What is the time complexity of First Completely Painted Row or Column?

The optimal solution has a time complexity of O(m*n + len(arr)).

What is the space complexity of First Completely Painted Row or Column?

The space complexity is O(m*n).

What data structures are used to solve First Completely Painted Row or Column?

This problem uses Array, Hash Table, Matrix. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving First Completely Painted Row or Column?

Insight 1: The core idea is to efficiently track which rows and columns have been fully painted after each element of `arr` is processed. Insight 2: Using a hash map (or array as hashmap) to store the position (row and column indices) of each number in `mat` allows for O(1) lookups, significantly improving the efficiency of finding the row and column index for a number in `arr`.

Which companies ask LeetCode 2661. First Completely Painted Row or Column in interviews?

This problem is frequently asked at Citadel.

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First Completely Painted Row or Column - LeetCode 2661 Solution

First Completely Painted Row or Column - Complete Solution Guide

First Completely Painted Row or Column is LeetCode problem 2661, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

You are given a 0-indexed integer array arr , and an m x n integer matrix mat . arr and mat both contain all the integers in the range [1, m * n] . Go through each index i in arr starting from index 0 and paint the cell in mat containing the integer arr[i] . Return the smallest index i at which either a row or a column will be completely painted in mat . Example 1: Input: arr = [1,3,4,2], mat = [[1,4],[2,3]] Output: 2 Explanation: The moves are shown in order, and both the first row and second c

Detailed Explanation

The problem presents a scenario where you're given an integer array `arr` and an `m x n` matrix `mat`, both containing the same unique integers from 1 to `m*n`. The goal is to find the smallest index `i` in `arr` where, after 'painting' the corresponding cells in `mat` (simulating visiting the numbers in `arr`), either a full row or a full column in `mat` has been completely painted. Painting a cell means virtually marking the cell in `mat` that corresponds to the current element in `arr`. The output is the smallest index `i` where a row or column is completely painted.

Solution Approach

The solution efficiently determines the first index where either a row or a column in the matrix is fully painted. It employs a position map to store the row and column indices for each number in the matrix, enabling quick lookup during the iteration through the `arr` array. Counters for each row and column track the number of painted cells, and the solution returns the index as soon as any row or column becomes completely painted.

Step-by-Step Algorithm

Step 1: Create a position map (`pos_map` in Python, `pos` array in Java/C/C++) that stores the row and column indices of each number in the matrix `mat`. This allows for O(1) lookup of the position of any number.
Step 2: Initialize `row_counts` and `col_counts` arrays to store the number of painted cells in each row and column, respectively. Initialize all counts to zero.
Step 3: Iterate through the array `arr`. For each number `num` at index `i`:
Step 4: Look up the row `r` and column `c` indices of `num` using the `pos_map`.
Step 5: Increment the count for row `r` and column `c` in the `row_counts` and `col_counts` arrays, respectively.
Step 6: Check if `row_counts[r]` equals the number of columns `n`, or if `col_counts[c]` equals the number of rows `m`. If either condition is true, it means either row `r` or column `c` is completely painted. Return the current index `i`.
Step 7: If the loop completes without finding a fully painted row or column, return -1 (although the problem constraints guarantee a solution). In C, remember to free the allocated memory before returning.

Key Insights

Insight 1: The core idea is to efficiently track which rows and columns have been fully painted after each element of `arr` is processed.
Insight 2: Using a hash map (or array as hashmap) to store the position (row and column indices) of each number in `mat` allows for O(1) lookups, significantly improving the efficiency of finding the row and column index for a number in `arr`.
Insight 3: Maintaining separate counters for each row and column enables quick determination of whether a row or column has been fully painted.

Complexity Analysis

Time Complexity: O(m*n + len(arr))

Space Complexity: O(m*n)

Topics

This problem involves: Array, Hash Table, Matrix.

Companies

Asked at: Citadel.

First Completely Painted Row or Column | LeetCode 2661

Medium

Array Hash Table Matrix

Time: O(m*n + len(arr))Space: O(m*n)

Solution Code

Available in:

class Solution {
    public int firstCompleteIndex(int[] arr, int[][] mat) {
        int m = mat.length;
        int n = mat[0].length;

        Integer[] pos = new Integer[m * n + 1];
        for (int r = 0; r < m; r++) {
            for (int c = 0; c < n; c++) {
                pos[mat[r][c]] = r * n + c;
            }
        }

        int[] row_count = new int[m];
        int[] col_count = new int[n];

        for (int i = 0; i < arr.length; i++) {
            int val = arr[i];
            int r = pos[val] / n;
            int c = pos[val] % n;
            
            row_count[r] += 1;
            col_count[c] += 1;
            
            if (row_count[r] == n || col_count[c] == m) {
                return i;
            }
        }
        return -1;
    }
}

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Problem Info

Description

Problem 2661: First Completely Painted Row or Column - Detailed explanation and solution approaches.

