JavaScript Coding Test Course, Finding the Sum of Intervals 3

October 5, 2023

1. Problem Introduction

The Range Sum Query 3 problem is a type of problem that you often encounter in algorithm problem-solving processes, especially demonstrating efficiency when calculating sums of large datasets.
This problem deals with methods to quickly calculate the sum of a specific interval through queries.
Computing the range sum algorithmically is particularly useful for database-related problems.
Today, we will analyze various techniques to solve this problem and try to solve it using JavaScript.

2. Problem Description

Given an array A with length N, when a positive integer query M is provided,
each query consists of two integers i and j, and we need to find the value of
A[i] + A[i+1] + ... + A[j]. There can be up to 100,000 queries, and each number in A can be up to 1,000,000.
In other words, we need to efficiently calculate the sums of ranges based on the given array A and the queries.

3. Problem Solving Strategy

To solve the range sum problem, we will use two main methods.
– First, the basic method which uses a double loop to calculate the sum for each query.
– Second, a method that pre-computes the range sums and quickly derives results during the queries.
In particular, the second method allows us to obtain query results in O(1) time through O(N) preprocessing.
Thus, this will help us solve the problem more efficiently.

4. Basic Method (O(N) x M)

This method is very intuitive, but its time complexity is O(N * M).
The implementation of this approach is as follows.


function simpleRangeSum(A, queries) {
    const results = [];
    for (let [i, j] of queries) {
        let sum = 0;
        for (let k = i; k <= j; k++) {
            sum += A[k];
        }
        results.push(sum);
    }
    return results;
}
        

This code calculates the sum at the respective index for each query by iterating through it. However, under the constraints of the problem,
this method is inefficient. Therefore, we need to move on to a more efficient approach.

5. Efficient Method (O(N) + O(1) per Query)

In exploring the efficient method, we start by creating an array to store the range sums of the original array.
First, the process of creating the range sum array is needed. Once the range sum array is created,
the result of each query can be obtained simply by taking the difference of two cumulative sums.


function prefixSum(A) {
    const prefix = new Array(A.length + 1).fill(0);
    for (let i = 0; i < A.length; i++) {
        prefix[i + 1] = prefix[i] + A[i];
    }
    return prefix;
}

function rangeSum(A, queries) {
    const prefix = prefixSum(A);
    const results = [];
    for (let [i, j] of queries) {
        results.push(prefix[j + 1] - prefix[i]);
    }
    return results;
}
        

In the above implementation, the prefixSum function calculates the cumulative sums for the entire dataset and stores them in the prefix array.
After that, each query can derive the range sum in O(1) time. This method is
very efficient as it can process queries in O(N) + O(1).

6. Code Explanation

Analyzing the code above, we first create an empty array with one more than the length of the array in the prefixSum function,
and compute the cumulative sums for each index of this array. Through this cumulative sum array,
the rangeSum function quickly calculates the range sum by taking the starting index i and ending index j from the given queries.

Now, when considering the large number of queries, we need to be mindful of the time complexity,
as the solution above is very efficient in this regard.
The unnecessary loops during the processing of each query were key,
and deriving the results through this process improved performance.

7. Example Test

Let’s test the code above with an example.
The array A = [1, 2, 3, 4, 5] and the queries are
[[0, 2], [1, 3], [2, 4]].


const A = [1, 2, 3, 4, 5];
const queries = [[0, 2], [1, 3], [2, 4]];
const results = rangeSum(A, queries);
console.log(results); // [6, 9, 12]
        

The results of the above test correctly yield the cumulative sums for each query. By testing, we can confirm that our code is functioning accurately,
which is an essential process for ensuring correctness.

8. Conclusion

The Range Sum Query 3 problem is an excellent example that demonstrates a variety of algorithm problem-solving skills.
Solving the range sum problem through preprocessing is commonly used in everyday data processing tasks.
Based on what we learned today, I hope you have developed the ability to solve similar problems and gained insight on how to structure algorithms when faced with problems.
I encourage you to continue building your problem-solving experience through JavaScript.

JavaScript Coding Test Course, Sorting Numbers 2

JavaScript Coding Test Course – Sorting Numbers 2

In this course, we will deeply analyze the algorithm problem called ‘Sorting Numbers 2’ and explain the step-by-step process to solve it. We will look into how to solve the problem using JavaScript along with its definition.

