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Suppose we are playing a unique game with three values n, k, and h. We start from 0 points, then we can select a number randomly between 1 and h (inclusive) and we will get that many points. We stop when we have scored a minimum of k points. We have to find the probability that we have n or fewer points when we stop. So, if the input is like n = 2, k = 2, h = 10, then the output will be 0.11. Algorithm Steps To solve this, we will follow these steps: ... Read More
Finding the longest sequence where all numbers have equal frequencies after removing at most one element is a complex frequency tracking problem. We need to monitor how frequencies change as we build the sequence and check if we can achieve uniform distribution. Problem Understanding Given a list of numbers, we want the longest prefix where we can remove at most one number to make all remaining numbers appear the same number of times ? # Example: [2, 4, 4, 7, 7, 6, 6] # All numbers appear twice, so we can use the entire sequence numbers ... Read More
Given a list of numbers, we can jump from index i to either i + nums[i] or i - nums[i] (if valid indices). We need to find the minimum jumps required from each position to reach a value with different parity (odd to even or even to odd). If the input is numbers = [7, 3, 4, 5, 6, 9, 6, 7], the output will be [-1, 1, 2, -1, -1, -1, 1, -1]. Understanding the Problem For each starting position, we use BFS to find the shortest path to any number with different parity. Two numbers ... Read More
Suppose we have an infinite grid of water. We can add blocks of land to that grid one by one. We have a list of coordinates called land_requests where each coordinate is in the form [r, c] where r is for row and c is for column. We need to find a list where each element represents the number of islands that exist after adding each block of land from land_requests. For example, if the input is land_requests = [[1, 1], [2, 4], [1, 2], [1, 4], [1, 3]], then the output will be [1, 2, 2, 2, 1]. ... Read More
Given a 2D matrix and a value k, we need to find the largest sum of a rectangle whose sum is at most k. This problem combines matrix manipulation with optimization techniques. Problem Understanding Consider this matrix with k = 15: 5 -2 7 10 We can form rectangles like [5, 7] with sum = 12, [5, -2, 7, 10] with sum = 20, etc. The largest sum ≤ 15 is 12. Algorithm Steps For each pair of rows (i1, i2), compress the matrix vertically Convert the ... Read More
Suppose we have a list of numbers called nums and another value k, we have to find the largest average value of any sublist whose length is at least k. So, if the input is like nums = [2, 10, -50, 4, 6, 6] and k = 3, then the output will be 5.33333333, as sublist [4, 6, 6] has the largest average value. Algorithm Steps To solve this, we will follow these steps − Initialize left := minimum of nums, right := maximum of nums Calculate initial sum ... Read More
Suppose we have two values n and k. We need to consider a list of numbers in range 1 through n [1, 2, ..., n] and generate every permutation of this list in lexicographic order. For example, if n = 4 we have [1234, 1243, 1324, 1342, 1423, 1432, 2134, 2143, 2314, 2341, 2413, 2431, 3124, 3142, 3214, 3241, 3412, 3421, 4123, 4132, 4213, 4231, 4312, 4321]. We have to find the kth value of this permutation sequence as a string. So, if the input is like n = 4, k = 5, then the output will be "1423" ... Read More
Suppose we have a string s containing digits from 0-9 and another number k. We need to find the number of different ways that s can be represented as a list of numbers from [1, k]. If the answer is very large, return result mod 10^9 + 7. So, if the input is like s = "3456", k = 500, then the output will be 7, as we can represent s like [3, 4, 5, 6], [34, 5, 6], [3, 4, 56], [3, 45, 6], [34, 56], [345, 6], [3, 456]. Algorithm Approach We'll use dynamic programming ... Read More
This problem involves finding the maximum coins we can collect by making two simultaneous journeys: one from top-left to bottom-right, and another from bottom-right back to top-left. We can only move right or down in the first journey, and left or up in the return journey. Problem Understanding The matrix contains three types of values: 0 for an empty cell 1 for a coin −1 for a wall (impassable) We need to maximize coin collection while ensuring we can complete both journeys. If either path is blocked, we return 0. Example Consider ... Read More
Suppose two players are playing a candy game where several candies are placed in a line. Person 1 is given a list of numbers called nums representing the point value of each candy. On each player's turn, they can pick 1, 2, or 3 candies from the front of the line, delete them from the list, and add their points to their score. The game ends when all candies are taken, and the player with the higher score wins. We need to determine if person 1 can win this game by playing optimally. Example Scenario If the ... Read More