Coding Solutions
Dashboard Download PDF

tags: - cocubes - coding - solutions

Coding Solutions and Methods

1. Unit digit of a power

Only the last digit of x matters. Last digits repeat in a short cycle.

Algorithm:

  1. If y = 0, answer is 1.
  2. Let d = x MOD 10.
  3. Use the last-digit cycle for d.
  4. Select position y MOD cycleLength; use final cycle entry when remainder is zero.

Example: 7 has cycle 7, 9, 3, 1. Unit digit of 7^103 is the third entry because 103 MOD 4 = 3.

2. Card total

Initialise total = 0 and positiveCount = 0. Scan values once. Add every value to total; if value > 0, increment positiveCount.

3. First unique character

  1. Scan string and count each character.
  2. Scan again in original order.
  3. First character with count 1 is answer.

Two scans preserve original ordering.

4. Pair with target sum

Scan left to right. For each x, needed = T − x. If needed is already in a set, answer exists. Otherwise add x.

Why it works: every earlier value is stored, so when the later member of a valid pair is reached, its complement is found.

5. Valid palindrome

Set left at start and right at end.

  1. Skip non-alphanumeric characters at both ends.
  2. Compare lowercased characters.
  3. If unequal, false.
  4. Move both inward until they cross.

6. Balanced brackets

Map closing bracket to matching opening bracket.

  1. Push each opening bracket.
  2. On closing bracket, stack must be nonempty and top must match; otherwise false.
  3. End result is true only when stack is empty.

7. Second largest distinct

Maintain largest and secondLargest.

For each x:

  • if x > largest: secondLargest = largest; largest = x;
  • else if x is distinct from largest and x > secondLargest: secondLargest = x.

Use a sentinel/optional values carefully to support negatives.

8. Equal-half digit substring

For every even length L from largest down to 2:

  1. For every starting index, compare the digit sum of first L/2 characters with sum of next L/2.
  2. Return the first valid L.

Use prefix sums to obtain any digit-range sum quickly. For a two-day assessment, write a simple correct version if constraints are modest; optimise only if constraints require it.

9. Count subarrays with sum K

Let prefix be sum so far. A previous prefix equal to prefix − K identifies a subarray summing to K.

  1. Start map with count[0] = 1.
  2. For each x: prefix += x.
  3. Add count[prefix − K] to answer.
  4. Increment count[prefix].

10. Grid shortest path

Use BFS:

  1. Enqueue start with distance 0 and mark visited.
  2. Repeatedly remove front cell.
  3. Explore valid unblocked unvisited up/down/left/right neighbours.
  4. Enqueue them with distance + 1.
  5. First time target is removed/reached gives shortest path.

[[05_Coding/Coding_Playbook|Coding playbook]] · [[05_Coding/Pattern_Catalog|Pattern catalog]]