# Jasmer Singh Sanjotra > Personal website of Jasmer Singh Sanjotra: research on causal reinforcement learning, world models, and machine learning for speech and signals, plus worked solutions to probability puzzles and competitive programming problems. Every writeup below links to its plain-Markdown version (the `.md` URL), which keeps the original LaTeX. The HTML page lives at the same path without `.md`, e.g. `/fun/probability/power-grid/`. Math on the HTML pages is rendered by KaTeX, so prefer the Markdown versions for reading formulas. ## About - [Home](https://thealphajas.github.io/): short bio and recent news - [CV](https://thealphajas.github.io/cv/): education, research experience, skills - [Publications](https://thealphajas.github.io/publications/): papers grouped by year - [Contact](https://thealphajas.github.io/contact/): email and profiles - [Academic CV (PDF)](https://thealphajas.github.io/Academic_CV.pdf) ## Publications - [Investigating the Relationship between Objective AI-Driven Metrics and Subjective MOS for In-the-Wild Speech](https://doi.org/10.21437/Interspeech.2026-2203). Jasmer Sanjotra, Nagendra Kumar, Shekhar Nayak. INTERSPEECH 2026 (main track), 2026. - [T-MPEDNet: Unveiling the Synergy of Transformer-aware Multiscale Progressive Encoder-Decoder Network with Feature Recalibration for Tumor and Liver Segmentation](https://doi.org/10.1016/j.bspc.2025.108225). Chandravardhan Singh Raghaw, Jasmer Singh Sanjotra, Mohammad Zia Ur Rehman, Shubhi Bansal, Shahid Shafi Dar, Nagendra Kumar. Biomedical Signal Processing and Control, Volume 110, 2025. - [Ethical framework for responsible foundational models in medical imaging](https://doi.org/10.3389/fmed.2025.1544501). Debesh Jha, Gorkem Durak, Abhijit Das, Jasmer Sanjotra, Onkar Susladkar, Suramyaa Sarkar, Ashish Rauniyar, Nikhil Kumar Tomar, Linkai Peng, Sirui Li, Koushik Biswas, et al.. Frontiers in Medicine, Volume 12, 2025. - [MNet-SAt: A Multiscale Network with Spatial-enhanced Attention for Segmentation of Polyps in Colonoscopy](https://doi.org/10.1016/j.bspc.2024.107363). Chandravardhan Singh Raghaw, Aryan Yadav, Jasmer Singh Sanjotra, Shalini Dangi, Nagendra Kumar. Biomedical Signal Processing and Control, Volume 102, 2025. - [LSTMSE-Net: Long Short Term Speech Enhancement Network for Audio-visual Speech Enhancement](https://doi.org/10.21437/AVSEC.2024-8). Arnav Jain*, Jasmer S. Sanjotra*, Harshvardhan Choudhary, Krish Agrawal, Rupal Shah, Rohan Jha, MD Sajid, Amir Hussain, M. Tanveer. 3rd COG-MHEAR Workshop on Audio-Visual Speech Enhancement (AVSEC), ISCA, 2024. ## Blogs (2) - [Monotonic Search with Non-Uniform Priors?](https://thealphajas.github.io/fun/blogs/monotonic-search-with-non-uniform-priors.md): Binary search always queries the midpoint — but that's only optimal when you're clueless about where the answer lies. Here's the information-theoretic argument for querying the median of your belief instead. - [I showed why binary has to be the way it is.. in a way](https://thealphajas.github.io/fun/blogs/why-binary-has-to-be-the-way-it-is.md): Put three natural constraints on a place-value representation system and the powers of two are not a choice any more — they are forced. ## Probability Corner (34) - [Basketball Practice II](https://thealphajas.github.io/fun/probability/basketball-practice-ii.md): Frank makes his first free throw and misses his second free throw. The probability of making the nth free throw is equal to the proportion of free throws he… - [Breaking Stick](https://thealphajas.github.io/fun/probability/breaking-stick.md): A stick of length L drops and breaks at a random point distributed uniformly across the length. What is the expected length of the smaller part? - [Chess Tournament I](https://thealphajas.github.io/fun/probability/chess-tournament-i.md): A chess tournament has 128 players, each with a distinct rating. Assume that the player with the higher rating always wins against a lower rated opponent