Subarray Sum Equals K

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Questions and Answers

What is the primary purpose of the `unordered_map prefixSumCount` in the `subarraySum` function?

To track the count of subarrays that sum to `k`.
To store the frequency of each number in the input array.
To store the cumulative sum up to each index of the array.
To store the frequency of each prefix sum encountered while iterating through the array. (correct)

The line `prefixSumCount[0] = 1;` is crucial for correctly counting subarrays that start from index 0 and sum up to `k`.

True (A)

Explain the condition `prefixSumCount.find(prefixSum - k) != prefixSumCount.end()` and its role in identifying subarrays that sum to `k`.

This condition checks if a previous prefix sum exists such that subtracting k from the current prefixSum yields that previous prefix sum. If found, it indicates a subarray exists between those two points with a sum of k.

The time complexity of the `subarraySum` function is O(n), where n is the number of elements in the input array, because of the use of a(n) __________.

unordered_map Signup and view all the answers

Match the following steps in the `subarraySum` function to their purpose:

Initialize <code>prefixSumCount[0] = 1;</code> = Accounts for subarrays summing to k that start from the beginning of the array. <code>prefixSum += num;</code> = Calculates the cumulative sum as the algorithm iterates through the array. <code>if (prefixSumCount.find(prefixSum - k) != prefixSumCount.end())</code> = Checks if a subarray summing to k exists, ending at the current element. <code>count += prefixSumCount[prefixSum - k];</code> = Increments the count of subarrays summing to k. <code>prefixSumCount[prefixSum]++;</code> = Updates the frequency of the current prefix sum. Signup and view all the answers

What would be the output of the `subarraySum` function if `nums = {1, 2, 3, 4, 5}` and `k = 9`?

2 (B) Signup and view all the answers

The `subarraySum` function will return 0 if the input array `nums` is empty, regardless of the value of `k`.

True (A) Signup and view all the answers

Explain how the `subarraySum` function handles negative numbers in the input array and their impact on prefix sums.

The function correctly handles negative numbers by updating the prefix sum with each number, whether positive or negative. Negative numbers can decrease the prefix sum, allowing for subarrays with a sum of <code>k</code> to be identified even with negative elements. Signup and view all the answers

If the input array `nums` is `{-1, -1, 1}` and `k` is 0, the `subarraySum` function will return __________.

1 Signup and view all the answers

Match the following input arrays and target sums `k` with the number of subarrays that sum to `k` according to the `subarraySum` function:

<code>nums = {1, 1, 1}, k = 2</code> = 2 <code>nums = {1, 2, 3}, k = 3</code> = 2 <code>nums = {1, -1, 0}, k = 0</code> = 3 <code>nums = {1, 2, 1, 2, 1}, k = 3</code> = 4 Signup and view all the answers

Which scenario would cause the most significant performance degradation in the `subarraySum` function?

An extremely large input array with a wide distribution of integers, leading to a large number of unique prefix sums. (D) Signup and view all the answers

If all elements in the array `nums` are zero, the `subarraySum` function will always return `n * (n + 1) / 2` when `k` is zero, where `n` is the number of elements in `nums`.

True (A) Signup and view all the answers

Describe a potential modification to the `subarraySum` function to handle the case where the number of subarrays summing to `k` exceeds the limits of an `int` data type.

One potential modification is to use a larger data type, such as <code>long long int</code>, for the <code>count</code> variable to accommodate a greater number of subarrays summing to <code>k</code>. Signup and view all the answers

If the `prefixSumCount` map grows excessively large, it can lead to increased memory usage and potential performance issues. A technique to mitigate this is to periodically __________ the map by removing entries that are no longer relevant.

clear Signup and view all the answers

Match the following example arrays `nums` and target values `k` with the correct output of the `subarraySum` function:

nums = {1, 0, -1, 0}, k = 0 = 4 nums = {1, 2, 3}, k = 6 = 1 nums = {-1, -1, -1}, k = -2 = 2 nums = {5, 5, 5}, k = 10 = 2 Signup and view all the answers

In the context of the `subarraySum` function, what is the purpose of the line `prefixSumCount[prefixSum]++;`?

To keep track of how many times the current prefix sum has been encountered. (C) Signup and view all the answers

The `subarraySum` function can be modified to find the longest subarray with a sum equal to `k` by storing the indices of the prefix sums instead of just their frequencies.

True (A) Signup and view all the answers

Explain a scenario where using a standard `map` instead of an `unordered_map` for `prefixSumCount` might be preferable, considering both time and space complexity.

