Jigsaw Puzzle Solving

All submissions for this problem are available.
Imagine a usual jigsaw puzzle. Let its picture be a completely white rectangle with the width of W pixels and the height of H pixels.
The puzzle was splitted into K pieces, then they've got mixed up. Now you want to restore it again. Ideally, you'd like merge these pieces in such a way that they'd form a rectangle W pixels wide and H pixels tall, again. However, it can be very hard. Therefore, even reconstructing a part of a puzzle will make you happy.
Let's formalize the things a bit. You have an empty matrix of H x W cells and K pieces, every piece is a connected component (see the further illustration for better understanding). By connected component, we mean that a piece is a figure where you can reach any pixel of a figure by going through sideadjacent pixels from the figure. You can place a piece anywhere in the matrix, in case it doesn't overlap with other pieces and doesn't crosses the border of the matrix. You can skip the piece and not to place it at all. You cannot rotate the pieces. Given that it is possible to place all the the pieces in such a way that the every cell of the matrix is exactly covered by one piece.
Your goal is to place some (maybe, all) of the pieces in such a way that no two pieces overlap, no piece crosses the border of the matrix, and the number of the cells that are covered by placed pieces is maximized.
Here is the example of the puzzle, splitted into pieces:
9 9 9 9 9 9 8 8 8 1
9 9 9 9 9 9 8 8 8 1
9 5 5 5 5 9 9 9 4 1
5 5 5 5 5 9 9 4 4 1
5 3 5 5 4 4 4 4 7 1
3 3 5 5 4 2 2 7 7 1
3 3 3 2 2 2 7 7 1 1
3 3 3 2 7 7 7 7 7 7
3 3 3 2 6 7 7 7 6 6
2 2 2 2 6 6 6 6 6 6
Input
The first line of input contains three space separated integers H, W and K  the number of rows, columns and pieces respectively.
Then K blocks, describing a piece follow.
Each description starts with a line, containing a single integer P, denoting the number of cells that this piece cover.
Then there are P lines, each contains a pair of integers X, Y (1 <= X <= H, 1 <= Y <= W), denoting 1based coordinates of piece's cell in its' bounding box. That is, the minimal Xcoordinate and the minimal Ycoordinate in each piece's description are both 1.
All the pieces are identified by consecutive positive integers (starting from 1) in the order of input.
Output
Output H lines of W integers separated by a single space. The jth integer in the ith line should denote the identification number of piece that covers the respective cell, or 0 if the cell is not covered by any piece.
Test data information
There will be several groups in this problem (20 test cases in total):
 The first group will contain 5 test cases. In these test cases, W and H will be chosen randomly between 10 and 50. K will be chosen randomly between W * H / 10 and W * H / 2, inclusively.
 The second group will contain 8 test cases. In these test cases, W and H will be chosen randomly between 100 and 200. K will be chosen randomly between W * H / 100 and W * H / 34, inclusively.
 The third group will contain 3 test cases. In these test cases, W and H will be chosen randomly between 600 and 800. K will be chosen randomly between W * H / 100 and W * H / 34, inclusively.
 The fourth group will contain 4 test cases. In these test cases, W and H will be chosen randomly between 500 and 1000. K will be chosen randomly between W * H / 50 and W * H / 5, inclusively.
In the test data provided, the maximal number of pixels in a piece and the minimal number of pixels in a piece will differ in no more than 3 times. That is, the max_P  min_P <= 3 * min_P.
Scoring
Your score for the test case equals to the percentage of the matrix that is covered by pieces. Your score for the problem is the average of your scores for all the test cases. Pay attention that during the contest only the score on 20% of the test cases will be revealed. These 20% will contain a single test case from each of the groups.
Example
Input: 10 10 9 8 1 2 2 2 3 2 4 2 5 2 6 2 7 2 7 1 11 1 7 1 6 2 5 2 6 5 3 5 1 5 2 2 4 3 4 4 4 5 4 12 4 3 5 3 5 1 5 2 1 2 2 2 2 1 3 1 3 2 3 3 4 1 4 2 8 1 5 2 5 2 4 3 4 3 1 4 1 3 2 3 3 14 2 4 3 4 2 3 3 3 4 3 4 4 1 2 2 2 2 1 3 1 1 3 1 4 1 5 2 5 9 1 1 2 1 2 2 2 3 2 4 2 5 2 6 1 6 1 5 14 5 2 5 3 4 4 5 4 4 5 4 6 1 5 2 5 2 4 3 4 4 2 4 1 3 3 4 3 6 1 2 1 1 1 3 2 3 2 1 2 2 18 1 1 1 2 2 1 3 1 2 2 2 3 2 4 2 5 3 8 3 7 4 7 4 6 2 6 3 6 1 4 1 3 1 6 1 5 Output: 0 1 8 8 8 0 0 2 2 0 0 1 8 8 8 2 2 2 3 0 0 1 0 0 0 2 0 3 3 0 0 1 0 0 0 2 0 3 3 3 0 1 2 2 2 2 4 3 3 3 0 1 0 0 0 4 4 3 3 3 1 1 4 4 4 4 5 5 5 5 0 0 4 0 0 5 5 5 5 5 0 0 0 0 0 5 0 5 5 0 0 0 0 0 0 0 0 5 5 0
Explanation
How to assign coordinates to the pieces. ?
Let us consider the 6th piece. Its coordinates will be (1, 1), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6). You can notice that x coordinate will increase when you go towards south direction, your y coordinate will increase when you towards east direction.
Another example:
Let us consider this piece.
010
110
011
Its actual coordinates will be given you in row major in following way.
(1 2), (2 1), (2 2), (3 2), (3 3).
This solution corresponding to given output would get 0.59 points.
Author:  xcwgf666 
Editorial  http://discuss.codechef.com/problems/CHPUZZLE 
Tags  challenge, feb15, xcwgf666 
Date Added:  16012015 
Time Limit:  5 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, SCM chicken, PYP3, CLOJ, FS 
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