Find the number of occurrences of a subsequence in a string

Question

For example, let the string be the first 10 digits of pi, 3141592653, and the subsequence be 123. Note that the sequence occurs twice:

Answer 1

psh. O(n) solutions are way better.

Think of it by building a tree:

iterate along the string if the character is '1', add a node to the the root of the tree. if the character is '2', add a child to each first level node. if the character is '3', add a child to each second level node.

return the number of third layer nodes.

this would be space inefficient so why don't we just store the number of nodes a each depth:

infile >> in;
long results[3] = {0};
for(int i = 0; i < in.length(); ++i) {
    switch(in[i]) {
        case '1':
        results[0]++;
        break;
        case '2':
        results[1]+=results[0];
        break;
        case '3':
        results[2]+=results[1];
        break;
        default:;
    }
}

cout << results[2] << endl;