and… - [Comparing Flips II](https://thealphajas.github.io/fun/probability/comparing-flips-ii.md): You and your friend are playing a game with a fair coin, tossing it and writing down the outcomes. You win if HTH appears before HHT, else your friend wins… - [Confused Ant II](https://thealphajas.github.io/fun/probability/confused-ant-ii.md): An ant walks the corner of a 3D cube and moves to one of the three adjacent vertices with equal probability at each step. Find the expected number of steps… - [Consecutive Tails](https://thealphajas.github.io/fun/probability/consecutive-tails.md): A fair coin is flipped 10 times. What is the probability that any tails which occur, occur only in consecutive pairs? For instance, THHTTHHTTH fails because… - [Contracts and Pricing III](https://thealphajas.github.io/fun/probability/contracts-and-pricing-iii.md): After being caught in an embarrassing high-profile data fabrication scandal, Calambya University decides to stop sharing data with the national college… - [Decreasing Uniform Chain](https://thealphajas.github.io/fun/probability/decreasing-uniform-chain.md): Let X1, X2, … ~ Unif(0,1) IID. Let N be the first index n where Xn ≠ min {X1,…,Xn}. Find E[X_(N-1)], i.e. the smallest value among the first N-1 values… - [Dice-Coin Paradigm](https://thealphajas.github.io/fun/probability/dice-coin-paradigm.md): We flip a fair coin until we obtain our first tails. Given the first tails occurs on the nth flip, we roll a fair 6-sided die n times. Find the probability… - [Graph Search I](https://thealphajas.github.io/fun/probability/graph-search-i.md): You are given an undirected graph with 10 nodes. From every node, you are able to access any other node (including itself), all with an equal probability of… - [Graph Search II](https://thealphajas.github.io/fun/probability/graph-search-ii.md): You are given an undirected graph with 11 nodes. From every node, you are able to access any other node (not including itself), all with an equal probability… - [Intersecting Chords](https://thealphajas.github.io/fun/probability/intersecting-chords.md): 10 chords with uniformly randomly chosen endpoints are drawn on a circle. What is the expected number of intersections? - [Local Maxima](https://thealphajas.github.io/fun/probability/local-maxima.md): 14 pieces of paper labelled 1–14 are placed in a line at random. We spot i is a local maxima if the paper at the ith position is strictly larger than all of… - [Matching Die Trio](https://thealphajas.github.io/fun/probability/matching-die-trio.md): Three fair 6−sided dice are rolled and their upfaces are recorded. Find the probability that the values showing upon rolling all three dice again is the same… - [Mean babysitter](https://thealphajas.github.io/fun/probability/mean-babysitter.md): 10 kids are really hungry! Their babysitter has 12 units of food to give. However, she decides she only wants to give 4 of the children food. How many ways… - [Modified RNG](https://thealphajas.github.io/fun/probability/modified-rng.md): Jimmy picks a number uniformly at random from (0,1). If Jimmy chooses x, then Jon picks a number from (x,1) uniformly at random. If Y represents the number… - [Multinomial Expansion](https://thealphajas.github.io/fun/probability/multinomial-expansion.md): How many terms are there in the expansion of (x1 + x2 + x3 + x4 + x5 + x6)^18 after all like terms have been combined? - [Multinomial Sum](https://thealphajas.github.io/fun/probability/multinomial-sum.md): Find the sum of all multinomial coefficients: C(7; b1, b2, b3, b4) where b1 + b2 + b3 + b4 = 7 and each bi ≥ 0 is an integer. - [Optimal Bidders I](https://thealphajas.github.io/fun/probability/optimal-bidders-i.md): Carter has come into contact with a bounty of gold. He takes it to an auction shop. The shop tells him that every bidder will place a bid uniformly between… - [Overlapping Subsets](https://thealphajas.github.io/fun/probability/overlapping-subsets.md): Consider