UVA 11383 Golden Tiger Claw golden Tiger Claw (km algorithm)

Test instructions: To a n*n matrix, each lattice has a positive integer w[i][j], try for each row and each column to determine a number row[i] and col[i], so that arbitrary lattice w[i][j]<=row[i]+col[j] constant set up. First lose row, then output col, and then output the total sum (the sum should be as small as possible).

Ideas:

Km the top mark in the algorithm is to keep the lx[i]+ly[j]>=g[i][j] and then the maximum right and matching, but this maximum power and does not matter. We can think of row[i] as a man, Col[i] as a woman, so that the total number of men and women is equal. In general, Lx[i] or ly[i] only need to take the largest number in the row/column to ensure that the requirements are met, but this is too large to be adjusted to make the sum smaller. The process of the KM algorithm is a process of adjustment, each pair of matching men and women of that side of the weight will meet the equal sign W[i][j=row[i]+col[j]], at least one to meet the equal sign, so as to ensure that row[i]+col[j] is the smallest, that is, from the J column to see, col[j ] satisfies the condition and the smallest, from the I line, row[i] satisfies the condition and the smallest. This is exactly the same as the KM algorithm for maximum power.

1#include <bits/stdc++.h>2 #defineLL Long Long_long_max3 #defineINF 0x7f7f7f7f4 #defineLL Long Long5 using namespacestd;6 Const intn=510;7 8 intGrid[n][n], girl[n];9 intLx[n], ly[n], slack[n];Ten BOOLS[n], t[n]; One intN; A  - BOOLDFS (intx) - { thes[x]=true; -      for(intI=1; i<=n; i++) -     { -         if(T[i])Continue; +         inttmp=lx[x]+ly[i]-Grid[x][i]; -         if(tmp==0) +         { At[i]=true; at             if(girl[i]==0||DFS (Girl[i])) -             { -girl[i]=x; -                 return true; -             } -         } in         Else if(tmp<Slack[i]) -slack[i]=tmp; to     } +     return false; - } the  *  $ Panax Notoginseng intKM () - { theMemset (Girl,0,sizeof(Girl)); +memset (Lx,0,sizeof(Lx)); Amemset (Ly,0,sizeof(Ly)); the      for(intI=1; i<=n; i++) +          for(intj=1; j<=n; J + +) -lx[i]=Max (Lx[i], grid[i][j]); $  $      for(intI=1; i<=n; i++)//for each tree -     { -          for(intj=1; j<=n; J + +) slack[j]=INF; the          while(1) -         {Wuyimemset (S),0,sizeof(S)); thememset (T,0,sizeof(T)); -             if(DFS (i)) Break;//find the matching ants. Wu  -  About             intD=INF; $              for(intj=1; j<=n; J + +)//Find minimum D -             { -                 if(! T[J] && d>Slack[j]) -D=Slack[j]; A             } +  the              for(intj=1; j<=n; J + +)//Update Tree -             { $                 if(S[j]) thelx[j]-=D; the             } the  the              for(intj=1; j<=n; J + +)//Update Ants -             { in                 if(T[j]) ly[j]+=D; the                 Elseslack[j]-=D; the             } About         } the     } the     intsum=0; the      for(intI=1; i<=n; i++) sum+=lx[i]+Ly[i]; +     returnsum; - } the Bayi  the  the  - intMain () - { theFreopen ("Input.txt","R", stdin); the      while(~SCANF ("%d",&N)) the     { thememset (Grid,0,sizeof(grid)); -          for(intI=1; i<=n; i++) the              for(intj=1; j<=n; J + +) thescanf"%d",&grid[i][j]); the 94         intans=KM (); theprintf"%d", lx[1]);//notable output formats.  the          for(intI=2; i<=n; i++) printf ("%d", Lx[i]); theprintf"\ n");98printf"%d", ly[1]); About          for(intI=2; i<=n; i++) printf ("%d", Ly[i]); -printf"\ n");101printf"%d\n", ans);102     }103     return 0;104}

AC Code

UVA 11383 Golden Tiger Claw golden Tiger Claw (km algorithm)