HDU 4085 Peach Blossom Spring memory-based search enumeration subset stanna tree

HDU 4085 Peach Blossom Spring memory-based search enumeration subset stanna tree

Question link: Click the open link

Question:

Enter n vertices and m in the first line. k individuals with undirected edges can be constructed.

The following section describes the costs of constructing a side and a side.

At the beginning, k people are at each point of 1-k (one person at each point)

Objective: To build partial edges from m fixed edges to minimize costs

Let k people move to k points after [n-k + 1, n] (put one person at each point ).

Ideas:

The first is a stanna tree, or a dp array first (solution: Click to open the link)

Dp [I] [j] indicates the minimum cost of using I as the root and j as the 8-Point sub-tree of I.

The question is how to find the answer.

Because the path from a person to his target point may not be connected with others, that is, multiple minimal spanning trees,

We enumerate the points of 2 * k points in a connected component,

In status x, the binary value of a person is low k bits, indicating that the target point is high k bits, and 1 in x indicates that these points are in a connected component,

The minimum cost for this x is min (dp [anypoint regard root] [x]).

X must ensure that the number of 1 in the low k bit and the number of 1 in the high k bit are the same (that is, the number of people and the target point are the same)

Then you can perform the memory-based search.

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        #include template 
        
         inline bool rd(T &ret) { char c; int sgn; if (c = getchar(), c == EOF) return 0; while (c != '-' && (c<'0' || c>'9')) c = getchar(); sgn = (c == '-') ? -1 : 1; ret = (c == '-') ? 0 : (c - '0'); while (c = getchar(), c >= '0'&&c <= '9') ret = ret * 10 + (c - '0'); ret *= sgn; return 1;}template 
         
          inline void pt(T x) { if (x <0) { putchar('-'); x = -x; } if (x>9) pt(x / 10); putchar(x % 10 + '0');}int Pow(int x, int y) { int ans = 1; while (y > 0) { if ((y & 1) > 0) ans *= x; y >>= 1; x = x * x; } return ans;}using namespace std;const int inf = 1e8;const int N = 55;const int M = 500010;int n, m, k, ans;int dis[N][N], dp[N][1 << 10];int e[10];int vis[N];int mem[1 << 10];int check(int x){ int a = 0, b = 0; for (int i = 0; i < k; i++) if ((x&(1 << i))>0)a++; for (int i = 0; i < k; i++) if ((x&(1 << (i + k)))>0)b++; if (a != b)return -1; int ans = inf; for (int i = 0; i < n; i++) ans = min(ans, dp[i][x]); return ans;}int dfs(int x){ if (mem[x] != -1)return mem[x]; int tmp = check(x); if (tmp == -1)return mem[x] = inf; int ans = tmp; for (int i = (x-1)&x; i > 0; i = (i - 1)&x){ ans = min(ans, dfs(i) + dfs(x - i)); } return mem[x] = ans;}void floyd(){ for (int z = 0; z < n; z++) for (int j = 0; j < n; j++) for (int i = 0; i < n; i++) dis[i][j] = min(dis[i][j], dis[j][z] + dis[z][i]);}void input(){ rd(n); rd(m); rd(k); for (int i = 0; i < n; i++)for (int j = 0; j < n; j++)dis[i][j] = (i==j)?0:inf; int u, v, d; while (m-->0){ rd(u); rd(v); rd(d); u--; v--; dis[u][v] = dis[v][u] = min(dis[u][v], d); } for (int z = 0; z < n; z++) for (int j = 0; j < n; j++) for (int i = 0; i < n; i++) dis[i][j] = min(dis[i][j], dis[j][z] + dis[z][i]);}int main(){ int T; rd(T); while (T-->0){ input(); floyd(); for (int i = 0; i < k; i++)e[i] = i; for (int i = 0; i < k; i++)e[i + k] = n - k + i; for (int i = 0; i < n; i++)for (int j = 0; j < (1 << (2 * k)); j++)dp[i][j] = inf; for (int i = 0; i < n; i++){ for (int j = 0; j < 2 * k; j++) dp[i][1 << j] = dis[i][e[j]]; } for (int i = 1; i < (1 << (2 * k)); i++){ if (0 == (i&(i - 1)))continue; for (int j = 0; j < n; j++){ for (int sub = i; sub > 0; sub = (sub - 1)&i) dp[j][i] = min(dp[j][i], dp[j][sub] + dp[j][i-sub]); } for (int j = 0; j < n; j++)vis[j] = 0; for (int j = 0; j < n; j++){ int a = inf, pos = 0; for (int z = 0; z < n; z++) if (vis[z] == 0 && dp[z][i] <= a) a = dp[pos = z][i]; vis[pos] = 1; for (int z = 0; z < n; z++) dp[pos][i] = min(dp[pos][i], dp[z][i] + dis[z][pos]); } } for (int j = k; j < 2 * k; j++)vis[j] = -1; memset(mem, -1, sizeof mem); mem[0] = 0; ans = dfs((1<<(2*k))-1); if (ans == inf)printf("No solution\n"); else printf("%d\n",ans); } return 0;}
         