Problem Definition

The problem is as follows. Given a set of numbers, write a program to sort these numbers in ascending order. Please note that the number of inputs can be up to 10,000. Below, we will provide the exact input and output formats along with examples.

Input

The first line contains the number of integers N (1 ≤ N ≤ 10,000). Then, N lines follow, each containing a single integer. This integer will be between -1,000,000 and 1,000,000, inclusive.

Output

The integers received as input must be printed in ascending order, one per line.

Example Input

5
5
3
2
1
4

Example Output

1
2
3
4
5

Problem Approach

The key to this problem is sorting the N given integers. There are many methods available, but it is important to choose an efficient sorting algorithm. In JavaScript, you can typically use the Array.sort() method.

The Array.sort() method performs string sorting by default, so a comparison function is necessary to sort actual numbers. Care is needed when using the built-in sort() method in JavaScript, especially considering time complexity when processing a large amount of numbers.

Solution Method

Let’s step through the process of solving the problem.

  1. Prepare the input data.

    First, you need to declare variables necessary for reading the input data presented by the problem and store the data in an array. At this time, we will use JavaScript’s Array to store the numbers dynamically.

  2. Sort the input numbers.

    Use the Array.sort() method to sort the input array. Define a comparison function to allow for number comparison.

  3. Output the sorted numbers.

    Use a function or method to print the values of the sorted array, outputting one number per line.

JavaScript Code Implementation

Based on the solution methods mentioned above, the JavaScript code can be implemented as follows:


function sortNumbers(input) {
  const N = parseInt(input[0]); // The first line is the number of integers
  const numbers = input.slice(1, N + 1).map(Number); // Convert the remaining N numbers to integers and store in an array

  numbers.sort((a, b) => a - b); // Sort in ascending order

  return numbers.join('\\n'); // Return sorted numbers to print one per line
}

// Example input
const input = [
  '5',
  '5',
  '3',
  '2',
  '1',
  '4'
];

console.log(sortNumbers(input)); // Output the result

Code Explanation

Let us look more closely at each part of the code:

  • Input Handling: parseInt(input[0]) is used to retrieve the number of integers from the first line. input.slice(1, N + 1) selects the numbers excluding the first line, and map(Number) converts the string array to a number array.
  • Sorting: numbers.sort((a, b) => a - b) compares two numbers and sorts them in ascending order. It returns a - b so that if the first argument is less than the second, it returns a negative number, if greater, a positive number, and if equal, 0.
  • Output Handling: join('\\n') connects each element of the array with a newline character to create a string that can be printed.

Test Cases

You can consider several test cases using the defined code:

Test Case 1

Input:
5
5
3
2
1
4

Output:
1
2
3
4
5

Test Case 2

Input:
4
10
30
20
40

Output:
10
20
30
40

Test Case 3

Input:
3
-1
-5
2

Output:
-5
-1
2

Final Words

In this course, we have learned how to solve the algorithm problem ‘Sorting Numbers 2’. Various sorting algorithms can be utilized, but it is essential to select an appropriate algorithm based on the scope and requirements of the problem. Furthermore, leveraging JavaScript’s powerful features allows for efficient implementation.

We will continue to share methods for solving various algorithm problems, so please stay tuned. Enhance your skills in well-organized problem-solving to open the door to employment!

JavaScript Coding Test Course, Finding the Minimum Number of Matrix Multiplications

Author: [Author Name] | Date: [Creation Date]

Problem Description

This problem requires finding the minimum number of operations needed to multiply a given N matrices.
The number of operations for matrix multiplication greatly varies based on the order of multiplication, and thus it is necessary to find the correct order.

When the size of matrix A is p × q and the size of matrix B is q × r,
the number of operations for multiplying the two matrices is p × q × r.
When multiplying several matrices at once, an efficient multiplication order must be found.

For instance, when multiplying three matrices of sizes 10 × 20, 20 × 30, 30 × 40,
the operation count for (10×20) * (20×30) * (30×40) is 10 × 20 × 30 + 10 × 30 × 40 = 6000 + 12000 = 18000.
If we multiply in the order of (10×30) * (30×40) * (20×30), the operation count becomes 10 × 30 × 40 + 10 × 20 × 40 = 12000 + 8000 = 20000.
Here, we can see that the order of the first case is more efficient.

