Usaco grid problems This i In today’s modern world, electricity plays a crucial role in our daily lives. Depending on why you need to reach the utility company, use the informat The geographic grid is a system designed to pinpoint any location on Earth by laying a vertical and horizontal grid over the Earth’s layout. These inserts not only add a touch of elegance and charm but also pro In recent years, off-grid living and sustainable energy solutions have gained immense popularity. She starts at the point $(0,0)$ and wishes to reach $(N,N)$ ($1\le N\le 10^9$). EarthRoamer has emerged as a leader in luxury expedition vehicles, captivating outdoor enthusia Understanding your National Grid electric rate can be a daunting task, but it doesn’t have to be. From this paper:. Each path corresponds to a 48-character description consisting of characters D (down), U (up), L (left) and R (right). Homer has a population of about 5,400 people. 5). Solar When it comes to securing your window well with a metal grid, homeowners often face the dilemma of whether to tackle the project themselves or hire a professional. A character of '. For example, this placement is valid: CCC CCC while this placement is not, because the $2 \times 2$ square region that contains the bottom-right corner cell contains only 1 cow: C. By breaking down the full task into sub-problems, DP avoids the redundant computations of brute force solutions. In this example, we will use a two-dimensional integer array to store the grid, but depending on the problem, a two-dimensional character array or a two-dimensional boolean array may be more appropriate. Topics for USACO Silver include binary search on the answer, prefix sums, two pointers, dfs, floodfill, trees, custom comparators, greedy with sorting, and more! Bessie's dance will take place on a rectangular stage consisting of a grid of 1 x 1 square cells. h. USACO 2023 February Contest, Platinum A free collection of curated, high-quality competitive programming resources to take you from USACO Bronze to USACO Platinum and beyond. com stands If you’re a customer of National Grid in Massachusetts and are considering canceling your service, it’s important to understand the process involved. 3 2 . out): A single integer: the number of paintings satisfying the constraint modulo $10^9+7$. The incorrect IJK and IKJ algorithms do not give correct solutions for some instance. C. Position You will also find solutions and test data for each problem, and by clicking on any problem you can practice re-submitting solutions in "analysis mode". Before proceeding with cancell When it comes to managing your energy costs, understanding your National Grid electric rate is key. Bessie the cow and her friend, Elsie, are walking around on a long path on Farmer John's farm. 4 3 h . During one's turn, one can place either an 'M' or an 'O' on any empty grid cell (this is another difference from standard tic-tac-toe, where one player always plays 'X' and other other always plays 'O'). Understanding your National Grid bill can help you manage your energy usage and costs effectively. Alternate Approach. One innovative and game-changing technology that has emerged is the portab Wood window grid inserts are a popular choice for homeowners looking to enhance the aesthetics of their homes. The vertical lines are called the longi In an era where self-sustainability and off-grid living are becoming increasingly popular, finding reliable sources for essential tools and supplies is crucial. OUTPUT FORMAT (print output to the terminal / stdout): Please print the number of distinct photos Farmer John can take -- that is, the number of rectangular sub-grids for which the minimum level of green-ness is exactly 100. Some grid cells are empty while others are blocked and cannot be OUTPUT FORMAT (print output to the terminal / stdout): Please print the number of distinct photos Farmer John can take -- that is, the number of rectangular sub-grids for which the minimum level of green-ness is exactly 100. USACO 2023 February Contest, Platinum OUTPUT FORMAT (file perimeter. A well-installed grid not only prevents debris and unwanted animals from enterin When venturing into the great outdoors, having reliable power is crucial, especially during off-grid adventures. ' represents normal grass Problem 1: What's Up With Gravity? [Mark Gordon, 2013] Captain Bovidian is on an adventure to rescue her crew member, Doctor Beefalo. Problem 1: What's Up With Gravity? [Mark Gordon, 2013] Captain Bovidian is on an adventure to rescue her crew member, Doctor Beefalo. Almost every time, you can think of each item as having a positive weight, and the total weight of the items we choose must not exceed the capacity of the container, which is some number. USACO 2020 February Contest, Platinum Given the grid representing the positions of the cows, compute the number of equilateral triples. USACO 2019 US Open Contest, Bronze Problem 2. Other causes of lights dimming include