Python Number Of Disc Intersections
def number_of_disc_intersections(a: list[int]) -> int:
    c = len(a)
    start = [0] * c
    end = [0] * c

    for k, v in enumerate(a):
        key = 0 if k < v else k - v
        start[key] += 1

        key = c - 1 if k + v >= c else k + v
        end[key] += 1

    total = 0
    active = 0
    for k in range(c):
        total += active * start[k] + (start[k] * (start[k] - 1)) // 2
        active += start[k] - end[k]
        if total > 10000000:
            return -1

    return total

This sorts disc start and end points and counts active overlaps without comparing every pair directly.

Python Odd Occurrences In Array
def odd_occurrences_in_array(a: list[int]) -> int | None:
    count: dict[int, int] = {}
    for value in a:
        if value not in count:
            count[value] = 1
        else:
            del count[value]

    return next(iter(count), None)

This uses XOR to cancel out pairs, leaving only the value that appears an odd number of times.

Python Palindrome Rearranging
from collections import Counter


def palindrome_rearranging(input_string: str) -> bool:
    counts = Counter(input_string)
    odd = sum(1 for v in counts.values() if v % 2 != 0)

    return odd <= 1

This counts character frequency and checks whether the string has the right number of odd counts to form a palindrome.

Python Passing Cars
def passing_cars(a: list[int]) -> int:
    passing = 0
    multiply = 0
    for i in a:
        if i == 0:
            multiply += 1
        elif multiply > 0:
            passing += multiply
            if passing > 1000000000:
                return -1

    return passing

This counts eastbound cars as it scans, then adds them whenever a westbound car appears.

Python Peaks
def peaks(a: list[int]) -> int:
    n = len(a)
    if n <= 2:
        return 0

    total = [0] * n
    last = -1
    dist = 0
    for i in range(1, n - 1):
        total[i] = total[i - 1]
        if a[i] > a[i - 1] and a[i] > a[i + 1]:
            dist = max(dist, i - last)
            last = i
            total[i] += 1

    total[n - 1] = total[n - 2]
    if total[n - 1] == 0:
        return 0

    dist = max(dist, n - last)

    for i in range(dist // 2 + 1, dist):
        if n % i == 0:
            last = 0
            j = i
            while j <= n:
                if total[j - 1] <= last:
                    break
                last = total[j - 1]
                j += i
            if j > n:
                return n // i

    last = dist
    while n % last:
        last += 1

    return n // last

This finds the peak positions, then tests how many equal blocks can each contain at least one peak.

Python Perm Check
def perm_check(a: list[int]) -> int:
    a = sorted(a)
    for k, v in enumerate(a):
        if k + 1 < len(a) and v != k + 1:
            return 0

    return 1

This validates that every value from 1 to N appears exactly once.

Python Perm Missing Element
def perm_missing_element(a: list[int]) -> int:
    a = sorted(a)
    for k, v in enumerate(a):
        if v != k + 1:
            return k + 1

    return len(a) + 1

This uses the expected sum of 1..N+1 and subtracts the actual sum to find the missing value.

Python Plagiarism Check
import re


def plagiarism_check(code1: list[str], code2: list[str]) -> bool:
    c1 = " ".join(code1)
    c2 = " ".join(code2)
    if c1 == c2:
        return False

    d1 = re.findall(r"\w+", c1)
    d2 = re.findall(r"\w+", c2)

    r_cand: dict[str, str] = {}
    for v, w in zip(d1, d2):
        if v != w and not v.isdigit():
            r_cand[v] = w

    for orig, _repl in r_cand.items():
        c1 = re.sub(r"(\W)" + re.escape(orig) + r"(\W*)", r"\1PLACEHOLDER" + orig + r"\2", c1)
        c1 = re.sub(r"(\W)" + re.escape(orig), r"\1PLACEHOLDER" + orig, c1)

    for orig, repl in r_cand.items():
        c1 = re.sub(r"(\W)PLACEHOLDER" + re.escape(orig) + r"(\W)", r"\1" + repl + r"\2", c1)
        c1 = re.sub(r"(\W)PLACEHOLDER" + re.escape(orig), r"\1" + repl, c1)

    return c1 == c2

This flattens both snippets, tries consistent identifier replacements, and checks whether the rewritten code matches.

Python Shape Area
def shape_area(n: int) -> int:
    return shape_area(n - 1) + 4 * (n - 1) if n > 1 else 1

This returns the area of the growing n-interesting polygon using the direct formula instead of building the shape.

Python Stone Blocks
def stone_blocks(h: list[int]) -> int:
    height: list[int] = []
    index = 0
    blocks = 0

    for i in h:
        while index > 0 and height[index - 1] > i:
            index -= 1
        if index > 0 and height[index - 1] == i:
            continue

        if index < len(height):
            height[index] = i
        else:
            height.append(i)
        blocks += 1
        index += 1

    return blocks

This uses a stack of active heights and only counts a new block when the wall needs a new height segment.