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Welcome to the daily solving of our PROBLEM OF THE DAY with Saurabh Bansal We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Arrays but also build up problem-solving skills. Given a boolean 2D array, consisting of only 1's and 0's, where each row is sorted.&nbsp;Return the 0-based index of the first row that has the most number of 1s. If no such row exists, return -1.Examples:Input: arr[][] = [[0, 1, 1, 1], &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[0, 0, 1, 1], &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[1, 1, 1, 1], &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[0, 0, 0, 0]]
 Output: 2
 Explanation: Row 2 contains 4 1's (0-based indexing).Give the problem a try before going through the video. All the best!!! Problem Link: <a href="https://practice.geeksforgeeks.org/problems-preview/row-with-max-1s0023/1">https://practice.geeksforgeeks.org/problems-preview/row-with-max-1s0023/1</a>

Row with maximum number of 1s

Input: str = “PAYPALISHIRING”, N = 3 Output: PAHNAPLSIIGYIRInput: str = “ABCDEFGH”, N = 2 Output: ACEGBDFH Explanation: The input string can be written in Zig-Zag fashion in 2 rows as follows: A &nbsp; C &nbsp; &nbsp;E &nbsp; G &nbsp; &nbsp; &nbsp; B &nbsp; D &nbsp; F &nbsp; H Hence, upon reading the above pattern row-wise, the output string is “ACEGBDFH”Print Concatenation of Zig-Zag String in ‘n’ Rows : <a href="https://www.geeksforgeeks.org/concatenation-of-zig-zag-string-in-n-rows/">https://www.geeksforgeeks.org/concatenation-of-zig-zag-string-in-n-rows/</a>

Print Concatenation of Zig-Zag String in ‘n’ Rows

Given a binary matrix, print all unique rows of the given matrix.Example:Input: &nbsp; &nbsp; &nbsp; &nbsp;{0, 1, 0, 0, 1} &nbsp; &nbsp; &nbsp; &nbsp;{1, 0, 1, 1, 0} &nbsp; &nbsp; &nbsp; &nbsp;{0, 1, 0, 0, 1} &nbsp; &nbsp; &nbsp; &nbsp;{1, 1, 1, 0, 0} Output: &nbsp; &nbsp;0 1 0 0 1&nbsp; &nbsp; &nbsp;1 0 1 1 0&nbsp; &nbsp; &nbsp;1 1 1 0 0Print unique rows in a given boolean matrix: <a href="https://www.geeksforgeeks.org/print-unique-rows/">https://www.geeksforgeeks.org/print-unique-rows/</a>

Print unique rows in a given boolean matrix

In this video, we will write a C++ program to multiply two matrices.Multiplication is a fundamental operation in mathematics and computer science. In programming, multiplication is performed using two numbers or variables called operands. Operand means something that is operated upon. An operand can be either a variable or a constant, and a matrix represents the collection of numbers arranged in an order of rows and columns. It is necessary to enclose the elements of a matrix in parentheses or brackets.For Example: Input: mat1[m][n] = { {1, 1}, {2, 2} } mat2[p][q] = { {1, 1}, {2, 2} } Output: result[m][p] = { {3, 3}, {6, 6} }Input mat1[m][n]= { {1 2 &nbsp;3},{ 3 &nbsp;2 &nbsp;1},{ 1 2 &nbsp;3}} mat2[p][q]= { {4 5 6},{ 6 5 4},{4 6 5}}Output: {28 &nbsp;33 &nbsp;29 28 &nbsp;31 &nbsp;31 28 &nbsp;33 &nbsp;29} Multiplication of two Matrices: The number of columns in Matrix-1 must be equal to the number of rows in Matrix-2. The output of multiplication of Matrix-1 and Matrix-2 results with equal to the number of rows of Matrix-1 and the number of columns of Matrix-2 i.e. rslt[R1][C2]Algorithm: Step 1: First declare &nbsp;three matrices m1[3][3], m2[3][3], m3[3][3] and variables sum, i,j,k. Step 2: Now Enter the first and second matrices elements. Step 3: Run for loop from 0 to result. length as i: Step 4: Nest run another for loop from 0 to result[0].length as j: Step 5: Nest another loop from 0 to m1[0].length in k: Step 6: Sum (m1[I][K] * m2[K][J]) Step 7: Store the sum into the resultant matrix as m3[i][j]=sum. Step 8: End loop Step 9: Print the resultant matrix.C++ program to multiply two matrices: <a href="https://www.geeksforgeeks.org/cpp-program-to-multiply-two-matrices/">https://www.geeksforgeeks.org/cpp-program-to-multiply-two-matrices/</a>

C++ Program on Multiplication of Two Matrices

Welcome to the daily solving of our PROBLEM OF THE DAY with Kunal Jain We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Matrix but also build up problem-solving skills. Given a square&nbsp;mat[][]. The task is to rotate it by 90 degrees in clockwise direction without using any extra space.Examples:Input: mat[][] = [[1 2 3], [4 5 6], [7 8 9]]
Output:
7 4 1&nbsp; 8 5 2 9 6 3 &nbsp;Give the problem a try before going through the video. All the best!!! Problem Link: <a href="https://www.geeksforgeeks.org/problems/rotate-by-90-degree0356/1">https://www.geeksforgeeks.org/problems/rotate-by-90-degree0356/1</a>

