How do I find total number of substrings with 1's more than 0's

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Given and string we need to find out the total number of substrings in which 1's are greater than 0's.

I approached this problem using Dynamic programming but I was not able to come up with a solution, I am successful in writing a naive-logic but I was not able to optimize the code (i.e time limit is exceeding)

Any help in optimizing or suggestions for a new approach will be help full. The time complexity of below code is O(n^3) Any solutions to reduce the time-complexity will be helpfull.

Thank in advance.

Note: The input is only series of 1's and 0's

Note:A substring is a contiguous sequence of characters within a string. For more information about substrings visit Wikipedia

What I have tried:

C++

#include<iostream>
#include<string>
#include<algorithm>

using namespace std;

int main(){
    int tc =0; //total count
    string st; //original string
    getline(cin,st);
    int lent = st.size(); //size of string
    for(int i =0;i<lent;i++){ //loop to generate all possible substrings
        int j = lent-1;
        while(j>=i){
            
            string st1(st.begin()+i,st.end()-j+i); // A substring
            int c1 = count(st1.begin(),st1.end(),'1'); // count of 1's in substring
            if(c1 > st1.size()-c1) tc++; // Condition to check if 1's are more
            j--;
        }
    }
    cout << tc; // Print total substrings
}

Posted 11-Jul-21 22:33pm

pendela neelesh

Updated 12-Jul-21 2:51am

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OriginalGriff · Answer 1 · 2021-07-11T22:37:00

While we are more than willing to help those that are stuck, that doesn't mean that we are here to do it all for you! We can't do all the work, you are either getting paid for this, or it's part of your grades and it wouldn't be at all fair for us to do it all for you. And "code challenges" count as homework!

So we need you to do the work, and we will help you when you get stuck. That doesn't mean we will give you a step by step solution you can hand in!
Start by explaining where you are at the moment, and what the next step in the process is. Then tell us what you have tried to get that next step working, and what happened when you did.

If you are having problems getting started at all, then this may help: How to Write Code to Solve a Problem, A Beginner's Guide[^]

Patrice T · Answer 2 · 2021-07-12T02:51:00

Quote:
I was not able to optimize the code (i.e time limit is exceeding)

With challenge sites, simple minded code is never the solution, you need to be agile in your head. And you need to avoid language features that make your life easier because they cost.

In the inner loop, you create a new string just to count the number of '1', this string is the difference between O(n)=N^3 and O(n)=N^2.
In the inner loop, what is the difference between 2 consecutive strings ? a single char !
Knowing number of '1' and '0' in previous string, do you need to recount everything or just update the number of '1' and '0' for this single char ?
A clever answer should lead you to an O(n)=N^2 solution.

How do I find total number of substrings with 1's more than 0's

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