If memory usage is a critical constraint and the range of prefix sums is relatively small, a standard <code>map</code> may be preferable due to its potentially lower memory overhead, although it would incur a logarithmic time complexity for lookups compared to the average constant time complexity of <code>unordered_map</code>. Signup and view all the answers

The `subarraySum` function assumes that integer overflow will not occur when calculating the `prefixSum`. In situations where overflow is possible, it is necessary to use a(n) __________ data type to store the prefix sum.

wider Signup and view all the answers

Match the following code snippets with their impact on the functionality of the `subarraySum` function:

<code>prefixSumCount[0] = 1;</code> = Allows to count subarrays starting from index 0. <code>prefixSum += num;</code> = Calculates the sum of subarray. <code>prefixSumCount[prefixSum]++;</code> = Keeps track of the frequency of the prefix sum. <code>count += prefixSumCount[prefixSum - k];</code> = Accumulates the counts of subarrays summing to k. Signup and view all the answers

Flashcards

unordered_map

A data structure that stores key-value pairs, allowing for efficient lookups, insertions, and deletions.

prefixSum

Accumulates the sum of elements from the start of the array up to the current element.

subarraySum Approach

A technique using prefix sums and a hash map to efficiently count subarrays with a specified sum.

count (in context)

The number of subarrays within the given array that add up to the target value 'k'.

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prefixSumCount Initialization

Initialize the prefix sum counter to 1 for a zero prefix to handle subarrays starting at index 0.

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Study Notes

The code calculates the number of subarrays in a given array that sum to a target value k.
It uses an unordered map to store the cumulative prefix sums and their counts.
The function subarraySum takes a vector of integers nums and an integer k as input.
It returns the number of subarrays that sum up to k.
prefixSumCount stores the number of times each prefix sum has occurred.
count stores the total number of subarrays that sum to k.
prefixSum stores the cumulative sum of elements up to the current index.
The map is initialized with a prefix sum of 0 occurring once, to handle subarrays starting from the beginning of the input array.
For each number in nums, the prefixSum is updated by adding the current number.
It checks if prefixSum - k exists in prefixSumCount. If it does, it means there was a previous prefix sum such that the subarray between that prefix sum's index and the current index sums to k.
The count is incremented by the number of times prefixSum - k has occurred.
The frequency of the current prefixSum in prefixSumCount is incremented.
The main function reads the number of elements n and the target sum k from standard input.
It reads n integers from standard input into the nums vector.
It calls the subarraySum function with nums and k and prints the returned count to standard output.

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Subarray Sum Equals K

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Questions and Answers

What is the primary purpose of the `unordered_map prefixSumCount` in the `subarraySum` function?

The line `prefixSumCount[0] = 1;` is crucial for correctly counting subarrays that start from index 0 and sum up to `k`.

Explain the condition `prefixSumCount.find(prefixSum - k) != prefixSumCount.end()` and its role in identifying subarrays that sum to `k`.

The time complexity of the `subarraySum` function is O(n), where n is the number of elements in the input array, because of the use of a(n) __________.

Match the following steps in the `subarraySum` function to their purpose:

What would be the output of the `subarraySum` function if `nums = {1, 2, 3, 4, 5}` and `k = 9`?

The `subarraySum` function will return 0 if the input array `nums` is empty, regardless of the value of `k`.

Explain how the `subarraySum` function handles negative numbers in the input array and their impact on prefix sums.

If the input array `nums` is `{-1, -1, 1}` and `k` is 0, the `subarraySum` function will return __________.

Match the following input arrays and target sums `k` with the number of subarrays that sum to `k` according to the `subarraySum` function:

Which scenario would cause the most significant performance degradation in the `subarraySum` function?

If all elements in the array `nums` are zero, the `subarraySum` function will always return `n * (n + 1) / 2` when `k` is zero, where `n` is the number of elements in `nums`.

Describe a potential modification to the `subarraySum` function to handle the case where the number of subarrays summing to `k` exceeds the limits of an `int` data type.

If the `prefixSumCount` map grows excessively large, it can lead to increased memory usage and potential performance issues. A technique to mitigate this is to periodically __________ the map by removing entries that are no longer relevant.

Match the following example arrays `nums` and target values `k` with the correct output of the `subarraySum` function:

In the context of the `subarraySum` function, what is the purpose of the line `prefixSumCount[prefixSum]++;`?

The `subarraySum` function can be modified to find the longest subarray with a sum equal to `k` by storing the indices of the prefix sums instead of just their frequencies.

Explain a scenario where using a standard `map` instead of an `unordered_map` for `prefixSumCount` might be preferable, considering both time and space complexity.

The `subarraySum` function assumes that integer overflow will not occur when calculating the `prefixSum`. In situations where overflow is possible, it is necessary to use a(n) __________ data type to store the prefix sum.

