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In a programming contest where we can attempt multiple problems but the contest ends when we solve one, we need to find the optimal strategy to maximize expected points. Given two lists points and chances of equal length, where chances[i] represents the percentage chance of solving problem i for points[i] points, and k representing the maximum problems we can attempt. The expected value of attempting the ith problem is points[i] * chances[i] / 100.0. We need to find the optimal strategy that maximizes expected points. Algorithm Approach We use dynamic programming with the following strategy: ... Read More
We need to find the minimum cost to purchase exactly one of every item from 0 to N-1. We have sets that contain ranges of items with purchase costs, and removals that let us discard extra items for a fee. This problem can be solved using Dijkstra's shortest path algorithm by modeling it as a graph where each node represents the number of items we need to collect. Understanding the Problem Given: sets: Each set [start, end, cost] lets us buy items from start to end (inclusive) for the given cost removals: Cost to remove one ... Read More
In Python, we can solve the problem of finding strings of the same size with specific constraints using dynamic programming with memoization. Given a string and a maximum allowed consecutive character count, we need to find how many strings are lexicographically smaller or equal to the input string while satisfying the consecutive character limit. Problem Understanding Given a string s of lowercase letters and an integer k, we need to count strings that: Have the same length as s Are lexicographically smaller than or equal to s Have no more than k consecutive equal characters ... Read More
Suppose we have two values p and q, we have to find the number of unique squares that can be generated from a grid with p rows and q columns in which the points are placed evenly. If the answer is very large return result mod 10^9 + 7. In this problem, a square is a set of 4 points that form the four vertices of a square. The sides of the square must have the same length, and it does not always have to be aligned with the axes of the grid. So, if the input is ... Read More
A tree has special nodes where every node in its subtree has a unique color. Given an n-ary tree as an adjacency list and node colors, we need to count how many nodes are special. For each node i: tree[i] contains its children and parent color[i] represents its color value A node is "special" if all nodes in its subtree (including itself) have distinct colors ? Example Consider this tree structure: .node-circle { fill: #e3f2fd; stroke: #1976d2; ... Read More
Given a list of words, we need to check if they can be chained to form a circle. A word A can be placed before word B if the last character of A matches the first character of B. Each word must be used exactly once. For example, with words = ["ant", "dog", "tamarind", "nausea", "gun"], we can form: ant → tamarind → dog → gun → nausea → ant (circle completed). Algorithm This problem is solved using graph theory concepts ? Build a directed graph where each character is a node Add edges from ... Read More
Suppose we have a 2D matrix named edges, that represents an undirected graph. Every item in the matrix edges represents an edge and is of the form (u, v, w). This means nodes u and v are connected and the edge has the weight w. We also have integers a and b, that represent an edge (a, b). We have to find out if the edge (a, b) is part of a minimum spanning tree. Note − the graph has to be connected and the edge (a, b) exists in the graph. So, if the input is like ... Read More
Suppose we have a 2D matrix and another value k. Our goal is to return a matrix that contains the minimum values of all k x k sub-matrices. So, if the input is like ? 3 5 6 8 6 5 ... Read More
Given a list of numbers, we need to find the sum of widths of all subsequences. The width of a subsequence is the difference between its maximum and minimum elements. We'll calculate this sum modulo 10^9 + 7 to handle large results. So, if the input is like nums = [7, 4, 9], then the output will be 15. The subsequences are: [7], [4], [9], [7, 4], [7, 9], [4, 9], [7, 4, 9] with widths 0, 0, 0, 3, 2, 5, 5 respectively, giving us a sum of 15. Algorithm To solve this efficiently, we follow ... Read More
Given a list of numbers, we can delete at most one element to maximize the number of sublists containing both the maximum and minimum values of the resulting list. This problem requires analyzing different scenarios when removing elements. Problem Understanding For the input nums = [3, 2, 6, 2, 4, 10], if we remove 10, we get [3, 2, 6, 2, 4] where min=2 and max=6. There are 8 sublists containing both values ? [2, 6] at indices (1, 2) [6, 2] at indices (2, 3) [2, 6, 2] at indices (1, 3) [3, 2, 6] ... Read More