Applying learned techniques to various subarray-related challenges (e.g., counting, specific sums).
Subarray problems are a common category of questions in coding interviews and competitive programming. They test your ability to apply a range of techniques, from brute-force to highly optimized linear-time solutions. Once you've mastered prefix sums, sliding windows, two-pointers, and Kadane's algorithm, you can tackle a wide variety of these problems. A classic example is 'find the number of subarrays with a given sum k'. A naive O(n^2) approach would check all subarrays. A more efficient O(n) solution uses a hash map combined with the concept of prefix sums. As we iterate through the array, we calculate the current prefix sum, `curr_sum`. We are looking for a previous index `j` such that `curr_sum - prefix_sum[j] = k`. This is equivalent to `prefix_sum[j] = curr_sum - k`. We can use a hash map to store the frequencies of prefix sums we've seen so far. At each index `i`, we check if `curr_sum - k` exists in the map. If it does, we add its frequency to our total count. Then, we update the map with the `curr_sum`. Other problems might involve XOR sums, products, or finding subarrays that meet more complex criteria, but the underlying patterns of efficient traversal and state management often remain the same.