1.
Introduction
1.1.
Problem Statement
1.2.
Sample Examples
2.
Approach
2.1.
Algorithm
2.2.
Implementation in C++
2.2.1.
Time Complexity
2.2.2.
Space complexity
3.
3.1.
Why are heaps used for implementing Priority Queue?
3.2.
How does a deque represent memory?
3.3.
What is a void pointer in C++?
4.
Conclusion
Last Updated: Mar 27, 2024
Medium

# Given 1â€™s, 2â€™s, 3â€™s â€¦â€¦kâ€™s Print them in ZigZag way

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Anubhav Sinha
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12 Jun, 2024 @ 01:30 PM

## Introduction

This blog covers a matrix problem. Matrices are among the most important and often asked data structures in programming contests and technical interviews. There are various standard matrix problems and techniques. This blog tackles a coding task that involves printing a given count of positive integers in a zig-zag pattern.

Must Read, Array Implementation of Queue and Rabin Karp Algorithm

### Problem Statement

Ninja is given a number of rows and columns and the number of 1's, 2's, 3's,..... k's that are to be printed. He is challenged with printing them in a zig-zag pattern. It is made sure that n*m (number of rows*columns) equals the number of 1's + 2's + 3's +..... + k's. Can you help him in completing this task?

### Sample Examples

Input - 1

``````2 3
1 2 1 2``````

Output

Explanation

``````Here,
number of 1's are 1
number of 2's are 2
number of 3's are 1
number of 4's are 2
These are printed in a 2*3 matrix in a zig-zag pattern.``````

Input - 2

``````4 5
1 2 6 3 2 3 3``````

Output

Explanation

``````Here,
number of 1's are 1
number of 2's are 2
number of 3's are 6
number of 4's are 3
number of 5's are 2
number of 6's are 3
number of 7's are 3
These are printed in a 4*5 matrix in a zig-zag pattern.``````

## Approach

The approach to the above problem is quite intuitive and straightforward. We will go through all the elements of the number array and insert all the numbers from the array of the i-th index into a two-dimensional array until it reaches zero. In the end, we will print out this newly-formed array. The resultant 2-d array will be in zig-zag pattern.

### Algorithm

1. Declare a two-dimensional array to store elements in a zig-zag pattern.

2. Start traversing all of the elements of the number array.

3. While traversing, insert all of the integers from the i-th index's array into the two-dimensional array until it reaches zero.

4. Return this two- dimensional array.

### Implementation in C++

``````#include <bits/stdc++.h>
using namespace std;

// function for printing a given number of 1's,
// 2's, 3's ....k's in a zig-zag pattern.

void printPattern(int row, int cols, int nums[])
{
int k = 0;
// declaring a two-dimensional array to store numbers in a zig-zag pattern.
int mat[row][cols];

for (int i = 0; i < row; i++)
{
// for even row
if (i % 2 == 0)
{
for (int j = 0; j < cols and nums[k] > 0; j++)
{
// storing the element.
mat[i][j] = k + 1;

// decrementing element at the kth index.
nums[k]--;

// if array contains zero then increments index
if (nums[k] == 0)
k++;
}
}

// for odd row.
else
{
for (int j = cols - 1; j >= 0 and nums[k] > 0; j--)
{
// storing element.
mat[i][j] = k + 1;

// decrementing element at the kth index.
nums[k]--;

// if array contains zero then increments index
if (nums[k] == 0)
k++;
}
}
}

// printing the array.
for (int i = 0; i < row; i++)
{
for (int j = 0; j < cols; j++)
cout << mat[i][j] << " ";

cout << endl;
}
}

// Driver code
int main()
{
int row = 4;
int cols = 5;
int nums[] = {1, 2, 6, 3, 2, 3, 3};
cout << "Number of rows and columns respectively are: " << endl
<< row << " " << cols << endl;
cout << "The given number array is: " << endl;
for (size_t i = 0; i < 7; i++)
{
cout << nums[i] << " ";
}

cout << endl;
cout << "The desired two-dimensional pattern is: " << endl;
printPattern(row, cols, nums);
return 0;
}``````

Output

#### Time Complexity

The time complexity for the given approach is O(m*n) as we traverse the entire matrix to fill up the elements in the n*m matrix and print them in a zig-zag pattern.

#### Space complexity

The Space Complexity of the above approach turns out to be O(n*m) as we require a matrix of size n*m to store the zig-zag pattern.

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### Why are heaps used for implementing Priority Queue?

Heaps are ideal for building a priority queue because of the biggest and smallest element at the root of the tree for a max-heap and a min-heap, respectively.

### How does a deque represent memory?

A deque is implemented in computer memory using either a circular array or a circular doubly linked list.

### What is a void pointer in C++?

In C, a void pointer is a pointer that has no data type associated with it. It denotes a data location in the storage.

## Conclusion

This article extensively discussed the problem of printing a given number of 1â€™s,2â€™s,3â€™s â€¦.kâ€™s in a zig-zag pattern in a 2-d matrix and its time and space complexities.

We hope this blog has helped you enhance your knowledge regarding matrices. After reading about the matrices, are you not feeling excited to read/explore more articles on this topic? Don't worry, Coding Ninjas has you covered. To learn, see Greedy AlgorithmsPair SumSum or ProductSet Matrix zeros and Maximum Subarray Sum.

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