🔥 Awesome — this is going to be your “Deep Python Lists in 3 Days” full mastery roadmap.

You’ll go from list internals (memory, references, slicing) → fundamental list algorithms → advanced sliding window and two-pointer problems → interval & array logic used in real interviews.

And yes — it includes all those problems + a clean visual cheat sheet at the end.

🧠 Deep Python Lists in 3 Days

Understand. Implement. Master.

📅 Overview

🩵 DAY 1 – Python List Internals & Foundational Algorithms

🎯 Goal

Understand how Python lists work under the hood (mutable dynamic arrays), and implement core problems using basic iteration, sets, and counting.

🧠 PART 1 – Python List Internals

🔹 How Lists Work Behind the Scenes

• Lists are dynamic arrays — contiguous memory blocks storing pointers to elements.
• Internally implemented as a C array of pointers (PyListObject).
• Dynamic resizing strategy (over-allocation):
  • When full, it grows by ~12.5% of its size.
  • This makes append() amortized O(1).

🔹 Mutability & References

a = [1, 2, 3]
b = a
b.append(4)
print(a)  # [1, 2, 3, 4] – same object

Use copy() or slicing a[:] to create shallow copies.

🔹 Slicing and Memory

nums = [10, 20, 30, 40]
slice_copy = nums[1:3]
print(slice_copy)  # [20, 30]
print(nums[1:3] is nums)  # False

✅ Each slice creates a new list.

🔹 Common Built-in Operations (O-notation)

🧩 PART 2 – List Basics Problems

1️⃣ Second Largest Number

def second_largest(nums):
    first = second = float('-inf')
    for n in nums:
        if n > first:
            first, second = n, first
        elif first > n > second:
            second = n
    return second

2️⃣ Is List Ascending?

def is_ascending(lst):
    return all(lst[i] <= lst[i+1] for i in range(len(lst)-1))

3️⃣ First Repeating Number (Nested Loops)

def first_repeating_nested(nums):
    for i in range(len(nums)):
        for j in range(i+1, len(nums)):
            if nums[i] == nums[j]:
                return nums[i]
    return None

4️⃣ First Repeating Number (Set)

def first_repeating(nums):
    seen = set()
    for n in nums:
        if n in seen:
            return n
        seen.add(n)
    return None

5️⃣ Find Duplicates

def find_duplicates(nums):
    seen, dup = set(), set()
    for n in nums:
        if n in seen:
            dup.add(n)
        seen.add(n)
    return list(dup)

6️⃣ Most Common Value

from collections import Counter

def most_common(nums):
    return Counter(nums).most_common(1)[0][0]

7️⃣ Missing Number (LeetCode #268)

def missing_number(nums):
    n = len(nums)
    return n * (n + 1) // 2 - sum(nums)

8️⃣ Max Profit (LeetCode #121)

def max_profit(prices):
    min_price = float('inf')
    profit = 0
    for p in prices:
        min_price = min(min_price, p)
        profit = max(profit, p - min_price)
    return profit

9️⃣ Two Sum (LeetCode #1)

def two_sum(nums, target):
    seen = {}
    for i, n in enumerate(nums):
        if target - n in seen:
            return [seen[target - n], i]
        seen[n] = i

🔟 Majority Element (LeetCode #169)

def majority_element(nums):
    count = 0
    candidate = None
    for n in nums:
        if count == 0:
            candidate = n
        count += (1 if n == candidate else -1)
    return candidate

11️⃣ Intersection of Two Arrays

def intersection(nums1, nums2):
    return list(set(nums1) & set(nums2))

12️⃣ Rotate List

def rotate(nums, k):
    k %= len(nums)
    nums[:] = nums[-k:] + nums[:-k]
    return nums

13️⃣ Move All Zeros to End

def move_zeros(nums):
    pos = 0
    for i in range(len(nums)):
        if nums[i] != 0:
            nums[pos], nums[i] = nums[i], nums[pos]
            pos += 1
    return nums

14️⃣ Remove Duplicates from Sorted Array

def remove_duplicates(nums):
    if not nums: return 0
    j = 0
    for i in range(1, len(nums)):
        if nums[i] != nums[j]:
            j += 1
            nums[j] = nums[i]
    return j + 1

15️⃣ Merge Two Sorted Arrays

def merge_sorted(a, b):
    i = j = 0
    merged = []
    while i < len(a) and j < len(b):
        if a[i] < b[j]:
            merged.append(a[i])
            i += 1
        else:
            merged.append(b[j])
            j += 1
    merged.extend(a[i:])
    merged.extend(b[j:])
    return merged

16️⃣ Find All Pairs with Given Sum

def find_pairs(nums, target):
    seen = set()
    pairs = set()
    for n in nums:
        if target - n in seen:
            pairs.add(tuple(sorted((n, target - n))))
        seen.add(n)
    return list(pairs)

17️⃣ Count Occurrences

from collections import Counter
def count_occurrences(nums):
    return dict(Counter(nums))

✅ End of Day 1 Focus:
You can now handle:

• Counting / Frequency
• Sorting / Searching
• Basic optimizations with O(n) space and time.

💎 DAY 2 – Intermediate & Advanced Array Patterns

🎯 Goal

Learn core array patterns: prefix sums, Kadane’s algorithm, and subarray problems.

