Freaks City

Given integers (N, M), a sequence of (N) integers (X = (X_1, X_2, \dots, X_N)), and a sequence of (M) integers (Y = (Y_1, Y_2, \dots, Y_M)). The task is to determine whether there exists an (N \times M) integer matrix (A) with entries between 1 and (N \times M) inclusive such that all entries are distinct, the maximum in row (i) equals (X_i), a ...

4.2 Greedy Algorithm 1) Greedy Approach The greedy algorithm is a method where at each step, the locally optimal choice is made in hopes of finding the global optimum. This approach divides the problem into steps and selects the best possible option at each stage. However, this does not guarantee the overall optimal solution. Greedy algorithms ...

Maximum Profit Scheduling Problem This problem addresses the optimization of sales revenue for a set of products, where each item possesses a specific profit margin and a hard expiration deadline. You possess a capacity to sell exactly one product per day. Once a product's deadline has passed, it cannot be sold. The objective is to determine th ...

A - Welcome to AtCoder Land This problem is a straightforward string comparison. We need to check if the first input string is "AtCoder" and the second input string is "Land". If both conditions are met, we output "Yes"; otherwise, we output "No". #include <iostream> #include <string> #includ ...

Fundamentals of Greedy Algorithms The core principle of a greedy algorithm is to make the locally optimal choice at each stage with the hope that these local choices will lead to a globally optimal solution. For instance, when counting currency, taking the largest denomination possible at each step ensures the minimum number of notes. Unlike d ...

Core Idea of Greedy Algorithms The essence of a greedy strategy is to build a globally optimal solution by repeatedly making locally optimal choices. The typical workflow involves: Breaking the problem into smaller subproblems. Determining a suitable greedy criterion. Obtaining the best posssible choice for each subproblem. Aggregating these l ...

738. Monotone Increasing Digits Problem Link: 738. Monotoen Increasing Digits Givan a non-negative integer N, find the largest number that is less than or equal to N and whose digits are monotonically increasing. An integer is monotonically increasing if for every adjacent pair of digits, x <= y. Example 1: Input: N = 10 Output: 9 Approach ...

Problem A: Maximum Value Boundary Analysis In this problem, we need to calculate the sum of counts $f(k)$ for pairs $(i, j)$ that satisfy specific boundary conditions related to two arrays $A$ and $B$. Let $f(k)$ represent the number of valid pairs where the second index $j$ equals $k$. We define $last\_k$ as the index where the maximum value o ...

Problem Statement Given three positive integers $n$, $x$, and $y$, we need to find the maximum size of a set $S$ satisfying: $S \subseteq {1, 2, \ldots, n}$ For any $a \in S$ and $b \in S$, $|a - b| \neq x$ and $|a - b| \neq y$ Output the maximum possible cardinality of $S$. Constraints: $1 \leq n \leq 10^9$, $1 \leq x, y \leq 22$ Observation ...

Problem 1: Lexicographical String Matching Solution Since the problem involves lexicographical order, a trie data structure is suitable. To find the solution, use a greedy approach. Determine if the string ending at the current node is the answer. If not, continue to traverse to one of the child nodes. The process is illustrated in the followi ...