Maximum count of 0s between two 1s in given range for Q queries | Set – 2

Given a binary string S of size N, and a 2D array Q[][] of queries consisting of M pairs of the form {L, R}, the task for each query is to find the maximum number of 0s lying between two 1s in the range [L, R].
Examples:

Input: S = “1001010”, Q[][] = {{0, 4}, {0, 5}}
Output: 2 3
Explanation:
The Queries are performed as per the following:

1. Query(0, 4): Print 2 as there are maximum 2 0’s lying between the indices 0 and 3 in the substring over the range [0, 4] i.e., “10010”. 
2. Query(0, 5): Print 3 as there are maximum 3 0’s lying between the indices 0 and 5 in the substring over the range [0, 5] i.e., “100101”.
   

Input: S = “101”, Q[][] = {{0, 2}}
Output: 1

Approach: Another variation is already discussed in Set1 of this problem. Keep track of two entities: location of 1’s and the Number of 1’s that appeared before any specific position. Use a set to store the location of 1’s and an array to store the answer. Now to find the answer in range [i,j] use the following observation:

Let first and last 1s between given range is located at (i+first) and (i+last), then

Total 0’s between 1’s = total elements between these two locations – total 1’s between these to locations
                                 = location difference between 1’s  – (1’s appeared before (i+last) – 1’s appeared before (i+first) )

Below is the implementation of the above approach:

C++

// C++ implementation of the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to get the number of
// 0s between two 1s
vector<int>
zBetweeno(string s,
          vector<vector<int> >& queries)
{
    // Store location of 1s
    set<int> ones;

    // Store number of candles before i
    vector<int> one(s.size(), 0);

    // Store result
    vector<int> res;

    // Storing number of candles before
    // a specific position
    // and locations of candles in a set
    for (int i = 0; i < s.size(); i++) {
        if (s[i] == '1') {
            ones.insert(i);
            one[i]++;
        }
        if (i != 0)
            one[i] += one[i - 1];
    }

    // Iterating over queries
    for (auto&& query : queries) {

        // Get the location of first 1
        int ss
            = *ones.lower_bound(query[0]);

        // Get the location of last 1
        int ee
            = s[query[1]] == '1'
                  ? query[1]
                  : *--ones.lower_bound(query[1]);

        // Check for corner cases
        if (ss > query[1]
            || ee < query[0]) {
            res.push_back(0);
            continue;
        }

        int tot
            = one[ee] - one[ss];
        int loc = ee - ss;

        // Storing result of the query
        res.push_back(loc
                      - tot);
    }

    return res;
}

// Driver code
int main()
{
    vector<vector<int> > queries
      = { { 0, 4 }, { 0, 5 } };
    string input = "1001010";

    vector<int> res =
      zBetweeno(input, queries);

    for (auto elem : res)
        cout << elem << " ";
    cout << endl;
}

Java

import java.util.*;
import java.io.*;

// Java program for the above approach
class GFG{

  // Function to get the number of
  // 0s between two 1s
  public static ArrayList<Integer> zBetweeno(String s, ArrayList<ArrayList<Integer>> queries)
  {
    // Store location of 1s
    TreeSet<Integer> ones = new TreeSet<Integer>();

    // Store number of candles before i
    int one[] = new int[s.length()];

    // Store result
    ArrayList<Integer> res = new ArrayList<Integer>();

    // Storing number of candles before
    // a specific position
    // and locations of candles in a set
    for (int i = 0 ; i < s.length() ; i++) {
      if (s.charAt(i) == '1') {
        ones.add(i);
        one[i]++;
      }
      if (i != 0){
        one[i] += one[i - 1];
      }
    }

    // Iterating over queries
    for (int i = 0 ; i < queries.size() ; i++) {
      ArrayList<Integer> query = queries.get(i);

      // Get the location of first 1
      int ss = ones.ceiling(query.get(0));

      // Get the location of last 1
      int ee = s.charAt(query.get(1)) == '1' ? query.get(1) : ones.floor(query.get(1)-1);

      // Check for corner cases
      if (ss > query.get(1) || ee < query.get(0)) {
        res.add(0);
        continue;
      }

      int tot = one[ee] - one[ss];
      int loc = ee - ss;

      // Storing result of the query
      res.add(loc - tot);
    }

    return res;
  }

  // Driver code
  public static void main(String args[])
  {
    ArrayList<ArrayList<Integer> > queries = new ArrayList<>(
      List.of(
        new ArrayList<Integer>(
          List.of(0, 4)
        ),
        new ArrayList<Integer>(
          List.of(0, 5)
        )
      )
    );

    String input = "1001010";

    ArrayList<Integer> res = zBetweeno(input, queries);

    for(int i = 0 ; i < res.size() ; i++){
      System.out.print(res.get(i) + " ");
    }
    System.out.println("");
  }
}

// This code is contributed by subhamgoyal2014.

Python3

# Python 3 implementation of the above approach
from bisect import bisect_left

# Function to get the number of
# 0s between two 1s
def zBetweeno(s, queries):

    # Store location of 1s
    ones = set([])

    # Store number of candles before i
    one = [0]*len(s)

    # Store result
    res = []

    # Storing number of candles before
    # a specific position
    # and locations of candles in a set
    for i in range(len(s)):
        if (s[i] == '1'):
            ones.add(i)
            one[i] += 1

        if (i != 0):
            one[i] += one[i - 1]

    # Iterating over queries
    for query in queries:

        # Get the location of first 1
        ss = bisect_left(list(ones), query[0])

        # Get the location of last 1
        if s[query[1]] == '1':
            ee = query[1]
        else:
            ee = bisect_left(list(ones), query[1])

        # Check for corner cases
        if (ss > query[1]
                or ee < query[0]):
            res.append(0)
            continue

        tot = one[ee] - one[ss]
        loc = ee - ss

        # Storing result of the query
        res.append(loc
                   - tot)
    return res

# Driver code
if __name__ == "__main__":

    queries = [[0, 4], [0, 5]]
    input = "1001010"

    res = zBetweeno(input, queries)

    for elem in res:
        print(elem, end=" ")

        # This code is contributed by ukasp.

Output

2 3 

Time Complexity: O(N*logN)
Auxiliary Space: O(N)