the set Ω = {1, 2, …, 20}. Two subsets A and B of Ω are uniformly at random selected from the power set of Ω, independently. It is possible that A =… - [Particle Reach](https://thealphajas.github.io/fun/probability/particle-reach.md): Consider a particle that performs a random walk on the integers starting at position 0. At each step, the particle moves from position i to position i+1 with… - [Party Groups](https://thealphajas.github.io/fun/probability/party-groups.md): There are 50 guests at a party and they are making groups for a game. To do this they each write their name on a piece of paper and put it into a hat. One by… - [Pass the ball](https://thealphajas.github.io/fun/probability/pass-the-ball.md): You and 4 other people are sitting in a circle. You are given a ball to start the game. Every second of this game, the person with the ball has three choices… - [Place or Take](https://thealphajas.github.io/fun/probability/place-or-take.md): You are playing a one-player game with two opaque boxes. At each turn, you can choose to either "place" or "take". "Place" places $1 from a third party into… - [Power Grid](https://thealphajas.github.io/fun/probability/power-grid.md): A 3 × 3 grid of light bulbs is formed. Then, each light bulb is powered on with probability 1/2. Find the probability that no two adjacent (grid cells that… - [Random Angle II](https://thealphajas.github.io/fun/probability/random-angle-ii.md): A right triangle is being formed with legs labeled A and B. The random lengths of legs A and B are both IID Uniform(0,1) random variables. Let θ be the angle… - [Random Ratio](https://thealphajas.github.io/fun/probability/random-ratio.md): p and q are two points chosen at random between 0 and 1. What is the probability that the ratio p/q lies between 1 and 2? - [Russian Roulette I](https://thealphajas.github.io/fun/probability/russian-roulette-i.md): You're playing a game of Russian Roulette with a friend. The six-chambered revolver is loaded with one bullet. Initially, the cylinder is spun to randomize… - [Russian Roulette II](https://thealphajas.github.io/fun/probability/russian-roulette-ii.md): You're playing a game of Russian Roulette with a friend. The six-chambered revolver is loaded with one bullet. Initially, the cylinder is spun to randomize… - [Show the Face](https://thealphajas.github.io/fun/probability/show-the-face.md): Roll a fair standard 6-sided die until a 6 appears. Given that the first 6 occurs before the first 5, find the expected number of times the die was rolled. - [Square Cross](https://thealphajas.github.io/fun/probability/square-cross.md): A square of side length 20 is placed in front of you. You select a point uniformly at random from its interior. Then, independently, a circle of radius R ~… - [Take and Roll II](https://thealphajas.github.io/fun/probability/take-and-roll-ii.md): You are given a fair 20-sided die and 100 actions in a game. The die starts with upface 1. The two options you can perform are to roll and to take. Performing… - [Differ by 2](https://thealphajas.github.io/fun/probability/differ-by-2.md): How many times do we have to roll a fair 6-sided die till we roll two numbers in a row that differ by 2? - [Exact 5 II](https://thealphajas.github.io/fun/probability/exact-5-ii.md): Abd continually rolls a fair 6-sided die until he obtains his first 6. What’s the expected number of times Abd rolls a 5 before he stops? ## CSES Problem Set (57) - [Apartments](https://thealphajas.github.io/fun/cses/apartments.md): Sort both arrays, then two-pointer sweep matching each applicant to the closest apartment within tolerance k. - [Array Division](https://thealphajas.github.io/fun/cses/array-division.md): Binary search on the maximum subarray sum, greedily checking whether that limit needs at most k subarrays. - [Building Roads](https://thealphajas.github.io/fun/cses/building-roads.md): Solution implementation - [Building Teams](https://thealphajas.github.io/fun/cses/building-teams.md): Solution