1️⃣ Longest Consecutive Sequence

def longest_consecutive(nums):
    s = set(nums)
    longest = 0
    for n in s:
        if n - 1 not in s:
            curr = n
            length = 1
            while curr + 1 in s:
                curr += 1
                length += 1
            longest = max(longest, length)
    return longest

2️⃣ Subarray Sum Equals K

def subarray_sum(nums, k):
    prefix_sum = 0
    seen = {0: 1}
    count = 0
    for n in nums:
        prefix_sum += n
        count += seen.get(prefix_sum - k, 0)
        seen[prefix_sum] = seen.get(prefix_sum, 0) + 1
    return count

3️⃣ Maximum Subarray (Kadane’s)

def max_subarray(nums):
    curr = best = nums[0]
    for n in nums[1:]:
        curr = max(n, curr + n)
        best = max(best, curr)
    return best

4️⃣ Product of Array Except Self

def product_except_self(nums):
    res = [1] * len(nums)
    prefix = 1
    for i in range(len(nums)):
        res[i] = prefix
        prefix *= nums[i]
    suffix = 1
    for i in range(len(nums)-1, -1, -1):
        res[i] *= suffix
        suffix *= nums[i]
    return res

5️⃣ 3Sum

def three_sum(nums):
    nums.sort()
    res = []
    for i in range(len(nums) - 2):
        if i > 0 and nums[i] == nums[i-1]:
            continue
        l, r = i + 1, len(nums) - 1
        while l < r:
            s = nums[i] + nums[l] + nums[r]
            if s == 0:
                res.append([nums[i], nums[l], nums[r]])
                l += 1
                r -= 1
                while l < r and nums[l] == nums[l-1]:
                    l += 1
                while l < r and nums[r] == nums[r+1]:
                    r -= 1
            elif s < 0:
                l += 1
            else:
                r -= 1
    return res

6️⃣ 4Sum

(similar to 3Sum but extra loop)

7️⃣ Trapping Rain Water

def trap(height):
    left, right = 0, len(height)-1
    lmax, rmax = 0, 0
    res = 0
    while left < right:
        if height[left] < height[right]:
            if height[left] >= lmax:
                lmax = height[left]
            else:
                res += lmax - height[left]
            left += 1
        else:
            if height[right] >= rmax:
                rmax = height[right]
            else:
                res += rmax - height[right]
            right -= 1
    return res

8️⃣ Container With Most Water

def max_area(height):
    l, r = 0, len(height)-1
    best = 0
    while l < r:
        area = (r-l) * min(height[l], height[r])
        best = max(best, area)
        if height[l] < height[r]:
            l += 1
        else:
            r -= 1
    return best

9️⃣ Merge Intervals

def merge_intervals(intervals):
    intervals.sort(key=lambda x: x[0])
    merged = [intervals[0]]
    for start, end in intervals[1:]:
        if start <= merged[-1][1]:
            merged[-1][1] = max(merged[-1][1], end)
        else:
            merged.append([start, end])
    return merged

🔟 Search in Rotated Sorted Array

def search_rotated(nums, target):
    l, r = 0, len(nums)-1
    while l <= r:
        mid = (l + r)//2
        if nums[mid] == target:
            return mid
        if nums[l] <= nums[mid]:
            if nums[l] <= target < nums[mid]:
                r = mid - 1
            else:
                l = mid + 1
        else:
            if nums[mid] < target <= nums[r]:
                l = mid + 1
            else:
                r = mid - 1
    return -1

✅ End of Day 2 Focus:
You now master:

• Prefix sums, Kadane’s
• Two-pointer for 3Sum, Trapping Water, Max Area
• Interval problems and binary search

🧠 DAY 3 – Two Pointers & Sliding Window Mastery

1️⃣ Max Consecutive Ones

def max_consecutive_ones(nums):
    best = curr = 0
    for n in nums:
        if n == 1:
            curr += 1
            best = max(best, curr)
        else:
            curr = 0
    return best

2️⃣ Max Consecutive Ones III (at most K zeros)

def longest_ones(nums, k):
    left = 0
    zeros = 0
    best = 0
    for right in range(len(nums)):
        if nums[right] == 0:
            zeros += 1
        while zeros > k:
            if nums[left] == 0:
                zeros -= 1
            left += 1
        best = max(best, right - left + 1)
    return best

3️⃣ Sort Colors (Dutch National Flag)

def sort_colors(nums):
    low, mid, high = 0, 0, len(nums)-1
    while mid <= high:
        if nums[mid] == 0:
            nums[low], nums[mid] = nums[mid], nums[low]
            low += 1; mid += 1
        elif nums[mid] == 1:
            mid += 1
        else:
            nums[mid], nums[high] = nums[high], nums[mid]
            high -= 1
    return nums

4️⃣ Remove Duplicates (Two Pointer)

def remove_duplicates(nums):
    slow = 0
    for fast in range(1, len(nums)):
        if nums[fast] != nums[slow]:
            slow += 1
            nums[slow] = nums[fast]
    return slow + 1

5️⃣ Find Pair with Given Difference

def has_pair_with_diff(nums, diff):
    nums.sort()
    i, j = 0, 1
    while j < len(nums):
        if i == j:
            j += 1
            continue
        d = nums[j] - nums[i]
        if d == diff:
            return True
        elif d < diff:
            j += 1
        else:
            i += 1
    return False

6️⃣ Is Subsequence (Revisited)

def is_subsequence(s, t):
    i = 0
    for ch in t:
        if i < len(s) and s[i] == ch:
            i += 1
    return i == len(s)

✅ By End of Day 3:

• You master two-pointer and sliding window patterns.
• You can build subarray, sum, and interval algorithms fluently.

🧾 CHEAT SHEET: Python Lists / Arrays Mastery

Would you like me to now generate a Jupyter Notebook version
📘 Deep_Python_Lists_in_3_Days.ipynb
→ with markdown explanations + runnable code cells (Day 1–3 + cheat sheet) — so you can practice interactively like the strings version?