Match the following code snippets with their impact on the functionality of the `subarraySum` function:

Flashcards

unordered_map

prefixSum

subarraySum Approach

count (in context)

prefixSumCount Initialization

Study Notes

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Subarray Sum Equals K

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Podcast

Questions and Answers

What is the primary purpose of the unordered_map prefixSumCount in the subarraySum function?

The line prefixSumCount[0] = 1; is crucial for correctly counting subarrays that start from index 0 and sum up to k.

Explain the condition prefixSumCount.find(prefixSum - k) != prefixSumCount.end() and its role in identifying subarrays that sum to k.

The time complexity of the subarraySum function is O(n), where n is the number of elements in the input array, because of the use of a(n) __________.

Match the following steps in the subarraySum function to their purpose:

What would be the output of the subarraySum function if nums = {1, 2, 3, 4, 5} and k = 9?

The subarraySum function will return 0 if the input array nums is empty, regardless of the value of k.

Explain how the subarraySum function handles negative numbers in the input array and their impact on prefix sums.

If the input array nums is {-1, -1, 1} and k is 0, the subarraySum function will return __________.

Match the following input arrays and target sums k with the number of subarrays that sum to k according to the subarraySum function:

Which scenario would cause the most significant performance degradation in the subarraySum function?

If all elements in the array nums are zero, the subarraySum function will always return n * (n + 1) / 2 when k is zero, where n is the number of elements in nums.

Describe a potential modification to the subarraySum function to handle the case where the number of subarrays summing to k exceeds the limits of an int data type.

If the prefixSumCount map grows excessively large, it can lead to increased memory usage and potential performance issues. A technique to mitigate this is to periodically __________ the map by removing entries that are no longer relevant.

Match the following example arrays nums and target values k with the correct output of the subarraySum function:

In the context of the subarraySum function, what is the purpose of the line prefixSumCount[prefixSum]++;?

The subarraySum function can be modified to find the longest subarray with a sum equal to k by storing the indices of the prefix sums instead of just their frequencies.

Explain a scenario where using a standard map instead of an unordered_map for prefixSumCount might be preferable, considering both time and space complexity.

The subarraySum function assumes that integer overflow will not occur when calculating the prefixSum. In situations where overflow is possible, it is necessary to use a(n) __________ data type to store the prefix sum.

Match the following code snippets with their impact on the functionality of the subarraySum function:

Flashcards

unordered_map

prefixSum

subarraySum Approach

count (in context)

prefixSumCount Initialization

Study Notes

Studying That Suits You

What is the primary purpose of the `unordered_map prefixSumCount` in the `subarraySum` function?

The line `prefixSumCount[0] = 1;` is crucial for correctly counting subarrays that start from index 0 and sum up to `k`.

Explain the condition `prefixSumCount.find(prefixSum - k) != prefixSumCount.end()` and its role in identifying subarrays that sum to `k`.

The time complexity of the `subarraySum` function is O(n), where n is the number of elements in the input array, because of the use of a(n) __________.

Match the following steps in the `subarraySum` function to their purpose:

What would be the output of the `subarraySum` function if `nums = {1, 2, 3, 4, 5}` and `k = 9`?

The `subarraySum` function will return 0 if the input array `nums` is empty, regardless of the value of `k`.

Explain how the `subarraySum` function handles negative numbers in the input array and their impact on prefix sums.

If the input array `nums` is `{-1, -1, 1}` and `k` is 0, the `subarraySum` function will return __________.

Match the following input arrays and target sums `k` with the number of subarrays that sum to `k` according to the `subarraySum` function:

Which scenario would cause the most significant performance degradation in the `subarraySum` function?

If all elements in the array `nums` are zero, the `subarraySum` function will always return `n * (n + 1) / 2` when `k` is zero, where `n` is the number of elements in `nums`.

Describe a potential modification to the `subarraySum` function to handle the case where the number of subarrays summing to `k` exceeds the limits of an `int` data type.

If the `prefixSumCount` map grows excessively large, it can lead to increased memory usage and potential performance issues. A technique to mitigate this is to periodically __________ the map by removing entries that are no longer relevant.

Match the following example arrays `nums` and target values `k` with the correct output of the `subarraySum` function:

In the context of the `subarraySum` function, what is the purpose of the line `prefixSumCount[prefixSum]++;`?

The `subarraySum` function can be modified to find the longest subarray with a sum equal to `k` by storing the indices of the prefix sums instead of just their frequencies.

Explain a scenario where using a standard `map` instead of an `unordered_map` for `prefixSumCount` might be preferable, considering both time and space complexity.

The `subarraySum` function assumes that integer overflow will not occur when calculating the `prefixSum`. In situations where overflow is possible, it is necessary to use a(n) __________ data type to store the prefix sum.

Match the following code snippets with their impact on the functionality of the `subarraySum` function: