Problem Link :- GFG POTD
Problem statement
Given a binary matrix (containing only 0 and 1) of order NxN. All rows are sorted already, We need to find the row number with the maximum number of 1s. Also, find the number of 1s in that row.
Note:
1. In case of a tie, print the smaller row number.
2. Row number should start from 0th index.
Note:
1. In case of a tie, print the smaller row number.
2. Row number should start from 0th index.
Significance of problem
The significance of the "Find Maximum 1s Row" problem lies in its relevance to binary matrix analysis, presenting a real-world scenario where optimized algorithms for identifying rows with the maximum number of 1s are crucial. This problem extends beyond simple matrix traversal, encapsulating key concepts in binary search and efficient row-wise computation.
Firstly, the code solution employs the binary search technique by utilizing upper_bound to efficiently locate the position of the first zero in each row. This approach minimizes the search space, exemplifying the significance of algorithmic efficiency in large-scale data processing scenarios where minimizing operations is paramount.
Secondly, the tie-breaking rule introduces a layer of complexity, emphasizing the need for careful consideration of edge cases and conditional logic. This mirrors real-world scenarios where tie-breakers can influence decision-making, fostering a holistic understanding of problem-solving strategies.
Moreover, the problem addresses a common scenario in data analysis where identifying rows with the maximum number of 1s is pivotal. Such tasks are prevalent in image processing, network connectivity analysis, and other fields where binary matrices represent relationships or patterns.
Furthermore, the problem reinforces the importance of optimized data traversal in large datasets. The iterative examination of each row and the efficient computation of ones underscore the significance of considering time complexity in algorithmic design, a critical skill for developing scalable and efficient solutions.
In essence, mastering the "Find Maximum 1s Row" problem equips developers with essential skills in binary search, efficient row-wise computation, and tie-breaking strategies. These skills are applicable in diverse computational scenarios, from image analysis to network connectivity evaluation, demonstrating the universal relevance of efficient algorithms in real-world problem-solving.
Firstly, the code solution employs the binary search technique by utilizing upper_bound to efficiently locate the position of the first zero in each row. This approach minimizes the search space, exemplifying the significance of algorithmic efficiency in large-scale data processing scenarios where minimizing operations is paramount.
Secondly, the tie-breaking rule introduces a layer of complexity, emphasizing the need for careful consideration of edge cases and conditional logic. This mirrors real-world scenarios where tie-breakers can influence decision-making, fostering a holistic understanding of problem-solving strategies.
Moreover, the problem addresses a common scenario in data analysis where identifying rows with the maximum number of 1s is pivotal. Such tasks are prevalent in image processing, network connectivity analysis, and other fields where binary matrices represent relationships or patterns.
Furthermore, the problem reinforces the importance of optimized data traversal in large datasets. The iterative examination of each row and the efficient computation of ones underscore the significance of considering time complexity in algorithmic design, a critical skill for developing scalable and efficient solutions.
In essence, mastering the "Find Maximum 1s Row" problem equips developers with essential skills in binary search, efficient row-wise computation, and tie-breaking strategies. These skills are applicable in diverse computational scenarios, from image analysis to network connectivity evaluation, demonstrating the universal relevance of efficient algorithms in real-world problem-solving.
Easiest Explanation
This problem requires you to find the row in a binary matrix that contains the maximum number of 1s. The matrix is of size NxN, which means it has N rows and N columns. All rows are already sorted in non-decreasing order, meaning that the number of 1s in each row will either remain the same or increase as you move from left to right.
To solve this problem, you need to iterate over each row of the matrix and count the number of 1s in each row. Keep track of the row number with the maximum number of 1s and the number of 1s in that row. If there are multiple rows with the same maximum number of 1s, choose the one with the smaller row number.
I hope that explanation helps! If you find any difficulty in solving, feel free to comment with your doubts.
To solve this problem, you need to iterate over each row of the matrix and count the number of 1s in each row. Keep track of the row number with the maximum number of 1s and the number of 1s in that row. If there are multiple rows with the same maximum number of 1s, choose the one with the smaller row number.
I hope that explanation helps! If you find any difficulty in solving, feel free to comment with your doubts.
class Solution { public: vector<int> findMaxRow(vector<vector<int>> mat, int N) { int maxcnt=0,row=0; for(int i=0;i<N;i++){ int zero = upper_bound(mat[i].begin(),mat[i].end(),0)-mat[i].begin(); int ones = N-zero; if(maxcnt<ones){ maxcnt = ones; row = i; } } return {row, maxcnt}; } };
Here's how the function works:
1. The function findMaxRow takes a 2D vector mat representing the binary matrix and an integer N representing its size.
2. It initializes two variables maxcnt and row to 0.
3. It then loops through each row of the matrix using a for loop with index i.
4. For each row, it uses the upper_bound function from the STL library to find the position of the first zero in the row. The upper_bound function returns an iterator to the first element greater than the given value, so subtracting the begin iterator gives the position of the first zero.
