Count Substrings with equal number of 0s, 1s and 2s

Given a string which consists of only 0s, 1s or 2s, count the number of substrings that have equal number of 0s, 1s and 2s.

Examples:

Input  :  str = “0102010”
Output :  2
Explanation : Substring str[2, 4] = “102” and 
              substring str[4, 6] = “201” has 
              equal number of 0, 1 and 2

Input : str = "102100211"
Output : 5

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

A simple solution is to iterate through all substring of str and checking whether they contain equal 0,1 and 2 or not. Total number of substring of str is O(n²) checking each substring for count takes O(n) times, So total time taken to solve this problem is O(n³) time with brute-force approach.

An efficient solution is to keep track of counts of 0, 1 and 2.

Let zc[i] denotes number of zeros between index 1 and i
    oc[i] denotes number of ones between index 1 and i
    tc[i] denotes number of twos between index 1 and i
for substring str[i, j] to be counted in result we should have :
    zc[i] – zc[j-1] = oc[i] – oc[j-1] = tc[i] - tc[j-1]
we can write above relation as follows :
z[i] – o[i] = z[j-1] – o[j-1]    and
z[i] – t[i] = z[j-1] – t[j-1]

The above relations can be tracked while looping in string, at each index i we’ll calculate this difference pair and we’ll check how many time this difference pair has previously occurred and we’ll add that count to our result, for keeping track of previous difference pair we have used map in below code. Total time complexity of this solution is O(n log n) considering the fact that map operations, like search and insert take O(Log n) time.

C++

// C++ program to find substring with equal 
// number of 0's, 1's and 2's 
#include <bits/stdc++.h> 
using namespace std; 
  
// Method to count number of substring which 
// has equal 0, 1 and 2 
int getSubstringWithEqual012(string str) 
{ 
    int n = str.length(); 
  
    // map to store, how many times a difference 
    // pair has occurred previously 
    map< pair<int, int>, int > mp; 
    mp[make_pair(0, 0)] = 1; 
  
    //  zc (Count of zeroes), oc(Count of 1s) 
    //  and tc(count of twos) 
    //  In starting all counts are zero 
    int zc = 0, oc = 0, tc = 0; 
  
    //  looping into string 
    int res = 0;  // Initialize result 
    for (int i = 0; i < n; ++i) 
    { 
        // increasing the count of current character 
        if (str[i] == '0') zc++; 
        else if (str[i] == '1') oc++; 
        else tc++;  // Assuming that string doesn't contain 
                    // other characters 
  
        // making pair of differences (z[i] - o[i], 
        // z[i] - t[i]) 
        pair<int, int> tmp = make_pair(zc - oc, 
                                       zc - tc); 
  
        // Count of previous occurrences of above pair 
        // indicates that the subarrays forming from 
        // every previous occurrence to this occurrence 
        // is a subarray with equal number of 0's, 1's 
        // and 2's 
        res = res + mp[tmp]; 
  
        // increasing the count of current difference 
        // pair by 1 
        mp[tmp]++; 
    } 
  
    return res; 
} 
  
//  driver code to test above method 
int main() 
{ 
    string str = "0102010"; 
    cout << getSubstringWithEqual012(str) << endl; 
    return 0; 
} 

Python3

# Python3 program to find substring with equal 
# number of 0's, 1's and 2's 
  
# Method to count number of substring which 
# has equal 0, 1 and 2 
def getSubstringWithEqual012(string): 
    n = len(string) 
  
    # map to store, how many times a difference 
    # pair has occurred previously 
    mp = dict() 
    mp[(0, 0)] = 1
  
    # zc (Count of zeroes), oc(Count of 1s) 
    # and tc(count of twos) 
    # In starting all counts are zero 
    zc, oc, tc = 0, 0, 0
  
    # looping into string 
    res = 0 # Initialize result 
    for i in range(n): 
  
        # increasing the count of current character 
        if string[i] == '0': 
            zc += 1
        elif string[i] == '1': 
            oc += 1
        else: 
            tc += 1 # Assuming that string doesn't contain 
                    # other characters 
  
        # making pair of differences (z[i] - o[i], 
        # z[i] - t[i]) 
        tmp = (zc - oc, zc - tc) 
  
        # Count of previous occurrences of above pair 
        # indicates that the subarrays forming from 
        # every previous occurrence to this occurrence 
        # is a subarray with equal number of 0's, 1's 
        # and 2's 
        if tmp not in mp: 
            res += 0
        else: 
            res += mp[tmp] 
  
        # increasing the count of current difference 
        # pair by 1 
        if tmp in mp: 
            mp[tmp] += 1
        else: 
            mp[tmp] = 1
  
    return res 
  
# Driver Code 
if __name__ == "__main__": 
    string = "0102010"
    print(getSubstringWithEqual012(string)) 
  
# This code is conributed by 
# sanjeev2552 

Output:

This article is contributed by Utkarsh Trivedi. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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My Personal Notes

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

C++

Python3

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