implementation - [Collecting Numbers](https://thealphajas.github.io/fun/cses/collecting-numbers.md): Single pass over the positions array, counting how often the next number appears before the current one. - [Collecting Numbers II](https://thealphajas.github.io/fun/cses/collecting-numbers-ii.md): Maintain the round count from Collecting Numbers and update it incrementally after each swap by rechecking only the neighborhoods of the two swapped values. - [Concert Tickets](https://thealphajas.github.io/fun/cses/concert-tickets.md): Keep ticket prices in a multiset and use upper_bound to find the most expensive ticket within each customer’s budget. - [Counting Rooms](https://thealphajas.github.io/fun/cses/counting-rooms.md): Solution implementation - [Course Schedule](https://thealphajas.github.io/fun/cses/course-schedule.md): Solution implementation - [Dice Combinations](https://thealphajas.github.io/fun/cses/dice-combinations.md): Solution implementation - [Distinct Numbers](https://thealphajas.github.io/fun/cses/distinct-numbers.md): Insert every value into a map and read off the number of distinct keys. - [Distinct Values Subarrays](https://thealphajas.github.io/fun/cses/distinct-values-subarrays.md): Sliding window tracking the most recent duplicate position, counting subarrays ending at i with all distinct values. - [Distinct Values Subarrays II](https://thealphajas.github.io/fun/cses/distinct-values-subarrays-ii.md): Sliding window capped at k distinct values, growing and shrinking the window while summing valid subarray lengths. - [Distinct Values Subsequences](https://thealphajas.github.io/fun/cses/distinct-values-subsequences.md): Count value frequencies, then multiply (count + 1) across all values and subtract 1 for the empty subsequence. - [Dynamic Range Minimum Queries](https://thealphajas.github.io/fun/cses/dynamic-range-minimum-queries.md): Solution implementation - [Dynamic Range Sum Queries](https://thealphajas.github.io/fun/cses/dynamic-range-sum-queries.md): Solution implementation - [Edit Distance](https://thealphajas.github.io/fun/cses/edit-distance.md): Solution implementation - [Factory Machines](https://thealphajas.github.io/fun/cses/factory-machines.md): Binary search on time, checking whether all machines together can produce enough units by that time. - [Ferris Wheel](https://thealphajas.github.io/fun/cses/ferris-wheel.md): Two-pointer greedy: try to pair the lightest remaining person with the heaviest, otherwise seat the heaviest alone. - [Flight Discount](https://thealphajas.github.io/fun/cses/flight-discount.md): Solution implementation - [Flight Routes](https://thealphajas.github.io/fun/cses/flight-routes.md): Solution implementation - [Game Routes](https://thealphajas.github.io/fun/cses/game-routes.md): Solution implementation - [High Score](https://thealphajas.github.io/fun/cses/high-score.md): Solution implementation - [Josephus Problem I](https://thealphajas.github.io/fun/cses/josephus-problem-i.md): Simulate directly with an ordered set of survivors, walking k steps forward before each elimination. - [Josephus Problem II](https://thealphajas.github.io/fun/cses/josephus-problem-ii.md): Binary search over a segment tree of alive positions to jump straight to the k-th surviving person after each elimination. - [Longest Flight Route](https://thealphajas.github.io/fun/cses/longest-flight-route.md): Solution implementation - [Maximum Subarray Sum](https://thealphajas.github.io/fun/cses/maximum-subarray-sum.md): Kadane's algorithm: extend the running sum while it helps, and reset once it turns negative. - [Maximum Subarray Sum II](https://thealphajas.github.io/fun/cses/maximum-subarray-sum-ii.md): Prefix sums plus a sliding multiset of window-start prefix sums to bound the subarray length between a and b. - [Message Route](https://thealphajas.github.io/fun/cses/message-route.md): Solution implementation - [Minimizing