Uva387-a puzzling problem

A puzzling problem

The goal of this problem is to write a program which will take from 1 to 5 puzzle pieces such as those shown below and arrange them, if possible, to form a square. an example set of pieces is shown here.

The pieces cannot be rotated or flipped from their original orientation in an attempt to form a square from the set. all of the pieces must be used to form the square. there may be more than one possible solution for a set of pieces, and not every arrangement will work even with a set for which a solution can be found. examples using the above set of pieces are shown here.

Input

The input file for this program contains several puzzles (I. e. sets of puzzle pieces) to be solved. the first line of the file is the number of pieces in the first puzzle. each piece is then specified by listing a single line with two integers, the number of rows and columns in the piece, followed by one or more lines which specify the shape of the piece. the shape specification consists of '0' and '1' characters, with the '1' characters indicating the solid shape of the puzzle (the '0' characters are merely placeholders ). for example, piece 'A' above wocould be specified as follows:

2 3111101

The pieces shoshould be numbered by the order they are encountered in the puzzle. that is, the first piece in a puzzle is piece #1, the next is piece #2, etc. all pieces may be assumed to be valid and no larger than 4 rows by 4 columns.

The line following the final line of the last piece contains the number of pieces in the next puzzle, again followed by the puzzle pieces and so on. the end of the input file is indicated by a zero in place of the number of puzzle pieces.

Output

Your program shocould report a solution, if one is possible, in the format shown by the examples below. A 4-row by 4-column square shoshould be created, with each piece occupying its location in the solution. the solid portions of piece #1 shoshould be replaced with '1' characters, of piece #2 with '2' characters, etc. the solutions for each puzzle shoshould be separated by a single blank line.

If there are multiple solutions, any of them is acceptable. For puzzles which have no possible solution simply report''No solution possible''.

Sample Input

42 31111014 2010111012 1113 210101141 411111 411111 411112 311100152 211112 31111003 21101011 31111 110

Sample output

1112141234223442No solution possible1133115322232444

 

// Question: Use n blocks to construct a 4*4 square. Each block must be exactly used once and cannot be rotated or flipped. Any solution
// Algorithm: This question is written in many ways. Because the scale is very small, a method that is not very efficient but better implemented is provided here: select an available building block for each layer of search, repeat a position to put it up.

 

One by one.

The code is clearer after piece is encapsulated.

#include<cstdio>#include<cstring>#include<iostream>#include<string>#include<algorithm>using namespace std;const int maxn=5;int board[maxn][maxn];int n;struct Piece {        int r, c, size;        char data[maxn][maxn];        void read() {                scanf("%d%d", &r, &c);                for(int i=0;i<r;i++)                {                        scanf("%s", data[i]);                        for(int j=0;j<c;j++)                                size+=data[i][j]-‘0‘;                }        }        bool can_place(int x, int y) {                if(x+r>4 || y+c>4) return false;                for(int i=0;i<r;i++)                        for(int j=0;j<c;j++)                                if(data[i][j]==‘1‘ && board[x+i][y+j]!=0)                                        return false;                return true;        }        void fill(int x, int y, int v) {                for(int i=0;i<r;i++)                        for(int j=0;j<c;j++)                                if(data[i][j]==‘1‘)                                        board[x+i][y+j]=v;        }}pieces[5];bool dfs(int d, int cnt){        if(d==n)        {                return cnt==16;        }        for(int i=0;i<4;i++)                for(int j=0;j<4;j++)                {                        if(pieces[d].can_place(i, j))                        {                                pieces[d].fill(i, j, d+1);                                if(dfs(d+1, cnt+pieces[d].size)) return true;                                pieces[d].fill(i, j, 0);                        }                }        return false;}int main(){#ifndef ONLINE_JUDGE        freopen("./uva387.in", "r", stdin);#endif        int kase=0;        while(scanf("%d", &n)==1 && n) {                kase++;                if(kase!=1)                        printf("\n");                memset(pieces, 0, sizeof(pieces));                memset(board, 0, sizeof(board));                int total=0;                for(int i=0;i<n;i++)                {                        pieces[i].read();                        total+=pieces[i].size;                }                if(total==16 && dfs(0, 0))                {                        for(int i=0;i<4;i++)                        {                                for(int j=0;j<4;j++)                                        printf("%d", board[i][j]);                                printf("\n");                        }                }                else                        printf("No solution possible\n");        }    return 0;}