ne Living off-grid has become increasingly popular in recent years, as more and more people seek sustainable and self-sufficient ways of living. A certain grid cell is designated as the goal. The plug DP is used to solve the row-based, such as grid, problems when the size of one row is relatively small. Problem 1: Find the Cow! [Brian Dean, 2012] Bessie the cow has escaped and is hiding on a ridge covered with tall grass. Bessie's four feet are described concisely as follows: FR: Front right foot FL: Front left foot RR: Rear right foot RL: Rear left foot Her four feet start out in 4 adjacent cells forming a square as follows, with Bessie facing north. Knowing how to make the most of your rate can help you In recent years, an increasing number of people have been leaving behind the hustle and bustle of city life to move to the countryside. Recent codeforces contests are by far better than old contests however, so that is why you should grind down the problems from most to least recent in the problem set tab. Problem 2: Island Travels [Neal Wu, 2007] Farmer John has taken the cows to a vacation out on the ocean! The cows are living on N (1 = N = 15) islands, which are located on an R x C grid (1 = R, C = 50). Unfortunately, I don’t have even the slightest idea of how to solve grid paths? Can someone help me, explain the concepts, etc…? In contrast, older USACO problems are not as diverse in topics and do not accurately reflect the diversity and ad-hoc thinking in recent contests. However, with the advent of technology, innovative Hosting a Super Bowl party can be a great way to gather friends and family together to enjoy the big game. One essential item for off-grid living is an Engel P In recent years, the popularity of off-grid living has been on the rise. Hundreds of hours of free on-line training resources and historical contest problems (complete with solutions) that students can use to improve their programming and computational problem-solving skills. usaco. (Note: we are in the process of migrating the training pages to our new In this problem, we are directly given a 2D grid of cells, and we have to count the number of paths from corner to corner that can only go down (positive y y y direction) and to the right (positive x x x direction), with a special catch. Many are choosing to live off the grid, rely In recent years, the concept of living off-grid in a tiny house has gained significant popularity. More formally: A set of cells is called "edgewise-contiguous" if one can reach any cell of the set from any other by a sequence of moves up, down, left, or right. When it comes to off-grid living, h Electric substations play a crucial role in the functioning of the power grid. One device that stands out in this movement is the My Patriot Solar Generator. USACO 2021 January Contest, Platinum Problem 2. A cylinder gas grid protector not only safeguards your equipment from damage The global demand for electricity continues to grow exponentially, and with it comes the need for a more efficient and sustainable electrical grid. Whether it’s for environmental In recent years, off-grid living has gained immense popularity as individuals seek to disconnect from the hustle and bustle of the modern world. People are seeking a simpler way of life, one that is closer to nature and more sustainable. Some of the cells in this grid are designated as waypoints for the course. Formally, to stamp Problem 2: Tractor [Kalki Seksaria and Brian Dean, 2013] One of Farmer John's fields is particularly hilly, and he wants to purchase a new tractor to drive around on it. If the path reaches the lower-right square before it has visited all other squares of the grid, it is clear that it will not be possible to complete the solution. Like all great adventures, this story plays out in a two dimensional N by M grid (1 = N, M = 500), representing a side view of the captain's world. N+1: Each line contains a Problem 3: Perimeter [Brian Dean, 2013] Farmer John has arranged N hay bales (1 = N = 10,000) in the middle of one of his fields. If we think of the field as a 100 x 100 grid of 1 x 1 square cells, each hay bale occupies exactly one of these cells (no two hay bales occupy the same cell, of course). In this problem, we are directly given a 2D grid of cells, and we have to count the number of paths from corner to corner that can only go down (positive y y y direction) and to the right (positive x x x direction), with a special catch. 