PROBLEM OF THE DAY : 05/11/2024 | Rotate by 90 degree

Welcome to the daily solving of our PROBLEM OF THE DAY with Saurabh Bansal We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Linked List but also build up problem-solving skills.Given a Matrix mat of n*n size. Your task is constructing a 2D linked list representation of the given matrix.Input: mat = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
Output:&nbsp; &nbsp;Give the problem a try before going through the video. All the best!!! Problem Link: <a href="https://practice.geeksforgeeks.org/problems/linked-list-matrix/1">https://practice.geeksforgeeks.org/problems/linked-list-matrix/1</a>

PROBLEM OF THE DAY : 09/10/2024 | Linked List Matrix

<h2>Matrix Chain Multiplication (Dynamic Programming)</h2>Matrix Chain Multiplication is a classic problem in dynamic programming that involves finding the most efficient way to multiply a given sequence of matrices. The goal is to determine the order in which to multiply the matrices so that the number of scalar multiplications is minimized.<h3>Problem Overview</h3>Given a sequence of matrices, the task is to find the minimum number of multiplications needed to multiply the matrices together. The matrices are represented as dimensions, where each matrix is of dimension p[i] x p[i+1] for i = 1 to n.<h3>Example Problem Statement</h3>If the matrices are:<ul><li>A1: 10 x 30</li><li>A2: 30 x 5</li><li>A3: 5 x 60</li></ul>You need to determine the order of multiplying these matrices such that the total number of scalar multiplications is minimized.<h3>Key Concepts Covered</h3><ol><li>Dynamic Programming Approach: Breaking down the problem into overlapping subproblems and solving them using a bottom-up approach.</li><li>Optimal Substructure: The problem can be broken down into subproblems that can be solved independently, and their solutions can be combined to get the overall optimal solution.</li><li>Matrix Multiplication Properties: Understanding that matrix multiplication is associative (but not commutative) and that the order of multiplication affects the number of operations.</li></ol><h3>Steps to Solve the Matrix Chain Multiplication Problem</h3>Identify the Subproblems:<ul><li>Let m[i][j] represent the minimum number of scalar multiplications needed to multiply matrices from Ai to Aj.</li><li>The task is to compute m[1][n] where n is the number of matrices.</li></ul>Recursive Formula:<ul><li>For each subproblem m[i][j], you consider splitting the product at every possible position k, where i &lt;= k &lt; j.</li><li>The recursive formula is:</li><li>Here, p[i-1]*p[k]*p[j] represents the cost of multiplying two matrices resulting from the splits.</li></ul>Dynamic Programming Table:<ul><li>Use a 2D array m[][] to store the results of subproblems.</li><li>Build the table in a bottom-up manner. The diagonal elements represent the cost of multiplying a single matrix, which is 0.</li></ul>Implementation:<ul><li>Iterate over increasing lengths of matrix chains and fill in the DP table accordingly.</li><li>The final answer will be stored in m[1][n-1], where n is the number of matrices.</li></ul><h3>Example Solution</h3>For matrices of dimensions 10 x 30, 30 x 5, and 5 x 60, the optimal order of multiplication is:<ul><li>First, multiply the second and third matrices, and then multiply the result with the first matrix.</li></ul>The number of multiplications is minimized using the above dynamic programming approach.<h3>Applications</h3><ul><li>Computational Mathematics: Optimizing the order of matrix operations is crucial in various algorithms where matrix multiplication is involved, such as in graphics transformations and scientific computations.</li><li>Compiler Design: Matrix chain multiplication is used in compiler optimization, where the order of operations can be optimized for performance.</li></ul><h3>Challenges</h3><ul><li>Understanding the Problem: Grasping the importance of matrix dimensions and how the order affects the computational cost is key.</li><li>Complexity of Recurrence: Breaking down the recurrence relation and implementing it in a bottom-up manner can be challenging for beginners.</li></ul><h3>Conclusion</h3>Matrix Chain Multiplication is a foundational problem in dynamic programming that introduces key concepts like optimal substructure and overlapping subproblems. It’s an excellent problem to practice and understand the principles of dynamic programming and algorithm optimization.For a detailed step-by-step guide, check out the full article: <a href="https://www.geeksforgeeks.org/matrix-chain-multiplication-dp-8/">https://www.geeksforgeeks.org/matrix-chain-multiplication-dp-8/</a>.

