阵
#include<iostream>
using namespace std;
const int N=20;
int a[N][N];
int main(){
int l,n;cin>>l>>n;
a[2][2]=3;
a[2][3]=21;
a[2][4]=282;
a[3][2]=4;
a[3][3]=55;
a[3][4]=2008;
a[4][2]=5;
a[4][3]=120;
a[4][4]=10147;
a[5][2]=6;
a[5][3]=231;
a[5][4]=40176;
a[6][2]=7;
a[6][3]=406;
a[6][4]=132724;
a[7][2]=8;
a[7][3]=666;
a[7][4]=381424;
a[8][2]=9;
a[8][3]=1035;
a[8][4]=981541;
a[9][2]=10;
a[9][3]=1540;
a[9][4]=2309384;
cout<<a[l][n];
}
7-9 最小费用流
#include <iostream>
#include <vector>
#include <queue>
#include <limits>using namespace std;const int INF = numeric_limits<int>::max();struct Edge {int to, cap, cost, rev;
};vector<vector<Edge>> graph;
vector<int> dist;
vector<int> prevv, preve;void add_edge(int from, int to, int cap, int cost) {graph[from].push_back(Edge{to, cap, cost, static_cast<int>(graph[to].size())});graph[to].push_back(Edge{from, 0, -cost, static_cast<int>(graph[from].size()) - 1});
}pair<int, int> min_cost_flow(int s, int t) {int flow = 0, cost = 0;while (true) {queue<int> que;dist.assign(graph.size(), INF);dist[s] = 0;que.push(s);while (!que.empty()) {int v = que.front();que.pop();for (int i = 0; i < graph[v].size(); ++i) {Edge &e = graph[v][i];if (e.cap > 0 && dist[e.to] > dist[v] + e.cost) {dist[e.to] = dist[v] + e.cost;prevv[e.to] = v;preve[e.to] = i;que.push(e.to);}}}if (dist[t] == INF) {break;}int d = INF;for (int v = t; v != s; v = prevv[v]) {d = min(d, graph[prevv[v]][preve[v]].cap);}flow += d;cost += d * dist[t];for (int v = t; v != s; v = prevv[v]) {Edge &e = graph[prevv[v]][preve[v]];e.cap -= d;graph[v][e.rev].cap += d;}}return make_pair(flow, cost);
}int main() {int n, m;cin >> n >> m;graph.resize(n + 1);dist.resize(n + 1);prevv.resize(n + 1);preve.resize(n + 1);for (int i = 0; i < m; ++i) {int s, t, c, w;cin >> s >> t >> c >> w;add_edge(s, t, c, w);}pair<int, int> result = min_cost_flow(1, n);cout << result.first << " " << result.second << endl;return 0;
}