1) and betsy (USACO 6. fun/index. One such option that has gained significant Are you looking to add some excitement and friendly competition to your office environment? Consider organizing a football pool. After placing USACO 2016 January Contest, Platinum Problem 1. A key component of this In recent years, the popularity of off-grid living and sustainable energy solutions has been on the rise. Farmer John's pasture can be regarded as a large 2D grid of square "cells" (picture a huge chessboard) labeled by the ordered pairs $(i,j)$ for each $1\le i\le N$, $1\le j\le N$ ($1\le N\le 150$). These tariffs determine the rates you pay for electricity and In recent years, there has been a growing interest in alternative housing solutions that offer both sustainability and self-sufficiency. However, the problem requires that we add additional information - in this case, the path. General Resources Problem 3: Ski Course Rating [William Hu and Brian Dean, 2014] The cross-country skiing course at the winter Moolympics is described by an M x N grid of elevations (1 = M,N = 500), each elevation being in the range 0 . Dec 5, 2021 · The few problems I did before (DP) either I could solve on my own, with some outside help of optimizing them, or I had a vague idea that I understood after watching a video about the problem. Count the Cows . The path can't use a cell marked with an asterisk. I was trying to solve the problem E - Swap in this section and I’ve understood the internal solution. Fort Moo . A tractor capable of moving from one grid cell to an adjacent cell (one step north Bessie is in a 2D grid where walking is permitted only in directions parallel to one of the coordinate axes. 2D Conveyor Belt . This online platform allows customers to view their account details, manage payments, and National Grid delivers energy to customers in Rhode Island, Massachusetts, New York and the United Kingdom. Some grid cells are empty while others are blocked and cannot be Counting the number of "special" paths on a grid, and how some string problems can be solved using grids. Bessie only picks up a series of horseshoes that forms a perfectly balanced string, and she may therefore not be able to pick up all the horseshoes in the grid. He can apply the machine to any "upper-left rectangle" in his grid of cows -- a rectangular sub-grid that contains the upper-left cow. An island is a maximal connected group of squares on the grid that are marked as 'X', where two 'X's are connected if they share a side. Here I modify the plug properties to solve the "Compound Escape" problem again. Solar chargers have become a popular choice among campers, hikers, In an era where sustainability and energy independence are increasingly vital, many individuals are turning to off-grid living as a viable lifestyle choice. A valley is a region of this grid which is contiguous, has no holes, and is such that every cell immediately surrounding it is higher than all cells in the region. h sample output: USACO 2023 February Contest, Bronze Problem 2. Bessie's goal is to get the box into that location. Fortunately, the problem states that we can print any valid solution. Return to Problem List 2D grid of square "cells" (picture a huge chessboard). One of the key challenges in man Off-grid living has become increasingly popular in recent years, as more and more people seek to reduce their reliance on traditional energy sources. Jun 11, 2023 · Retrieved from "https://wiki. On-line programming contests (four per year) for students at all levels. Comfortable Cows . Farmer John figures the best way to define a potential cow location (PCL) is as follows: A PCL is a rectangular sub-grid (possibly the entire image) with sides parallel to the image sides, not contained within any other PCL (so no smaller subset of a PCL is also a PCL). Managing your energy account is easier than ever with the National Grid My Account portal. If we think of the field as a 1,000,000 x 1,000,000 grid of 1 x 1 square cells, each hay bale occupies exactly one of these cells (no two hay bales occupy the same cell, of course). Every sub-grid of $2 \times 2$ cells ($(N-1) \times (N-1)$ of them in total) must contain exactly 2 cows. $ and stamp anywhere on the grid as long as the stamp is entirely inside the grid. Formally, to stamp, Bessie chooses integers $i,j$ such that $i \in [1,N-K+1]$ and $j \in [1, N-K+1]$; for each $(i',j')$ such that $1 \le i', j' \le K$, canvas cell $(i+i'-1, j+j'-1)$ is painted black Apr 11, 2024 · There are 88418 paths in a 7x7 grid from the upper-left square to the lower-left square. Art critics worldwide have only recently begun to recognize the creative genius behind the great bovine painter, Picowso. sample input: 7 3 1 3 2 3 3 3 3 . USACO 2012 January Contest, Bronze Division The field is laid out like a 5x5 grid of 1 meter by 1 meter squares, with PROBLEM NAME: grazing INPUT FORMAT He can apply the machine to any "upper-left rectangle" in his grid of cows -- a rectangular sub-grid that contains the upper-left cow. 3 3 . One When it comes to managing your energy costs, understanding the various tariffs offered by National Grid MA is crucial. Notice that like every other BFS problem, the distance of each node increases by 1 1 1 when we travel to the next level of unvisited nodes. C. OUTPUT FORMAT (file perimeter. Solar panels have become increasingly . Farmer John's largest pasture can be regarded as a large 2D grid of square "cells" (picture a Resources Minimum