Codeforces Contest — Problem Intuitions

Problem A — Letter Home

Given a sorted array of positions and a starting point, you must reach both ends of the array in the minimum number of steps.

Optimal Strategy:

Move to the nearest boundary (either the smallest or largest position).
Then traverse the entire array to the opposite end.
The answer is: abs(max_x - min_x) + min(abs(s - min_x), abs(s - max_x))

Why: You must visit both ends, so always minimize the initial distance to the closest end.

Problem B — Above the Clouds

Core Idea:
Partition the string into three non-empty substrings a, b, c such that b is a substring of a+c.

Key Insight:

For every possible split, check if the middle part (b) appears as a substring in the concatenation of the first and third parts (a+c).

Approach:

Iterate over all valid split points.
For each, check the substring condition.
Output "Yes" if any split works, otherwise "No".

Problem C — Those Who Are With Us

Core Idea:
You can decrease all elements in a chosen row and column by 1. Find the minimal possible maximum value in the matrix after one such operation.

Key Insight:

The only way to reduce the global maximum is to "cover" all columns containing the maximum value with a single row (except possibly one column).

Approach:

For each row, count how many unique columns it covers where the maximum occurs only in that row.
If removing that row leaves at most one column with the maximum, you can reduce the global maximum.
Otherwise, the maximum remains unchanged.

Problem D — 1709

Sort two arrays using only adjacent swaps and swaps between the same index in both arrays, so that both arrays are strictly increasing and a[i] < b[i] for all i.

Key Insight:

Use adjacent swaps to sort both arrays.
If after sorting, any a[i] > b[i], swap them at that index.
Repeat sorting if necessary.

Approach:

Bubble sort both arrays with allowed swaps.
After sorting, for any a[i] > b[i], swap them.
Re-sort if needed until all constraints are satisfied.

Problem E — Sponsor of Your Problems

Given two numbers l and r (same length), find the minimum value of $$$f(l, x) + f(x, r)$$$ for all $$$x$$$ in $$$[l, r]$$$, where $$$f(a, b)$$$ is the count of matching digits at the same positions.

Key Insight:

This is a classic Digit DP problem.
At each digit, you can choose any value between the corresponding digits of $$$l$$$ and $$$r$$$ (depending on tight bounds).
The cost at each digit is the number of matches with $$$l$$$ and $$$r$$$.

Approach:

Use DP with state $$$(pos, tightL, tightR)$$$ to represent the current digit position and whether you are still matching the prefix of $$$l$$$ and $$$r$$$.
For each digit, try all possible values within the allowed bounds.
Minimize the total cost recursively.

If you found these intuitions helpful, consider sharing or upvoting to encourage more such educational posts!

[contest:https://codeforces.me/contest/2121]

Full text and comments »