5. The number of ones in the row is then calculated as N minus the position of the first zero.
6. If the number of ones in the current row is greater than maxcnt, maxcnt and row are updated with the new values.
7. Finally, the function returns a vector containing the row number and the maximum number of ones found in any row.
2. It initializes two variables maxcnt and row to 0.
3. It then loops through each row of the matrix using a for loop with index i.
4. For each row, it uses the upper_bound function from the STL library to find the position of the first zero in the row. The upper_bound function returns an iterator to the first element greater than the given value, so subtracting the begin iterator gives the position of the first zero.
5. The number of ones in the row is then calculated as N minus the position of the first zero.
6. If the number of ones in the current row is greater than maxcnt, maxcnt and row are updated with the new values.
7. Finally, the function returns a vector containing the row number and the maximum number of ones found in any row.
Learning Outcomes
Solving the "Find Maximum 1s Row" problem imparts a range of valuable learning outcomes, contributing to a well-rounded skill set in algorithmic design, binary matrix analysis, and efficient data traversal. Firstly, learners gain proficiency in binary search techniques by utilizing the upper_bound function, showcasing the practical application of this fundamental algorithmic concept. Understanding how to efficiently locate the position of the first zero in each row highlights the significance of leveraging existing algorithms to streamline computations and reduce time complexity.
Secondly, the tie-breaking rule introduces a nuanced layer of problem-solving, emphasizing the importance of conditional logic and careful consideration of edge cases. This aspect fosters adaptability in algorithmic design, a crucial skill in scenarios where tie-breakers influence decision-making processes.
Moreover, the problem deepens expertise in efficient row-wise computation within matrices. The iterative examination of each row and the computation of ones contribute to a holistic understanding of data traversal in large datasets. This skill is applicable in various domains, including image processing, network connectivity analysis, and database querying, where optimizing operations on binary matrices is essential for computational efficiency.
Furthermore, learners enhance their ability to handle real-world scenarios in data analysis. Identifying rows with the maximum number of 1s aligns with tasks prevalent in diverse fields, where binary matrices represent relationships, patterns, or connectivity. This problem thus bridges theoretical concepts with practical applications, fostering a comprehensive understanding of algorithmic strategies in real-world problem-solving.
Secondly, the tie-breaking rule introduces a nuanced layer of problem-solving, emphasizing the importance of conditional logic and careful consideration of edge cases. This aspect fosters adaptability in algorithmic design, a crucial skill in scenarios where tie-breakers influence decision-making processes.
Moreover, the problem deepens expertise in efficient row-wise computation within matrices. The iterative examination of each row and the computation of ones contribute to a holistic understanding of data traversal in large datasets. This skill is applicable in various domains, including image processing, network connectivity analysis, and database querying, where optimizing operations on binary matrices is essential for computational efficiency.
Furthermore, learners enhance their ability to handle real-world scenarios in data analysis. Identifying rows with the maximum number of 1s aligns with tasks prevalent in diverse fields, where binary matrices represent relationships, patterns, or connectivity. This problem thus bridges theoretical concepts with practical applications, fostering a comprehensive understanding of algorithmic strategies in real-world problem-solving.
Conclusion
In conclusion, tackling the "Find Maximum 1s Row" problem imparts a robust set of skills crucial for algorithmic proficiency and real-world problem-solving. The utilization of binary search techniques, exemplified by the upper_bound function, underscores the significance of optimizing computations in large-scale datasets. The tie-breaking rule introduces learners to nuanced decision-making scenarios, fostering adaptability in algorithmic design—a trait valuable in diverse problem-solving contexts.
Furthermore, the problem deepens expertise in efficient matrix traversal, offering practical insights applicable in domains such as image processing and network connectivity analysis. The identification of rows with the maximum number of 1s aligns with real-world tasks where binary matrices represent meaningful relationships or patterns, emphasizing the universal relevance of the acquired skills.
Mastering this problem encapsulates a synthesis of theoretical concepts and practical applications, providing a foundation for addressing challenges in algorithmic design, binary matrix analysis, and decision-making scenarios. Overall, the problem serves as a pivotal learning experience, cultivating a skill set essential for developing scalable, efficient, and adaptable solutions to computational challenges across diverse domains.
Furthermore, the problem deepens expertise in efficient matrix traversal, offering practical insights applicable in domains such as image processing and network connectivity analysis. The identification of rows with the maximum number of 1s aligns with real-world tasks where binary matrices represent meaningful relationships or patterns, emphasizing the universal relevance of the acquired skills.
Mastering this problem encapsulates a synthesis of theoretical concepts and practical applications, providing a foundation for addressing challenges in algorithmic design, binary matrix analysis, and decision-making scenarios. Overall, the problem serves as a pivotal learning experience, cultivating a skill set essential for developing scalable, efficient, and adaptable solutions to computational challenges across diverse domains.
Stay up-to-date with our latest content by subscribing to our channel! Don't miss out on our next video - make sure to subscribe today.
No comments:
Post a Comment