        
       
      
    
   
  
 

import java.io.BufferedReader;import java.io.InputStreamReader;import java.io.PrintWriter;import java.math.BigInteger;import java.text.DecimalFormat;import java.util.ArrayDeque;import java.util.ArrayList;import java.util.Arrays;import java.util.Collections;import java.util.Comparator;import java.util.Deque;import java.util.HashMap;import java.util.Iterator;import java.util.LinkedList;import java.util.Map;import java.util.PriorityQueue;import java.util.Scanner;import java.util.Stack;import java.util.StringTokenizer;import java.util.TreeMap;import java.util.TreeSet;import java.util.Queue;import java.io.File;import java.io.FileInputStream;import java.io.FileNotFoundException;import java.io.FileOutputStream;public class Main {int n, m, k, ans;int[][] dis = new int[N][N], dp = new int[N][1<<10];int[] e = new int[10];int[] vis = new int[N], mem = new int[1<<10];int check(int x){int a = 0, b = 0;for (int i = 0; i < k; i++)if ((x&(1 << i))>0)a++;for (int i = 0; i < k; i++)if ((x&(1 << (i + k)))>0)b++;if (a != b)return -1;int ans = inf;for (int i = 0; i < n; i++)ans = min(ans, dp[i][x]);return ans;}int dfs(int x){if (mem[x] != -1)return mem[x];int tmp = check(x);if (tmp == -1)return mem[x] = inf;int ans = tmp;for (int i = (x-1)&x; i > 0; i = (i - 1)&x){ans = min(ans, dfs(i) + dfs(x - i));}return mem[x] = ans;}void floyd(){for(int z = 0; z < n; z++)for(int j = 0; j < n; j++)for(int i = 0; i < n; i++)dis[i][j] = min(dis[i][j], dis[j][z] + dis[z][i]);}void input() throws Exception{for(int i = 0; i < n; i++)for(int j = 0; j < n; j++)dis[i][j] = (i==j)?0:inf;while(m-->0){int u = Int() - 1, v = Int() - 1, d = Int();dis[u][v] = dis[v][u] = min(dis[u][v], d);}}void work() throws Exception{int T = Int(); while(T-->0){n = Int(); m = Int(); k = Int();input();floyd();for (int i = 0; i < k; i++)e[i] = i; for (int i = 0; i < k; i++)e[i + k] = n - k + i;for (int i = 0; i < n; i++)for (int j = 0; j < (1 << (2 * k)); j++)dp[i][j] = inf;for (int i = 0; i < n; i++){for (int j = 0; j < 2 * k; j++)dp[i][1 << j] = dis[i][e[j]];}for (int i = 1; i < (1 << (2 * k)); i++){if (0 == (i&(i - 1)))continue;for (int j = 0; j < n; j++){for (int sub = i; sub > 0; sub = (sub - 1)&i)dp[j][i] = min(dp[j][i], dp[j][sub] + dp[j][i-sub]);}for (int j = 0; j < n; j++)vis[j] = 0;for (int j = 0; j < n; j++){int a = inf, pos = 0;for (int z = 0; z < n; z++)if (vis[z] == 0 && dp[z][i] <= a)a = dp[pos = z][i];vis[pos] = 1;for (int z = 0; z < n; z++)dp[pos][i] = min(dp[pos][i], dp[z][i] + dis[z][pos]);}}for(int i = 1; i < (1<<(2*k)); i++)mem[i] = -1;mem[0] = 0;ans = dfs((1<<(2*k))-1);if(ans == inf)out.println("No solution");else out.println(ans);}}    public static void main(String[] args) throws Exception{        Main wo = new Main();    in = new BufferedReader(new InputStreamReader(System.in));    out = new PrintWriter(System.out);  //  in = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));  //  out = new PrintWriter(new File("output.txt"));        wo.work();        out.close();    }static int N = 55;static int M = 2005;DecimalFormat df=new DecimalFormat("0.0000");static int inf = (int)1e8;static long inf64 = (long) 1e18*2;static double eps = 1e-8;static double Pi = Math.PI;static int mod = 1000000009 ;private String Next() throws Exception{    while (str == null || !str.hasMoreElements())        str = new StringTokenizer(in.readLine());    return str.nextToken();    }    private int Int() throws Exception{    return Integer.parseInt(Next());    }    private long Long() throws Exception{    return Long.parseLong(Next());    }    private double Double() throws Exception{    return Double.parseDouble(Next());    }    StringTokenizer str;    static Scanner cin = new Scanner(System.in);    static BufferedReader in;    static PrintWriter out;  /*  class Edge{int from, to, dis, nex;Edge(){}Edge(int from, int to, int dis, int nex){this.from = from;this.to = to;this.dis = dis;this.nex = nex;}}Edge[] edge = new Edge[M<<1];int[] head = new int[N];int edgenum;void init_edge(){for(int i = 0; i < N; i++)head[i] = -1; edgenum = 0;}void add(int u, int v, int dis){edge[edgenum] = new Edge(u, v, dis, head[u]);head[u] = edgenum++;}/**/int upper_bound(int[] A, int l, int r, int val) {// upper_bound(A+l,A+r,val)-A;int pos = r;r--;while (l <= r) {int mid = (l + r) >> 1;if (A[mid] <= val) {l = mid + 1;} else {pos = mid;r = mid - 1;}}return pos;}int Pow(int x, int y) {int ans = 1;while (y > 0) {if ((y & 1) > 0)ans *= x;y >>= 1;x = x * x;}return ans;}double Pow(double x, int y) {double ans = 1;while (y > 0) {if ((y & 1) > 0)ans *= x;y >>= 1;x = x * x;}return ans;}int Pow_Mod(int x, int y, int mod) {int ans = 1;while (y > 0) {if ((y & 1) > 0)ans *= x;ans %= mod;y >>= 1;x = x * x;x %= mod;}return ans;}long Pow(long x, long y) {long ans = 1;while (y > 0) {if ((y & 1) > 0)ans *= x;y >>= 1;x = x * x;}return ans;}long Pow_Mod(long x, long y, long mod) {long ans = 1;while (y > 0) {if ((y & 1) > 0)ans *= x;ans %= mod;y >>= 1;x = x * x;x %= mod;}return ans;}int gcd(int x, int y){if(x>y){int tmp = x; x = y; y = tmp;}while(x>0){y %= x;int tmp = x; x = y; y = tmp;}return y;}int max(int x, int y) {return x > y ? x : y;}int min(int x, int y) {return x < y ? x : y;}double max(double x, double y) {return x > y ? x : y;}double min(double x, double y) {return x < y ? x : y;}long max(long x, long y) {return x > y ? x : y;}long min(long x, long y) {return x < y ? x : y;}int abs(int x) {return x > 0 ? x : -x;}double abs(double x) {return x > 0 ? x : -x;}long abs(long x) {return x > 0 ? x : -x;}boolean zero(double x) {return abs(x) < eps;}double sin(double x){return Math.sin(x);}double cos(double x){return Math.cos(x);}double tan(double x){return Math.tan(x);}double sqrt(double x){return Math.sqrt(x);}}