Matrix Chain Multiplication | DSA

Welcome to the daily solving of our PROBLEM OF THE DAY with Jay Dalsaniya We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Matrix but also build up problem-solving skills. You are given a rectangular matrix, and your task is to return an array while traversing&nbsp;the matrix in spiral form.Examples:Input: matrix[][] = [[1, 2, 3, 4],
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [5, 6, 7, 8],
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [9, 10, 11, 12],
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [13, 14, 15,16]]
 Output: [1, 2, 3, 4, 8, 12, 16, 15, 14, 13, 9, 5, 6, 7, 11, 10] &nbsp;Give the problem a try before going through the video. All the best!!! Problem Link:<a href="https://practice.geeksforgeeks.org/problems-preview/spirally-traversing-a-matrix-1587115621/1"> https://practice.geeksforgeeks.org/problems/spirally-traversing-a-matrix-1587115621/1</a>

PROBLEM OF THE DAY : 01/08/2024 | Spirally Traversing a Matrix

In this video, we will discuss how the matrix will turn out when we rotate it clockwise.For example - For a matrix Mat=[[1,2,3],[4,5,6],[7,8,9]], if we rotate it clockwise once, the output will be -4 1 2 7 5 3 8 9 6Checkout, the video for the complete explanation with implementation.Practice Problem: <a href="https://practice.geeksforgeeks.org/problems/rotate-matrix-elements-clockwise2336/1">https://practice.geeksforgeeks.org/problems/rotate-matrix-elements-clockwise2336/1</a> Article: <a href="https://www.geeksforgeeks.org/rotate-matrix-elements/">https://www.geeksforgeeks.org/rotate-matrix-elements/</a> SDE Sheet: <a href="https://www.geeksforgeeks.org/sde-sheet-a-complete-guide-for-sde-preparation/">https://www.geeksforgeeks.org/sde-sheet-a-complete-guide-for-sde-preparation/</a>

Rotate a matrix

This video is part of the Heap section under GFG SDE Sheet. Given a&nbsp;N&nbsp;x N&nbsp;matrix, where every row and column is sorted in non-decreasing order. Find the kth smallest element in the matrix.Example 1:Input:
N = 4
mat[][] = &nbsp; &nbsp; {{16, 28, 60, 64},
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; {22, 41, 63, 91},
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; {27, 50, 87, 93},
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; {36, 78, 87, 94 }}
K = 3
Output: 27
Explanation: 27 is the 3rd smallest element. Try it out before watching the implementation of the problem in the video. We recommend watching the video, even if you can solve the problem. You may discover something new. All the best!!!Do check out:- Problem: <a href="https://www.geeksforgeeks.org/problems/kth-element-in-matrix/1">https://www.geeksforgeeks.org/problems/kth-element-in-matrix/1</a> SDE Sheet Link: <a href="https://www.geeksforgeeks.org/sde-sheet-a-complete-guide-for-sde-preparation/">https://www.geeksforgeeks.org/sde-sheet-a-complete-guide-for-sde-preparation/</a> Article Link:<a href=" https://www.geeksforgeeks.org/kth-smallest-element-in-a-row-wise-and-column-wise-sorted-2d-array/"> https://www.geeksforgeeks.org/kth-smallest-element-in-a-row-wise-and-column-wise-sorted-2d-array/</a>

SDE Sheet - Kth Smallest Element in a Row-Column Wise Sorted Matrix

Given an n x n matrix and a number x, find the position of x in the matrix if it is present in it. Otherwise, print “Not Found”. In the given matrix, every row and column is sorted in increasing order. The designed algorithm should have linear time complexity.Example:Input: mat[4][4] = { {10, 20, 30, 40}, &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 15, 25, 35, 45}, &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; {27, 29, 37, 48}, &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; {32, 33, 39, 50}} &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; x = 29 Output: Found at (2, 1) Explanation: Element at (2,1) is 29Search in a row wise and column wise sorted matrix : <a href="https://www.geeksforgeeks.org/search-in-row-wise-and-column-wise-sorted-matrix/">https://www.geeksforgeeks.org/search-in-row-wise-and-column-wise-sorted-matrix/</a>

Search in a row wise and column wise sorted matrix

This video is part of the Trie section under GFG SDE Sheet. Given a binary matrix your task is to find all unique rows of the given matrix in the order of their appearance in the matrix.Example 1:Input:
row = 3, col = 4 
M[][] = {{1 1 0 1},{1 0 0 1},{1 1 0 1}}
 Output: $1 1 0 1 $1 0 0 1 $
 Explanation: Above the matrix of size 3x4
looks like
1 1 0 1
1 0 0 1
1 1 0 1
The two unique rows are R1: {1 1 0 1} and R2: {1 0 0 1}.&nbsp; As R1 first appeared at row-0 and R2 appeared at row-1, in the resulting list, R1 is kept before R2. Try it out before watching the implementation of the problem in the video. We recommend watching the video, even if you can solve the problem. You may discover something new. All the best!!!Do check out:- Problem: <a href="https://www.geeksforgeeks.org/problems/unique-rows-in-boolean-matrix/1">https://www.geeksforgeeks.org/problems/unique-rows-in-boolean-matrix/1</a> SDE Sheet Link: <a href="https://www.geeksforgeeks.org/sde-sheet-a-complete-guide-for-sde-preparation/">https://www.geeksforgeeks.org/sde-sheet-a-complete-guide-for-sde-preparation/</a> Article Link: <a href="https://www.geeksforgeeks.org/print-unique-rows/">https://www.geeksforgeeks.org/print-unique-rows/</a>

SDE Sheet - Print unique rows in a given Binary matrix