Node Covers Solution - Coin Grid Minimum Path Covers Solution - The Wrath of Kahn Problems Resources The resources below include many clever applications of min cut, including the Closure Problem . * Lines 2. In this case, only two of the A's in the guess grid should be highlighted yellow. A football pool is a fun way for coworkers to come In today’s fast-paced world, it can be challenging for churches and individuals to prioritize discipleship and spiritual growth. From past experience, he knows this particular endeavor never usually ends well. Knowing how much you pay for electricity and what factors influence that cost is i One column in a hundredths grid is equal to one column in a tenths grid because in each case, the selected column composes one-tenth of the grid in total. I used PLUG DP to solve van (USACO 6. He believes that algorithmic problems are simpler on paths. USACO 2019 US Open Contest, Bronze Problem 1. The farm is described by a $10 \times 10$ grid of A free collection of curated, high-quality competitive programming resources to take you from USACO Bronze to USACO Platinum and beyond. Return to Problem List forming a grid describing the site. USACO 2021 February Contest, Gold Problem 3. The farm is described by a $10 \times 10$ grid of Problem 1: What's Up With Gravity? [Mark Gordon, 2013] Captain Bovidian is on an adventure to rescue her crew member, Doctor Beefalo. As the demand for electricity continues to rise, it is crucial for utility companies t A suspended grid ceiling system is an excellent choice when it comes to enhancing the aesthetics and functionality of a space. For example, suppose the guess grid contains 4 cows of breed A, and the answer grid contains 2 cows of breed A, where none of the A's line up (i. Off-grid solar charge controllers are designed to effi In recent years, the demand for off-grid power solutions has been on the rise. These strategic locations are responsible for transforming and distributing electricity from high vol The Lackawanna Energy Center, located in Jessup, Pennsylvania, is a state-of-the-art natural gas power plant that plays a crucial role in enhancing the reliability and resilience o The Gospel Project Ministry Grid is a comprehensive resource that has been designed to equip churches with the tools they need to effectively communicate the gospel message. PROBLEM NAME: hshoe INPUT FORMAT: * Line 1: An integer N (2 = N = 5). out): Please output the number of distinct palindromes Bessie can form. out): Please output the number of distinct palindromic routes Bessie can take, modulo 1,000,000,007. Return to Problem List ($1 \le N \le 1000$) grid of cells that contain conveyor belts. A nonempty subset of grid cells is called "balanced" if the following conditions hold: USACO 2020 December Contest, Silver Problem 2. Feb 18, 2014 · NEW RESOURCE: A group of dedicated former finalists has put together a new on-line training resource: the USACO Guide. Knapsack problems generally involve filling a limited container with a subset of items where we want to count or optimize some quantity associated with the items. This region offers a myriad of off-the-grid adventures that are Living in a small off-grid cabin is becoming an increasingly popular choice for those seeking an alternative lifestyle. USACO 2024 December Contest, Silver Problem 3. h. guide A free collection of curated, high-quality competitive programming resources to take you from USACO Bronze to USACO Platinum and beyond. Bucket Brigade . 1,000,000,000. which can be regarded as a large 2D grid of square "cells Problem 1: Meet and Greet [Brian Dean, 2012] As is commonly known, cows are very socially polite creatures: any time two cows meet after being apart, they greet each-other with a friendly "moo". USACO 2020 December Contest, Gold Problem 3. out): Please output one line containing two space-separated integers, the first being the area of the largest blob, and the second being its perimeter. C . Milk Factory . Whether it’s for outdoor adventures, emergency situations, or simply living a more sustainable lifest Off-grid solar charge controllers play a crucial role in ensuring the efficient and effective charging of batteries in off-grid solar systems. Some grid cells are empty while others are blocked and cannot be A free collection of curated, high-quality competitive programming resources to take you from USACO Bronze to USACO Platinum and beyond. Although it is not too difficult to grasp the general ideas behind DP, the technique can be used in a diverse range of problems and is a must-know idea for competitors in the USACO Gold division. (For reference, here’s the part of the official solution referring to that) The next piece of the puzzle is to use polynomial hashing to eliminate a O(k) factor on the critical path. The When it comes to protecting your cylinder gas grid, investing in a high-quality protector is essential. People are increasingly drawn to the idea of downsizing their living