Topics

Array Hash Table Matrix

Companies

Citadel

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:2661

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

7 steps

1
Step 1: Create a position map (`pos_map` in Python, `pos` array in Java/C/C++) that stores the row and column indices of each number in the matrix `mat`. This allows for O(1) lookup of the position of any number.
2
Step 2: Initialize `row_counts` and `col_counts` arrays to store the number of painted cells in each row and column, respectively. Initialize all counts to zero.
3
Step 3: Iterate through the array `arr`. For each number `num` at index `i`:
4
Step 4: Look up the row `r` and column `c` indices of `num` using the `pos_map`.
5
Step 5: Increment the count for row `r` and column `c` in the `row_counts` and `col_counts` arrays, respectively.
6
Step 6: Check if `row_counts[r]` equals the number of columns `n`, or if `col_counts[c]` equals the number of rows `m`. If either condition is true, it means either row `r` or column `c` is completely painted. Return the current index `i`.
7
Step 7: If the loop completes without finding a fully painted row or column, return -1 (although the problem constraints guarantee a solution). In C, remember to free the allocated memory before returning.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(m*n + len(arr))

💾

Space Complexity

O(m*n)

📝

Why?

The time complexity is determined by the construction of the `pos_map` and the single loop through `arr`. The space complexity arises mainly from storing the positions of the elements in the matrix within `pos_map`.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Without a Position Map

Instead of using a position map, we could search the `mat` matrix for each element in `arr` to find its row and column. This involves iterating through the matrix for each element of `arr`.

Time: O(len(arr) * m * n)Space: O(m + n)

Trade-offs: This approach avoids the initial cost of creating the position map but results in a significantly slower overall time complexity, especially for large matrices. The main solution is preferred.

✨

Key Insights

1Insight 1: The core idea is to efficiently track which rows and columns have been fully painted after each element of `arr` is processed.
2Insight 2: Using a hash map (or array as hashmap) to store the position (row and column indices) of each number in `mat` allows for O(1) lookups, significantly improving the efficiency of finding the row and column index for a number in `arr`.
3Insight 3: Maintaining separate counters for each row and column enables quick determination of whether a row or column has been fully painted.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Hash Table

A data structure that maps keys to values for quick lookup. Like a dictionary!

Edge Cases

Edge case 1: A very small matrix (e.g., 1x1 or 2x2). The solution handles this correctly because the loops and counters will still work as intended.
Edge case 2: The `arr` array is empty (although this violates problem constraints). The code would still execute but likely return -1 which is an exceptional case not covered by the prompt.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not creating a position map, which results in an O(m*n) search for each element in `arr`, leading to a much slower algorithm.

✗Common mistake 2: Forgetting to increment the row and column counts after finding the position of an element in `arr`.

✗Common mistake 3: Not handling edge cases correctly, such as small matrices.

✗Common mistake 4: In C, failing to allocate memory dynamically or failing to free dynamically allocated memory which can cause memory leaks or crashes.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Resource allocation in a grid-based system. Imagine allocating servers in a data center. The `mat` represents the data center grid, and `arr` represents the order in which servers become available. The algorithm finds when a full row or column of servers becomes available for a specific task.

🏦Real-world scenario 2: Game development: Consider a grid-based game board. `mat` is the game board, and `arr` represents the order in which tiles are filled. The algorithm determines when a row or column is completed, triggering specific in-game events or bonuses.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Medium problems are the bread and butter of technical interviews. Practice explaining your approach before coding.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: October 20, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 14

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 7

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJun 30

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

How do I choose between a hash map and a hash set?

Use a hash set when you only need to track presence/absence of elements (like detecting duplicates). Use a hash map when you need to associate values with keys (like counting frequencies or storing indices). Hash sets use less memory since they only store keys.

How much time should I spend on a medium problem in interviews?

In a 45-minute interview, aim for: 5-10 minutes understanding and clarifying, 5-10 minutes discussing approach, 20-25 minutes coding, and 5-10 minutes testing. If stuck after 15 minutes of thinking, verbalize your thought process and ask for hints.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "First Completely Painted Row or Column"?

For this medium-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether hash table techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

🤖 Need help with this problem?