Skip to content

Latest commit

 

History

History
146 lines (85 loc) · 5.5 KB

explanation.md

File metadata and controls

146 lines (85 loc) · 5.5 KB
Raw

Shortest Subarray with Sum at Least K - Step-by-Step Explanation

This README provides a step-by-step explanation of solving the problem of finding the shortest subarray with a sum of at least k in C++, Java, JavaScript, Python, and Go. Each step corresponds to a key part of the algorithm, with an explanation for its role in the solution.

C++ Code Explanation

Step 1: Initialize Variables

  • Create a prefix array to store the cumulative sums of the input array.
  • Use a deque to keep track of indices in a monotonic order.
  • Set minLength to a very large value (INT_MAX) to store the result.

Step 2: Compute Prefix Sums

  • Iterate through the input array to compute the cumulative sum of elements up to each index. Store these sums in the prefix array.

Step 3: Check for Valid Subarray

  • Traverse the prefix array:
    • Check if subtracting the smallest prefix sum from the current prefix sum yields a value greater than or equal to k.
    • If so, calculate the length of this subarray and update minLength.

Step 4: Maintain Monotonicity

  • Remove indices from the back of the deque if the current prefix sum is smaller than or equal to the last element in the deque.
  • This ensures that the deque contains indices in increasing order of prefix sums.

Step 5: Return the Result

  • If no valid subarray is found, return -1.
  • Otherwise, return minLength.

Java Code Explanation

Step 1: Initialize Variables

  • Use a long[] array called prefix to store cumulative sums.
  • Initialize a Deque to maintain indices in a monotonic order.
  • Set minLength to Integer.MAX_VALUE to store the result.

Step 2: Compute Prefix Sums

  • Loop through the input array and calculate prefix sums. Each prefix sum represents the sum of elements up to that index.

Step 3: Validate Subarrays

  • For each index in the prefix array:
    • Check if the difference between the current prefix sum and the smallest prefix sum in the deque is greater than or equal to k.
    • If true, update the result with the length of the subarray and remove the front of the deque.

Step 4: Update the Deque

  • Remove elements from the back of the deque if the current prefix sum is smaller or equal to the last prefix sum in the deque. This maintains monotonicity.

Step 5: Return the Final Result

  • Return -1 if no valid subarray is found; otherwise, return minLength.

JavaScript Code Explanation

Step 1: Setup Variables

  • Create an array prefix to store cumulative sums.
  • Use an empty array as a deque to maintain indices in increasing order of prefix sums.
  • Set minLength to Infinity as the initial result.

Step 2: Calculate Prefix Sums

  • Iterate through the input array, updating the prefix array to reflect the cumulative sum up to each index.

Step 3: Evaluate Subarrays

  • For each index in the prefix array:
    • Check if the difference between the current prefix sum and the smallest prefix sum in the deque is at least k.
    • If so, update minLength and remove the front element from the deque.

Step 4: Maintain Monotonic Order

  • Remove elements from the back of the deque if the current prefix sum is smaller than or equal to the last element in the deque. This ensures that the deque maintains increasing order.

Step 5: Return the Shortest Subarray

  • If no valid subarray is found, return -1. Otherwise, return minLength.

Python Code Explanation

Step 1: Initialize Structures

  • Create a prefix array to hold cumulative sums of the input array.
  • Use a deque to maintain indices in increasing order of prefix sums.
  • Initialize min_length with infinity (float('inf')).

Step 2: Compute Prefix Sums

  • Compute prefix sums using a loop. Each element in the prefix array represents the sum of elements up to that index.

Step 3: Find Valid Subarrays

  • Traverse the prefix array:
    • Check if subtracting the smallest prefix sum (at the front of the deque) from the current prefix sum yields a value greater than or equal to k.
    • If true, calculate the length of this subarray and update min_length.

Step 4: Update the Deque

  • Remove indices from the back of the deque if the current prefix sum is smaller or equal to the last element in the deque. This ensures monotonicity.

Step 5: Return the Result

  • Return -1 if no valid subarray is found. Otherwise, return min_length.

Go Code Explanation

Step 1: Initialize Variables

  • Create a prefix array of type int64 to store cumulative sums.
  • Use a slice as a deque to maintain indices in a monotonic order.
  • Set minLength to a large value (e.g., n+1) to store the shortest subarray length.

Step 2: Compute Prefix Sums

  • Iterate through the input array to compute the prefix sums. Store these sums in the prefix array.

Step 3: Check Valid Subarrays

  • Traverse the prefix array:
    • Check if the difference between the current prefix sum and the smallest prefix sum in the deque is at least k.
    • If true, calculate the length of this subarray and update minLength.

Step 4: Maintain Monotonic Order

  • Remove indices from the back of the deque if the current prefix sum is smaller or equal to the last prefix sum in the deque. This ensures that the deque only contains useful indices.

Step 5: Return the Result

  • If no valid subarray is found, return -1.
  • Otherwise, return minLength.