Character recognition


http://wangsc.ga/posts/20170224-interview-char-rec/
Character recognition is the conversion of images into text. For now we consider each character in the picture is a N*M matrix with only zeros and ones, and we need to recognize K characters. You are to write a program to find minimal number of pixels so that we can recognize each character.

For example, we have only two characters T and L, and the matrix size is 3*3, we can think T and L are
1 1 1 1 0 0
0 1 0 1 0 0
0 1 0 1 1 1
So we can recognize the character with only botton-left pixel, the anwser is 1;

Limits

  • Memory limit per test: 256 megabytes
  • Time limit per test: The faster the better

Compile & Environment

C++
g++ Main.cc –o Main –fno-asm –Wall –lm –static –std=c++0x –DONLINE_JUDGE
Java
J2SE8
Maximum stack size is 50m

Input

The first line of input is three integers NMK (1 <= N, M <=102 <= K <= 6).
Which represents the size of matrix and number of characters. Then is following K blocks, which represents the matrix. Notice that each block starts with a blank line

Output

You should output the minimum number of pixels, which is the anwser.

Test Case

input
1 3 3
1 1 0
0 0 1
1 0 1
output
2
input
3 3 2
1 1 1
0 1 0
0 1 0
1 0 0
1 0 0
1 1 1
output
1

Generalize problem

Given K bit serie with same length (N*M), find the minimum bits required to distinguish them.
input
2
101110
010010
3
11110
11001
11101
4
111111
010101
000101
110111
5
0000101101
0000101010
1001010011
1001010110
0001111101
output
1
2
3
?

/**
* return min min: number of indices required for distinguish series
*/
private static int minDigit(List<char[]> series, int k, int l) {
// store all the subsets of {0,..., l-1}
Set<List<Integer>> subsets = new HashSet<List<Integer>>();
// init .. empty set is not included
subsets = getSubsets(l);
int min = l;
for (List<Integer> list : subsets) {
// if longer than minimum length
// we don't need to consider
if (list.size() > min)
continue;
if (isValidIndex(list, series)) {
min = list.size();
}
}
return min;
}
/**
* validation of indices
*/
private static boolean isValidIndex(List<Integer> list, List<char[]> series) {
Set<String> set = new HashSet<String>();
for (char[] arr : series) {
String tmp = "";
for (int i = 0; i < list.size(); i++) {
tmp = tmp + arr[list.get(i)];
}
// if the combination exist in the set
// means the list of index is not valid
if (set.contains(tmp)) {
return false;
} else {
set.add(tmp);
}
}
return true;
}
/**
* get subsets
*/
private static Set<List<Integer>> getSubsets(int num) {
Set<List<Integer>> subsets = new HashSet<List<Integer>>();
List<Integer> ls = null;
int ind = 0;
// i start from 1, because, if i start from 0
// an empty set will be generate.
for (int i = 1; i < Math.pow(2, num); i++) {
// init
int tmp = i;
ind = 0;
ls = new ArrayList<Integer>();
while (tmp != 0) {
if ((tmp & 1) == 1) {
ls.add(ind);
}
tmp = tmp >> 1;
ind++;
}
subsets.add(ls);
}
return subsets;
}

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