HDU3488 Tour —— 二分圖最大權匹配 KM算法
阿新 • • 發佈:2017-11-13
sed exceptio total icpc def i++ after ive pac
Every city should be just in one route.
A loop should have at least two cities. In one route, each city should be visited just once. (The only exception is that the first and the last city should be the same and this city is visited twice.)
The total distance the N roads you have chosen should be minimized.
Input
An integer T in the first line indicates the number of the test cases.
In each test case, the first line contains two integers N and M, indicating the number of the cities and the one-way roads. Then M lines followed, each line has three integers U, V and W (0 < W <= 10000), indicating that there is a road from U to V, with the distance of W.
It is guaranteed that at least one valid arrangement of the tour is existed.
A blank line is followed after each test case.
Output
For each test case, output a line with exactly one integer, which is the minimum total distance.
題目鏈接:https://vjudge.net/problem/HDU-3488
Tour
Time Limit: 3000/1000 MS (Java/Others) Memory Limit: 65535/65535 K (Java/Others)
Total Submission(s): 3720 Accepted Submission(s): 1777
Every city should be just in one route.
A loop should have at least two cities. In one route, each city should be visited just once. (The only exception is that the first and the last city should be the same and this city is visited twice.)
The total distance the N roads you have chosen should be minimized.
In each test case, the first line contains two integers N and M, indicating the number of the cities and the one-way roads. Then M lines followed, each line has three integers U, V and W (0 < W <= 10000), indicating that there is a road from U to V, with the distance of W.
It is guaranteed that at least one valid arrangement of the tour is existed.
A blank line is followed after each test case.
Sample Input 1 6 9 1 2 5 2 3 5 3 1 10 3 4 12 4 1 8 4 6 11 5 4 7 5 6 9 6 5 4
Sample Output 42
Source 2010 ACM-ICPC Multi-University Training Contest(6)——Host by BIT
Recommend zhouzeyong
題解:
代碼如下:
1 #include <bits/stdc++.h> 2 using namespace std; 3 typedef long long LL; 4 const int INF = 0x3f3f3f3f; 5 const LL LNF = 9e18; 6 const int mod = 1e9+7; 7 const int MAXN = 2e2+10; 8 9 int nx, ny; 10 int g[MAXN][MAXN]; 11 int linker[MAXN], lx[MAXN], ly[MAXN]; 12 int slack[MAXN]; 13 bool visx[MAXN], visy[MAXN]; 14 15 bool DFS(int x) 16 { 17 visx[x] = true; 18 for(int y = 1; y<=ny; y++) 19 { 20 if(visy[y]) continue; 21 int tmp = lx[x] + ly[y] - g[x][y]; 22 if(tmp==0) 23 { 24 visy[y] = true; 25 if(linker[y]==-1 || DFS(linker[y])) 26 { 27 linker[y] = x; 28 return true; 29 } 30 } 31 else 32 slack[y] = min(slack[y], tmp); 33 } 34 return false; 35 } 36 37 int KM() 38 { 39 memset(linker, -1, sizeof(linker)); 40 memset(ly, 0, sizeof(ly)); 41 for(int i = 1; i<=nx; i++) 42 { 43 lx[i] = -INF; 44 for(int j = 1; j<=ny; j++) 45 lx[i] = max(lx[i], g[i][j]); 46 } 47 48 for(int x = 1; x<=nx; x++) 49 { 50 for(int i = 1; i<=ny; i++) 51 slack[i] = INF; 52 while(true) 53 { 54 memset(visx, 0, sizeof(visx)); 55 memset(visy, 0, sizeof(visy)); 56 57 if(DFS(x)) break; 58 int d = INF; 59 for(int i = 1; i<=ny; i++) 60 if(!visy[i]) 61 d = min(d, slack[i]); 62 63 for(int i = 1; i<=nx; i++) 64 if(visx[i]) 65 lx[i] -= d; 66 for(int i = 1; i<=ny; i++) 67 { 68 if(visy[i]) ly[i] += d; 69 else slack[i] -= d; 70 } 71 } 72 } 73 74 int res = 0; 75 for(int i = 1; i<=ny; i++) 76 if(linker[i]!=-1) 77 res += g[linker[i]][i]; 78 return res; 79 } 80 81 int main() 82 { 83 int T, n, m; 84 scanf("%d", &T); 85 while(T--) 86 { 87 scanf("%d%d", &n,&m); 88 nx = ny = n; 89 memset(g, 0, sizeof(g)); 90 for(int i = 1; i<=nx; i++) 91 for(int j = 1; j<=ny; j++) 92 g[i][j] = -INF; 93 for(int i = 1; i<=m; i++) 94 { 95 int u, v, w; 96 scanf("%d%d%d", &u, &v, &w); 97 g[u][v] = max(g[u][v], -w); 98 } 99 100 printf("%d\n", -KM()); 101 } 102 }View Code
HDU3488 Tour —— 二分圖最大權匹配 KM算法