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

  • Last Updated : 24 Mar, 2022

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;
}

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)

 


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