Lecture Notes: Codeforces Round 957 Discussion

Introduction

• Host: Abhinav
• Main Focus: Problems A to E of Codeforces Round 957
• Remarks: The first four problems are easy, while the fifth is of a good level. Problems F and G are not covered due to time constraints.

Problem A: Only Pluses

• Given: Three integers a, b, and c.
• Task: A monk can increase any of these integers by 1 up to 5 times and find the maximum possible value of a * b * c.
• Approach:
  • Iterate through all possible combinations of increases for a, b, and c.
  • Ensure the total number of increases does not exceed 5.
  • Use brute force to calculate the product for each combination and track the maximum value.
• Key Steps:
  1. Loop through all combinations of increases where a + b + c <= 5.
  2. Compute the product a * b * c for each combination.
  3. Track and return the highest product value.

Problem B: Angry Monk

• Given: Some potatoes divided into k pieces.
• Task: Join all potatoes using two operations only: combine with a 1-sized piece or split the potato into pieces of size a-1 and 1.
• Approach:
  • Sort the potatoes by size.
  • Combine potatoes of size one with a larger potato or split larger potatoes into pieces.
  • Focus on minimizing the number of operations.
• Key Steps:
  1. Sort the array of potato sizes.
  2. For each potato of size n except the largest, perform splits to reduce it to 1-sized pieces.
  3. Combine the 1-sized pieces with other pieces iteratively until all pieces are combined.

Problem C: Permutation Equation

• Given: n, m, k integers and a permutation of these n integers.
• Task: Calculate and maximize the sum of differences for g and f values.
• Approach:
  • Sort the permutation and rearrange to maximize g and minimize f values.
  • Consider the prefix sums and their relation to m and k.
• Key Steps:
  1. Sort the permutation such that larger values come first (maximize f).
  2. Calculate prefix sums for g and f and determine their differences.
  3. Track the maximum summation of g-f differences.

Problem D: The Test of Love

• Given: A sequence with logs, water, and crocodile sections.
• Task: Determine if Julian can swim to the end of the sequence within given constraints.
• Approach:
  • Use dynamic programming to keep track of possible positions at each step.
  • Consider the type of operation: swimming or jumping.
• Key Steps:
  1. Use a recursive approach with memoization to handle multiple states (current position, remaining jumps, and swims).
  2. Check all possible jumps and calculate minimum swims required to reach the end.
  3. Return results based on feasibility within given constraints.

Problem E: String Multiplication

• Given: A number n, and other numbers a and b.
• Task: Determine pairs of a and b such that a * n - b can be calculated as a repeated string.
• Approach:
  • Iterate through possible values of a and find suitable b such that the resultant string forms a valid repeated sequence.
  • Calculate and compare to ensure the string length matches the expected outcome from the mathematical operation.
• Key Steps:
  1. Convert n, a, and b into string representations and check possible repeated sequences.
  2. Validate if multiplying the string meets the condition a * n - b.
  3. Ensure the results meet both mathematical and string manipulation constraints.
  4. Print all valid pairs of a and b.