Algorithm to find the smallest snippet from searching a document?

Question

I\'ve been going through Skiena\'s excellent \"The Algorithm Design Manual\" and got hung up on one of the exercises.

The question is: \"Given a search string of three w

Answer 1

O(n log k) solution, where n is the total number of indices and k is the number of words. The idea is to use a heap to identify the smallest index at each iteration, while also keeping track of the maximum index in the heap. I also put the coordinates of each value in the heap, in order to be able to retrieve the next value in constant time.

#include 
#include 
#include 
#include 
#include 

using namespace std;

int snippet(const vector< vector >& index) {
    // (-index[i][j], (i, j))
    priority_queue< pair< int, pair > > queue;
    int nmax = numeric_limits::min();
    for (size_t i = 0; i < index.size(); ++i) {
        if (!index[i].empty()) {
            int cur = index[i][0];
            nmax = max(nmax, cur);
            queue.push(make_pair(-cur, make_pair(i, 0)));
        }
    }
    int result = numeric_limits::max();
    while (queue.size() == index.size()) {
        int nmin = -queue.top().first;
        size_t i = queue.top().second.first;
        size_t j = queue.top().second.second;
        queue.pop();
        result = min(result, nmax - nmin + 1);
        j++;
        if (j < index[i].size()) {
            int next = index[i][j];
            nmax = max(nmax, next);
            queue.push(make_pair(-next, make_pair(i, j)));
        }
    }
    return result;
}

int main() {
    int data[][3] = {{1, 4, 5}, {4, 9, 10}, {5, 6, 15}};
    vector > index;
    for (int i = 0; i < 3; i++) {
        index.push_back(vector(data[i], data[i] + 3));
    }
    assert(snippet(index) == 2);
}