Coins](https://thealphajas.github.io/fun/cses/minimizing-coins.md): Solution implementation - [Missing Coin Sum](https://thealphajas.github.io/fun/cses/missing-coin-sum.md): Sort the coins and greedily extend the reachable prefix sum, stopping at the first gap. - [Monsters](https://thealphajas.github.io/fun/cses/monsters.md): Solution implementation - [Movie Festival](https://thealphajas.github.io/fun/cses/movie-festival.md): Greedy interval scheduling: sort by end time and take a movie whenever it starts after the last one ends. - [Movie Festival II](https://thealphajas.github.io/fun/cses/movie-festival-ii.md): Greedy interval scheduling generalized to k halls, tracked as a multiset of k free end times. - [Nearest Smaller Values](https://thealphajas.github.io/fun/cses/nearest-smaller-values.md): Coordinate-compress the values and query a segment tree for the most recent earlier index holding a smaller value. - [Nested Ranges Check](https://thealphajas.github.io/fun/cses/nested-ranges-check.md): Sort ranges by (start, -end) and sweep once forward and once backward to mark containment. - [Nested Ranges Count](https://thealphajas.github.io/fun/cses/nested-ranges-count.md): Compress coordinates and sweep with a Fenwick-style segment tree to count containing and contained ranges. - [Playlist](https://thealphajas.github.io/fun/cses/playlist.md): Sliding window keeping the last-seen position of every song, shrinking the window whenever a repeat appears. - [Reading Books](https://thealphajas.github.io/fun/cses/reading-books.md): Sum all reading times, but double the longest book’s time if it alone exceeds the rest combined (parallel reading). - [Restaurant Customers](https://thealphajas.github.io/fun/cses/restaurant-customers.md): Sort arrivals and departures separately, binary searching departures to count customers still present at each arrival. - [Room Allocation](https://thealphajas.github.io/fun/cses/room-allocation.md): Sweep arrival/departure events in time order, assigning the smallest currently free room number. - [Round Trip](https://thealphajas.github.io/fun/cses/round-trip.md): Solution implementation - [Shortest Routes I](https://thealphajas.github.io/fun/cses/shortest-routes-i.md): Solution implementation - [Shortest Routes II](https://thealphajas.github.io/fun/cses/shortest-routes-ii.md): Solution implementation - [Static Range Minimum Queries](https://thealphajas.github.io/fun/cses/static-range-minimum-queries.md): Solution implementation - [Static Range Sum Queries](https://thealphajas.github.io/fun/cses/static-range-sum-queries.md): Solution implementation - [Stick Lengths](https://thealphajas.github.io/fun/cses/stick-lengths.md): Sort the sticks and align every stick to the median, which minimizes total absolute distance. - [Subarray Divisibility](https://thealphajas.github.io/fun/cses/subarray-divisibility.md): Prefix sums modulo n, counting subarrays with remainder 0 via combinatorics on matching remainders. - [Subarray Sums I](https://thealphajas.github.io/fun/cses/subarray-sums-i.md): Prefix sums with a hashmap of counts to find subarrays summing to a fixed target. - [Subarray Sums II](https://thealphajas.github.io/fun/cses/subarray-sums-ii.md): Same prefix-sum-and-hashmap approach as Subarray Sums I, extended to arrays with negative values. - [Sum of Four Values](https://thealphajas.github.io/fun/cses/sum-of-four-values.md): Fix the first two values, then two-pointer over the sorted remainder to complete the target sum. - [Sum of Three Values](https://thealphajas.github.io/fun/cses/sum-of-three-values.md): Fix the first value, then two-pointer over the sorted remainder to complete the target sum. - [Sum of Two Values](https://thealphajas.github.io/fun/cses/sum-of-two-values.md): Hashmap of value positions to find a complementary pair in one pass. - [Tasks and Deadlines](https://thealphajas.github.io/fun/cses/tasks-and-deadlines.md): Greedy: sort tasks by duration and process the shortest first to maximize