Leetcode 974.Subarray Sums Divisible by K

From Claude with some prompting
Find Subarrays with Same Remainder First, we calculate the prefix sum, which is the cumulative sum up to each element in the array. For example, the prefix sum for [4, 5, 0, -2, -3, 1] is [4, 9, 9, 7, 4, 5]. Then, we find the remainder when each prefix sum is divided by k. In this case, with k=5, the remainders are [4, 4, 4, 2, 4, 0].

Count Subarrays with Same Remainder We count the number of subarrays that have the same remainder. For instance, if the remainder 4 appears 3 times, it means there are 3 subarrays ending with a sum divisible by 5 and leaving a remainder of 4. We store these counts in a remainder_count array.

Calculate Answer For the remainder 0, we assume there is always at least one subarray (the empty subarray), so we initialize remainder_count[0] = 1. Then, we calculate the combinations of subarrays with the same remainder. If there are remainder_count[r] subarrays with the same remainder r, the number of combinations is (remainder_count[r] * (remainder_count[r] – 1)) / 2. We sum up these values for all remainders to get the final answer.

In summary, this algorithm utilizes the remainders of prefix sums to count the number of subarrays with the same remainder, and then combines these counts to find the total number of subarrays whose sum is divisible by k.

Leetcode 234.Palindrome Linked List

From DALL-E with some prompting
Scenario:

  • Linked-List: You can only read one element at the same time.
  • Memory Map: Allows direct access to all data.
  • Optimization: There are 2 key points to optimize:
    • Point 1: Find out the center of the list.
    • Point 2: Reverse the ordering of the second half of the list and compare it with the first half.
    The diagram illustrates two examples with nodes that show how you would first read all data (in the Linked-List), then direct access allows you to compare elements starting from the ends towards the center (in the Memory Map). For optimization, the steps include finding the center of the list, reversing the order of the second half of the list, and then comparing the two halves to determine if the list is a palindrome.

Leetcode 1582. Special Positions in a Binary Matrix

From ChatGPT4 < image interpretation>
The image presents a problem statement and a solution approach for identifying special positions in a binary matrix from a programming challenge. The task is to find positions in the matrix where the value is ‘1’, and all other values in the same row and column are ‘0’. The solution involves three steps:

  1. Interpretation: It involves identifying the type of ‘1’ cells that are unique in their row and column with no other ‘1’s in any of the four quadrant directions.
  2. Creating ‘1’ count maps: This step counts the number of ‘1’s in each row and column to create horizontal and vertical direction maps.
  3. Final count: It counts the cells that contain a ‘1’ and checks if there are no other ‘1’s in the corresponding horizontal and vertical directions.

The code snippets provided outline the loops and conditions used to implement this logic in a programming language.

leetcode 1464. Maximum Product of Two Elements in an Array

From DALL-E with some prompting

The image displays a programming challenge titled “1464. Maximum Product of Two Elements in an Array”. The task is to choose two different indices i and j from an array of integers to maximize the value of (nums[i]-1)*(nums[j]-1).

Example 1 gives the array [3,4,5,2], selecting indices i=1 and j=2 yields the maximum value (4-1)(5-1) = 12. In Example 2, the array [1,5,4,5] yields a maximum value of (5-1)(5-1) = 16 when indices i=1 and j=3 are chosen. For Example 3, with the array [3,7], any selection of indices results in (3-1)*(7-1) = 12.

The suggested solution involves sorting the array in descending order and then selecting the first two numbers. Alternatively, while quicksort could be used, it is noted that a more efficient O(1) method exists for directly finding the first and second largest numbers. Code snippets are provided, demonstrating the iteration over the array to find the largest and second-largest numbers.

The constraints specify that the length of the nums array is between 2 and 500 and each element in the array is less than or equal to 10^3.