Shooting competition (POJ 1719)

"Problem description"

We assume that the target of the shot is a rectangular grid of r*c (2≤r≤c≤1000) small squares. Each column in the grid has 2 white squares and R-2 a small black square. The rows that define the grid are numbered 1~r from top to bottom, and the columns are numbered 1~c from left to right. The shooter can shoot C times. In a continuous C shot, the shot is correct if there is exactly one white square shot in each column and no white squares are shot in the row. Now gives the n set of data, for each set of data, if there is the correct shooting method, then ask to find it, if not present, output No.

"Sample Input"

2
4 4

2 4

3 4

1 3

1 4

5 5

1 5

2 4

3 4

2 4

2 3

"Sample Output"

2 3 1 4

NO

"Problem-solving ideas"

This is titled 1997 Ceoi last Question, the thinking of solving problems mainly lies in the greedy strategy and the proof of greed.

Greedy strategy:

1. Count the number of white cells that all rows contain.

2. Select a minimum number of white lattices from a row that has not yet been shot.

3. Check the selected row (1) If the selected row has a white number of 0, then the output is no solution, or (2) Otherwise, select one of the white cells of the selected row as the shooting cell, and subtract 1 from the number of rows in the other white grid that is in the same column as the grid.

4. Return to the 2nd step until all the lines have a shot lattice.

5, if there is no selection of shooting lattice, then in the column to choose a white lattice as a shooting lattice can be.

Greedy Proof:

Use H[i] to denote the number of white cells in line I.        If at first: ①min{h[i]}=0: line I has no way to find the white lattice that can be used as a shooting lattice, then the problem can only be solved. ②min{h[i]}=1: Then the first line of this white lattice must be used as a shooting lattice, otherwise there will be no shooting lattice on line I to cause problems without solution.

③min{h[i]}≥2: So in this line of choice a white lattice, at most, will only cause the remaining line has a line h value of 1, and then processing that line, at most will only cause the remaining line has a line h value of 1, so reciprocating, will maintain the H value of 1 of the number of rows not more than 1 lines, Finally, the worst case scenario is that the H value of the last line is 1, and all rows are selected for the shot lattice. Therefore, if the original problem has a solution, the greedy method must be able to find a correct scheme. It can be proved that this greedy method is correct. Determine the greedy standard.

"Code Implementation"

1 varA:Array[1.. +] ofLongint;2B:Array[1.. +,1.. +] ofBoolean;3FR,FC:Array[1.. +] ofBoolean;4AnsArray[1.. +] ofLongint;5 N,i,j,r,c,x1,x2,k,pos,min,code,q:longint;6 Flag:boolean;7 begin8 READLN (code);9   forq:=1  toCode DoTen   begin One Fillchar (Fr,sizeof (FR), false); A Fillchar (fc,sizeof (FC), false); -Fillchar (A,sizeof (a),0); -Fillchar (b,sizeof (b),0);//note initialization, not initializing WA several times ... the readln (r,c); -     fori:=1  toC Do -     begin - readln (x1,x2); +b[x1,i]:=true;b[x2,i]:=true; - Inc (A[X1]); Inc (A[X2]); +     End; A    Repeat atmin:=Maxlongint; -flag:=true; -      fori:=1  toR Do -      if  not(Fr[i]) Then - Break ; -     if  not(Fr[i]) Then inflag:=false; -     ifFlag ThenBreak ; to     fori:=1  toR Do +     if(a[i]<min) and( not(Fr[i])) Then -      begin themin:=A[i]; *pos:=i; $      End;Panax Notoginseng    ifa[pos]=0  Then -     begin theWriteln ('NO'); + Break ; A     End; thefr[pos]:=true; +     forj:=1  toC Do -     if(B[pos,j]) and( not(Fc[j])) Then $      begin $ans[j]:=pos;fc[j]:=true; -        fork:=1  toR Do -        if(B[k,j]) and(K<>pos) Then the Dec (a[k]); - Break ;Wuyi      End; the    untilFlag; -    ifa[pos]=0  Then Wu continue; -     fori:=1  toC Do About     ifans[i]=0  Then $       forj:=1  toR Do -       ifB[j,i] Then -        begin -ans[i]:=J; A Break ; +        End; theWrite (ans[1]); -     fori:=2  toC Do $Write' ', Ans[i]); the Writeln; the   End; the End.

View Code

Shooting competition (POJ 1719)