UVa 11205 The broken pedometer: enumerating good questions & skillfully using binary

11205-the Broken Pedometer

Time limit:3.000 seconds

Http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=107&page=show_ problem&problem=2146

The Problem

A marathon runner uses a pedometer with which it has problems. In the pedometer the symbols are represented by seven segments (or LEDs):

But the pedometer does not work properly (possibly the sweat affected the batteries) and only some of the LEDs active. The runner wants to know if all possible symbols:

can be correctly identified. For example, when the active LEDs are:

Numbers 2 and 3 are seen as:

So they cannot to be distinguished. But when the active LEDs are:

The numbers are seen as:

And all of them have a different representation.

Because the runner teaches algorithms at University, and him has some hours to do you are running, he has thought up A programming problem which generalizes the problem of his sweat pedometer. The problem consists of obtaining the minimum number of active LEDs necessary to identify each one of the symbols, given a Number P of LEDs, and N symbols to is represented with this LEDs (along with the codification of each symbol).

For example, in the previous sample P = 7 and N = 10. Supposing the LEDs are numbered as:

The Codification the symbols is: "0" = 1 1 1 0 1 1 1; "1" = 0 0 1 0 0 1 0; "2" = 1 0 1 1 1 0 1; "3" = 1 0 1 1 0 1 1; "4" = 0 1 1 1 0 1 0; "5" = 1 1 0 1 0 1 1; "6" = 1 1 0 1 1 1 1; "7" = 1 0 1 0 0 1 1; "8" = 1 1 1 1 1 1 1; "9" = 1 1 1 1 0 1 1. In this case, LEDs 5 and 6 can be suppressed without losing information, so the solution is 5.

The Input

The input file consists of a-a and the number of problems to solve. Each problem consists of a, a I with the number of LEDs (P), a second line with the number of symbols (n), and N Lin Es one with the codification of a symbol. For each symbol, the codification are a succession of 0s and 1s, with a space between them. A 1 means the corresponding LED is part of the codification of the symbol. The maximum value of P is-maximum value of N is 100. All the symbols have different codifications.

The Output

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The output would consist of a line for each problem, with the minimum number of active LEDs necessary to identify all the G Iven symbols.

Sample Input

2
7
of
1 1 1
0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 0
1 1 0 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 6 0 1 1 1 0 0 1 0 0 0
C24/>0 1 1 0 0 0