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LeetCode link: 209. Minimum Size Subarray Sum, difficulty: Medium.

Given an array of positive integers nums and a positive integer target, return the minimal length of a subarray whose sum is greater than or equal to target. If there is no such subarray, return 0 instead.

A subarray is a contiguous non-empty sequence of elements within an array.

Input: target = 7, nums = [2,3,1,2,4,3]

Output: 2

Explanation:

The subarray [4,3] has the minimal length under the problem constraint.

Input: target = 4, nums = [1,4,4]

Output: 1

Explanation: target = 11, nums = [1,1,1,1,1,1,1,1]

Input: target = 11, nums = [1,1,1,1,1,1,1,1]

Output: 0

• 1 <= target <= 10^9
• 1 <= nums.length <= 10^5
• 1 <= nums[i] <= 10^4

For subarray problems, you can consider using Sliding Window Technique, which is similar to the Fast & Slow Pointers Approach.

1. Iterate over the nums array, the index of the element is named fastIndex. Although inconspicuous, this is the most important logic of the Fast & Slow Pointers Approach. Please memorize it.

2. sum += nums[fast_index].

   var minLength = Integer.MAX_VALUE;
   var sum = 0;
   var slowIndex = 0;
   
   for (var fastIndex = 0; fastIndex < nums.length; fastIndex++) { // This line the most important logic of the `Fast and Slow Pointers Technique`.
       sum += nums[fastIndex]; // 1
   }
   
   return minLength;

3. Control of slowIndex:

   var minLength = Integer.MAX_VALUE;
   var sum = 0;
   var slowIndex = 0;
   
   for (var fastIndex = 0; fastIndex < nums.length; fastIndex++) {
       sum += nums[fastIndex];
   
       while (sum >= target) { // 1
           minLength = Math.min(minLength, fastIndex - slowIndex + 1); // 2
           sum -= nums[slowIndex]; // 3
           slowIndex++; // 4
       }
   }
   
   if (minLength == Integer.MAX_VALUE) { // 5
       return 0; // 6
   }
   
   return minLength;

• Time complexity: O(N).
• Space complexity: O(1).

class Solution {
    public int minSubArrayLen(int target, int[] nums) {
        var minLength = Integer.MAX_VALUE;
        var sum = 0;
        var slowIndex = 0;

        for (var fastIndex = 0; fastIndex < nums.length; fastIndex++) { // This line is the most important. You'd better memorize it.
            sum += nums[fastIndex];

            while (sum >= target) {
                minLength = Math.min(minLength, fastIndex - slowIndex + 1);
                sum -= nums[slowIndex];
                slowIndex++;
            }
        }

        if (minLength == Integer.MAX_VALUE) {
            return 0;
        }

        return minLength;
    }
}

class Solution:
    def minSubArrayLen(self, target: int, nums: List[int]) -> int:
        min_length = float('inf')
        sum_ = 0
        slow_index = 0

        for fast_index, num in enumerate(nums): # This line is the most important. You'd better memorize it.
            sum_ += num

            while sum_ >= target:
                min_length = min(min_length, fast_index - slow_index + 1)
                sum_ -= nums[slow_index]
                slow_index += 1

        if min_length == float('inf'):
            return 0

        return min_length

var minSubArrayLen = function (target, nums) {
  let minLength = Number.MAX_SAFE_INTEGER
  let sum = 0
  let slowIndex = 0

  nums.forEach((num, fastIndex) => { // This line is the most important. You'd better memorize it.
    sum += num

    while (sum >= target) {
      minLength = Math.min(minLength, fastIndex - slowIndex + 1)
      sum -= nums[slowIndex]
      slowIndex++
    }
  })

  if (minLength == Number.MAX_SAFE_INTEGER) {
    return 0
  }

  return minLength
};

public class Solution
{
    public int MinSubArrayLen(int target, int[] nums)
    {
        int minLength = Int32.MaxValue;
        int sum = 0;
        int slowIndex = 0;

        for (int fastIndex = 0; fastIndex < nums.Length; fastIndex++) // This line is the most important. You'd better memorize it.
        {
            sum += nums[fastIndex];

            while (sum >= target)
            {
                minLength = Math.Min(minLength, fastIndex - slowIndex + 1);
                sum -= nums[slowIndex];
                slowIndex++;
            }
        }

        if (minLength == Int32.MaxValue)
            return 0;

        return minLength;
    }
}

func minSubArrayLen(target int, nums []int) int {
    minLength := math.MaxInt32
    sum := 0
    slowIndex := 0

    for fastIndex := 0; fastIndex < len(nums); fastIndex++ { // This line is the most important. You'd better memorize it.
        sum += nums[fastIndex]

        for sum >= target {
            minLength = min(minLength, fastIndex - slowIndex + 1)
            sum -= nums[slowIndex]
            slowIndex++
        }
    }

    if minLength == math.MaxInt32 {
        return 0
    }

    return minLength
}

func min(a, b int) int {
    if a < b {
        return a
    }
    return b
}

# @param {Integer} target
# @param {Integer[]} nums
# @return {Integer}
def min_sub_array_len(target, nums)
  min_length = Float::INFINITY
  sum = 0
  slow_index = 0

  nums.each_with_index do |num, fast_index| # This line is the most important. You'd better memorize it.
    sum += num

    while sum >= target
      min_length = [min_length, fast_index - slow_index + 1].min
      sum -= nums[slow_index]
      slow_index += 1
    end
  end

  min_length == Float::INFINITY ? 0 : min_length
end

class Solution {
public:
    int minSubArrayLen(int target, vector<int>& nums) {
        int min_length = INT_MAX;
        int sum = 0;
        int slow_index = 0;
        
        for (int fast_index = 0; fast_index < nums.size(); fast_index++) {
            sum += nums[fast_index];
            
            while (sum >= target) {
                min_length = min(min_length, fast_index - slow_index + 1);
                sum -= nums[slow_index];
                slow_index++;
            }
        }
        
        if (min_length == INT_MAX) {
            return 0;
        }
        
        return min_length;
    }
};

// Welcome to create a PR to complete the code of this language, thanks!

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Original link: 209. Minimum Size Subarray Sum - LeetCode Python/Java/C++/JS/C#/Go/Ruby Solutions.

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