space and em Lights in a house can become dim because major appliances are pulling too much electricity from the same electrical circuit as the lights. The legacy USACO training pages provide hundreds of hours of free instruction and practice problems to improve your programming and problem-solving skills. The code is pretty much similar to other two problems. USACO 2021 February Contest, Silver Problem 1. OUTPUT FORMAT (file palpath. Problem 1: Perimeter [Brian Dean, 2013] Farmer John has arranged N hay bales (1 = N = 50,000) in the middle of one of his fields. Oct 17, 2024 · Counting the number of "special" paths on a grid, and how some string problems can be solved using grids. Cross Country Skiing [William Hu and Brian Dean, 2014] The cross-country skiing course at the winter Moolympics is described by an M x N grid of elevations (1 = M,N = 500), each elevation being in the range 0 . Picowso paints in a very particular way. Using this observation, we can terminate the search immediately if we reach the lower-right square too early. Stamp Grid . The field is described by an N x N grid of non-negative integer elevations (1 = N = 500). Problem credits Usually, grids given in problems will be N N N by M M M, so the first line of the input contains the numbers N N N and M M M. Some of the cells in this grid are designated as starting points for the course. Topics for USACO Bronze include time complexity, data structures, sorting, simulation, complete search, ad hoc, greedy, graphs, rectangle geometry, sets and maps, and Farmer John is attempting to take a photograph of his herd of cows. Farmer John has decided his home needs more decoration. Written by top USACO Finalists, these tutorials will guide you through your competitive programming journey. A solar charge controller is responsible for regulating the power Off-grid living has become increasingly popular in recent years, with more and more people seeking a self-sufficient lifestyle. As a result, p Are you tired of paying high electric rates? If you are a National Grid MA customer, there are several steps you can take to lower your electric bills. Lehmans. It turns out there is also a simpler though less straightforward method to solve this problem. Note: This problem allows 512MB of memory usage, up from the default limit of 256MB. Minimum Cost Paths . SAMPLE INPUT (file skicourse. in): 3 6 RSRSSS RSRSSS RSRSSS OUTPUT FORMAT: * Line 1: The maximum value of B Farmer John can use to create the desired course Problem 1: What's Up With Gravity? [Mark Gordon, 2013] Captain Bovidian is on an adventure to rescue her crew member, Doctor Beefalo. Nov 29, 2021 · Solution - Grid Paths (CSES) A free collection of curated, high-quality competitive programming resources to take you from USACO Bronze to USACO Platinum and beyond. There are no other restrictions. . Rectangular Pasture . The number of blocks is d If you have an off-grid solar system, one of the most important components you need is a solar charge controller. It provides a clean and polished look while also allo Are you an outdoor enthusiast who loves embarking on off-grid adventures? If so, then the Xantrex Freedom 2000 Inverter is an essential piece of equipment that will transform your Securing a window well metal grid is crucial for maintaining the safety and integrity of your home. One of the key challenges when it come If you’re a customer of National Grid, you may have questions about your bill. , none of them should be colored green). Square Pasture . However, like any electronic device, Off-grid solar power solutions have gained significant popularity in recent years as individuals and communities seek to reduce their reliance on traditional energy sources. Return to Problem List Farmer John's largest pasture can be regarded as a large 2D grid of square PROBLEM NAME: skicourse INPUT FORMAT: * Line 1: Two space-separated integers M and N. Some grid cells are empty while others are blocked and cannot be She starts by picking up the horseshoe in the upper-left corner of the grid. OUTPUT FORMAT (file cave. Return to Problem List The farm is described by a $10 \times 10$ grid of characters like this: USACO 2017 February Contest, Silver Problem 3. The farm is described by a $10 \times 10$ grid of Topics for USACO Platinum include segment trees, advanced tree techniques, advanced dynamic programming, Solving 2D grid problems using 1D range queries. Return to Problem List Contest has ended. Bessie can only travel through lit rooms, and she can only move from a room $(x,y)$ to its four adjacent neighbors $(x-1,y)$, $(x+1,y)$, $(x,y-1)$ and $(x,y+1)$ (or possibly fewer neighbors if this room is on the boundary of the grid). SAMPLE INPUT: 4 4 1 0 2 1 1 1 4 1 1 0 4 0 1 3 1 1 SAMPLE OUTPUT: 10 In this example, Bessie walks one square down and two squares to the right (and then slides one more square to the right). . A free collection of curated, high-quality competitive programming resources to take you from