Input Format

The first line contains the number of matrices N. (1 ≤ N ≤ 100)

The second line contains N + 1 integers separated by spaces.
The i-th integer represents the size of the matrix A[i] × A[i+1].
(1 ≤ A[i] ≤ 500)

Output Format

Print the minimum number of operations required as a single integer.

Problem Solving Process

Step 1: Understanding Dynamic Programming Technique

This question is an optimization problem for matrix multiplication, which can be solved using dynamic programming.
To find the minimum, a 2D array can be used to store the number of operations for each ordering of matrix multiplication.

Step 2: Initializing the Array

First, receive an array m representing N matrices. The length of this array is N + 1.
It stores the dimension information of each matrix.


let m = [10, 20, 30, 40];
        

Next, declare a 2D array dp to store the number of operations, initialized to Infinity.
The diagonal elements are set to 0.


let dp = Array.from(Array(n), () => Array(n).fill(Infinity));
for (let i = 0; i < n; i++) {
    dp[i][i] = 0;
}
        

Step 3: Completing the Dynamic Programming Table

Using a nested loop, partition the matrices and calculate the minimum number of operations for each multiplication.
The outer loop represents the length of the multiplication chain, while the inner loop represents the indices attempting the multiplications.


for (let len = 2; len <= n; len++) {
    for (let i = 0; i <= n - len; i++) {
        let j = i + len - 1;
        for (let k = i; k < j; k++) {
            dp[i][j] = Math.min(dp[i][j], dp[i][k] + dp[k + 1][j] + m[i] * m[k + 1] * m[j + 1]);
        }
    }
}
        

Step 4: Outputting the Result

Finally, print the value of the one-dimensional array dp[0][n – 1] to check the minimum.


console.log(dp[0][n - 1]);
        

Complete Code Example


function matrixChainOrder(m) {
    const n = m.length - 1;
    let dp = Array.from(Array(n), () => Array(n).fill(Infinity));
    
    for (let i = 0; i < n; i++) {
        dp[i][i] = 0;
    }

    for (let len = 2; len <= n; len++) {
        for (let i = 0; i <= n - len; i++) {
            let j = i + len - 1;
            for (let k = i; k < j; k++) {
                dp[i][j] = Math.min(dp[i][j], dp[i][k] + dp[k + 1][j] + m[i] * m[k + 1] * m[j + 1]);
            }
        }
    }

    return dp[0][n - 1];
}

let m = [10, 20, 30, 40]; // Matrix sizes
console.log(matrixChainOrder(m)); // Output
        

Through this article, please understand how to solve algorithm problems in JavaScript.

Wishing you successful preparation for your coding test!

JavaScript Coding Test Course, Preparing for Resignation

To prepare for a resignation in a rational and effective manner, various skills and knowledge are required. In particular, proficiency in programming languages such as JavaScript plays a crucial role in preparing for coding tests. In this post, I will introduce an algorithm problem using JavaScript and explain the process of solving it in detail.

Problem Description

Problem: Sum of Two Numbers

Given an integer array nums and an integer target, return the indices of the two numbers in nums such that their sum equals target.

It is assumed that there is exactly one solution for each input, and you may not use the same element twice. The returned value should be the indices of the two numbers.

Example Input:

nums = [2, 7, 11, 15]

target = 9

Example Output:

[0, 1]

This example shows that nums[0] + nums[1] = 2 + 7 = 9.

Problem Solving Strategy

There are various methods to approach this problem. Here are some representative approaches:

  • My Approach: Using a double loop to compare two numbers
  • Approach using hashmap: Allows quick lookup when necessary

1. Approach Using Double Loop

The most intuitive way is to use a double loop to check all combinations of two numbers. We validate whether we reach the target sum by checking every combination of numbers. However, this method has a time complexity of O(n2), which can degrade performance.

function twoSum(nums, target) {
    for (let i = 0; i < nums.length; i++) {
        for (let j = i + 1; j < nums.length; j++) {
            if (nums[i] + nums[j] === target) {
                return [i, j];
            }
        }
    }
}

// Example execution
const nums = [2, 7, 11, 15];
const target = 9;
console.log(twoSum(nums, target)); // [0, 1]

