Count the Number of Substrings With Dominant Ones-Java — Algorithm Visualization & Coding Challenge

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Understanding Count the Number of Substrings With Dominant Ones-Java

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Problem Overview

Count the Number of Substrings With Dominant Ones

Difficulty: Medium Topics: Binary strings, substrings, combinatorics
Condition: A substring has dominant ones if:

#ones >= (#zeros)^2

📌 Problem Statement

You are given a binary string s (characters '0' and '1' only).

Return the number of substrings of s that have dominant ones.

A substring has dominant ones if:

the number of ones in the substring is greater than or equal to the square of the number of zeros in that substring.

Formally:

ones(substring) >= zeros(substring)^2

🔍 Examples

Example 1

Input: s = "00011"
Output: 5

Explanation (dominant substrings):

i	j	s[i..j]	#Zeros	#Ones
3	3	`1`	0	1
4	4	`1`	0	1
2	3	`01`	1	1
3	4	`11`	0	2
2	4	`011`	1	2

Example 2

Input: s = "101101"
Output: 16

There are 21 total substrings; 5 do not satisfy the inequality, so 16 do.

Non-dominant examples (for clarity):

i	j	s[i..j]	#Zeros	#Ones
1	1	`0`	1	0
4	4	`0`	1	0
1	4	`0110`	2	2
0	4	`10110`	2	3
1	5	`01101`	2	3

⚖️ Constraints

1 ≤ s.length ≤ 4 × 10⁴
s consists only of characters '0' and '1'.

🧪 I/O Examples

Input:"00011"
Output: 5

Input:  "101101"
Output: 16

Happy coding — may your substrings be dominated by ones!

— Written by Saurabh Patil • B.Tech CSE • Software Developer

Reference Link

https://leetcode.com/problems/count-the-number-of-substrings-with-dominant-ones/description

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