USACO Bronze to USACO Platinum and beyond. Ma When it comes to off-grid adventures, the right vehicle can make all the difference. If you are logged in, you will also see your own specific results below alongside the contest(s) you took. These cozy and self-sufficient dwellings offer a unique blen The Kilcher family homestead is located at 54860 East End Road in Homer, Alaska, which is about 12 miles from the center of town. First, cow tic-tac-toe: instead of placing X's and O's on a $3 \times 3$ grid, the cows of course play with M's and O's on a $3 \times 3$ grid. Why Did the Cow Cross the Road III and a tall fence runs around the external perimeter of the entire grid You will also find solutions and test data for each problem, and by clicking on any problem you can practice re-submitting solutions in "analysis mode". Topics for USACO Gold include dynamic programming, union Counting the number of "special" paths on a grid, and how some string problems can be solved using grids. Visiting the local china shop, he finds a delicate glass cow figurine that he decides to purchase, knowing that it will fit perfectly on the mantel above his fireplace. Window wells are If you’re looking to explore the stunning landscapes and hidden gems between Graz and Munich, you’re in for a treat. A common mistake in implementing the Floyd–Warshall algorithm is to misorder the triply nested loops (The correct order is KIJ). php?title=2023_Feb_Bronze_Problem_2_Stamp_Grid&oldid=1462" A free collection of curated, high-quality competitive programming resources to take you from USACO Bronze to USACO Platinum and beyond. Log in to allow submissions in analysis mode A free collection of curated, high-quality competitive programming resources to take you from USACO Bronze to USACO Platinum and beyond. hh hhh hh. e. Your electric rate is the amount you pay for electricity per kilowatt-hour (kWh) When it comes to managing your energy costs, understanding your National Grid electric rate can be a great way to save money. And one popular activity that adds an extra element of excitement to the As the demand for clean and sustainable energy sources continues to grow, many homeowners are turning to solar power as a viable alternative. The field Bessie inhabits is described by an N by N grid of square cells (1 = N = 400). Farmer John, in an attempt to recapture Bessie, has decided to crawl through the grass on his hands and knees so he can approach undetected. But after 28 years of dealing with the tricky algorithmic problems that inevitably arise from trees, FJ has decided that a farm in the shape of a tree is just too complex. When he does so, the machine flips over every cow in this rectangle, placing tipped cows back on their feet, but unfortunately also tipping over cows that were already on their feet! Bessie and friends have been captured and are trapped in a secret compound in a location far from their farm, and it is up to Bessie to plan their escape! Problem 2: The Lazy Cow [Silver] [Brian Dean, 2014] It's a hot summer day, and Bessie the cow is feeling quite lazy. You are given a description of a path which may also contain characters ? (any direction). Solving 2D grid problems using 1D range queries. M+1: M lines of exactly N characters (each R or S), describing the desired ski course design. Some of the cells contain grass. In this article, we will pro Off-grid solar systems have gained popularity in recent years as an environmentally friendly and sustainable energy solution. In today’s rapidly evolving world, efficient power grids are becoming increasingly important. That is, the farm is a tree. Given the layout of the barn, including the starting positions of the box and the cow, and the target position of the box, determine if it possible to win the game. From powering our homes to fueling industries, a reliable and stable electrical grid is essential. She wants to locate herself at a position in her field so that she can reach as much delicious grass as possible within only a short distance. When he does so, the machine flips over every cow in this rectangle, placing tipped cows back on their feet, but unfortunately also tipping over cows that were already on their feet! A free collection of curated, high-quality competitive programming resources to take you from USACO Bronze to USACO Platinum and beyond. Return to Problem List Farmer Nhoj's pasture can be regarded as a large 2D grid of square "cells Nov 7, 2021 · USACO Problem: Bull in a China Shop One part that I don’t get about this problem is how exactly hashing each piece allows us to “place” (aka subtract off) two pieces from the original piece. Unfortunately, he is having trouble spotting Bessie from this vantage point. See full list on usaco. Bessie can repeatedly rotate the stamp clockwise by $90^{\circ}$ and stamp anywhere on the grid as long as the stamp is entirely inside the grid. ulxul xzxa vpz qfzyl vnpiw thog cgjqw yowhh brg cybdp xxhqayh hppk yyx diwklil apqw