2. Approach Using Hashmap

A more efficient method is to use a hashmap. As we iterate through the numbers, we store each number’s value as a key and its index as a value. Then, we compute the required difference for each value and look up this difference in the hashmap, allowing us to solve the problem in linear time complexity O(n).

function twoSum(nums, target) {
    const numMap = new Map();
    
    for (let i = 0; i < nums.length; i++) {
        const complement = target - nums[i];
        if (numMap.has(complement)) {
            return [numMap.get(complement), i];
        }
        numMap.set(nums[i], i);
    }
}

// Example execution
const nums = [2, 7, 11, 15];
const target = 9;
console.log(twoSum(nums, target)); // [0, 1]

Time Complexity

The first method has a time complexity of O(n2), while the second method has a time complexity of O(n). Thus, the second method is much more efficient. The second method has a space complexity of O(n) as it makes use of an additional hashmap.

Conclusion

This problem allowed me to improve my coding skills in JavaScript and try various approaches. In particular, the problem-solving method utilizing a hashmap can be very useful in coding tests.

As you prepare for resigning, you will need to prepare for coding tests. I hope to enhance my algorithm problem-solving abilities through repeated practice and increase my application skills in actual coding tests. Please look forward to the next post where I will tackle more complex problems!

JavaScript Coding Test Course, Bubble Sort

Today, we will learn about one of the most basic sorting algorithms in JavaScript, Bubble Sort. Bubble sort is a simple but inefficient sorting algorithm, primarily used for educational purposes or to learn the fundamentals of algorithms.

Overview of Bubble Sort

Bubble sort works by repeatedly traversing a given list, comparing two adjacent elements and swapping their order. This process continues until it is determined that the list is sorted. In the worst case, the time complexity is O(n^2).

How It Works

The basic operation of bubble sort is as follows:

  1. Start from the first element of the list and compare two adjacent elements.
  2. If the left element is greater than the right element, swap their positions.
  3. Repeat this process until the end of the list. After one pass, the largest element will move to the end.
  4. Repeat the above process (steps 1-3) for the remaining elements.

Problem Definition

Problem Description

You are given an array arr. Write a function that uses the bubble sort algorithm to sort this array in ascending order and return the sorted array.

Example Input

arr = [64, 34, 25, 12, 22, 11, 90]

Example Output

[11, 12, 22, 25, 34, 64, 90]

Solution Process

Step 1: Function Definition

First, we will define a function to perform bubble sort. We will name the function bubbleSort. It will take an array as input.

Step 2: Using Nested Loops

Bubble sort is implemented using nested loops. The outer loop progresses to the last element of the array, while the inner loop compares two adjacent elements to sort them.

Step 3: Implementing the Comparison and Swap Logic

In the inner loop, compare two adjacent elements and swap their order. We can use a simple conditional statement for this.

function bubbleSort(arr) {
        let n = arr.length;
        for (let i = 0; i < n - 1; i++) {
            for (let j = 0; j < n - 1 - i; j++) {
                if (arr[j] > arr[j + 1]) {
                    // Swap elements
                    let temp = arr[j];
                    arr[j] = arr[j + 1];
                    arr[j + 1] = temp;
                }
            }
        }
        return arr;
    }

Step 4: Adding a Utility Function (Optional)

You may write a utility function to print the array to check the sorted result. You can use a simple console.log to verify the results.

const arr = [64, 34, 25, 12, 22, 11, 90];
    console.log(bubbleSort(arr)); // [11, 12, 22, 25, 34, 64, 90]

Time Complexity of Bubble Sort

The time complexity of bubble sort is O(n^2) in the worst case. This is because the entire array is iterated twice. In the best case (when it is already sorted), it is O(n), but generally it is inefficient.

The space complexity is O(1), which makes it efficient since the additional memory used is constant.

Significance and Use of Bubble Sort

Due to its simple implementation, bubble sort is suitable for learning algorithms. However, its performance is relatively poor in real industrial applications, where other sorting algorithms are preferred. Nevertheless, it is an important fundamental concept that can be understood while studying algorithms.

Conclusion

In this article, we learned how to implement bubble sort in JavaScript. I hope this helps you understand basic sorting algorithms and serves as a stepping stone to learn more complex algorithms. If you have any questions or need additional information, please leave a comment!

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