total points from finish times. - [Towers](https://thealphajas.github.io/fun/cses/towers.md): Patience-sorting greedy: place each cube on the smallest existing tower it still fits on, else start a new tower. - [Traffic Lights](https://thealphajas.github.io/fun/cses/traffic-lights.md): Maintain a multiset of light positions and a parallel multiset of gap lengths, updating both as each new light is added. - [Weird Algorithm](https://thealphajas.github.io/fun/cses/cses-001.md): Simple simulation following the algorithm rules ## USACO / Competitive Programming (48) - [Cow Navigation](https://thealphajas.github.io/fun/usaco/usaco-001.md): USACO 2017 January Contest, Gold solution in C++. BFS with state representation including position, direction, and whether each cow has reached the goal - [C GCD On Blackboard](https://thealphajas.github.io/fun/usaco/c-gcd-on-blackboard.md): USACO Silver solution in C++ - [C Good Subarrays](https://thealphajas.github.io/fun/usaco/c-good-subarrays.md): USACO Silver solution in C++ - [D Irreducible Anagrams](https://thealphajas.github.io/fun/usaco/d-irreducible-anagrams.md): USACO Silver solution in C++ - [D Multiple Of 2019](https://thealphajas.github.io/fun/usaco/d-multiple-of-2019.md): USACO Silver solution in C++ - [D Running Miles](https://thealphajas.github.io/fun/usaco/d-running-miles.md): USACO Silver solution in C++ - [H Queries For Number Of Palindromes](https://thealphajas.github.io/fun/usaco/h-queries-for-number-of-palindromes.md): USACO Silver solution in C++ - [Haybale Stacking](https://thealphajas.github.io/fun/usaco/haybale-stacking.md): USACO Silver solution in C++ - [Maximum Subarray Sum](https://thealphajas.github.io/fun/usaco/maximum-subarray-sum.md): USACO Silver solution in C++ - [N Nusret Gökçe](https://thealphajas.github.io/fun/usaco/n-nusret-g-k-e.md): USACO Silver solution in C++ - [Problem 2 Farmer John's Favorite Operation](https://thealphajas.github.io/fun/usaco/problem-2-farmer-john-s-favorite-operation.md): USACO Silver solution in C++ - [Problem 2 Hoof Paper Scissors](https://thealphajas.github.io/fun/usaco/problem-2-hoof-paper-scissors.md): USACO Silver solution in C++ - [Problem 2 Rectangular Pasture](https://thealphajas.github.io/fun/usaco/problem-2-rectangular-pasture.md): USACO Silver solution in C++ - [Problem 2 Subsequences Summing To Sevens](https://thealphajas.github.io/fun/usaco/problem-2-subsequences-summing-to-sevens.md): USACO Silver solution in C++ - [Problem 2 The Lazy Cow](https://thealphajas.github.io/fun/usaco/problem-2-the-lazy-cow.md): USACO Silver solution in C++ - [Problem 2 Why Did The Cow Cross The Road II](https://thealphajas.github.io/fun/usaco/problem-2-why-did-the-cow-cross-the-road-ii.md): USACO Silver solution in C++ - [Problem 3 Breed Counting](https://thealphajas.github.io/fun/usaco/problem-3-breed-counting.md): USACO Silver solution in C++ - [Static Range Sum](https://thealphajas.github.io/fun/usaco/static-range-sum.md): USACO Silver solution in C++ - [Subarray Divisibility](https://thealphajas.github.io/fun/usaco/subarray-divisibility.md): USACO Silver solution in C++ - [Subarray Sums II](https://thealphajas.github.io/fun/usaco/subarray-sums-ii.md): USACO Silver solution in C++ - [A Maximum Distance](https://thealphajas.github.io/fun/usaco/a-maximum-distance.md): USACO Bronze solution in C++ - [Problem 1 Censoring Bronze](https://thealphajas.github.io/fun/usaco/problem-1-censoring-bronze.md): USACO Bronze solution in C++ - [Problem 1 Cow Gymnastics](https://thealphajas.github.io/fun/usaco/problem-1-cow-gymnastics.md): USACO Bronze solution in C++ - [Problem 1 Diamond Collector](https://thealphajas.github.io/fun/usaco/problem-1-diamond-collector.md): USACO Bronze solution in C++ - [Problem 1 FEB](https://thealphajas.github.io/fun/usaco/problem-1-feb.md): USACO Bronze solution in C++ - [Problem 1 Milk Pails](https://thealphajas.github.io/fun/usaco/problem-1-milk-pails.md): USACO Bronze solution in C++ - [Problem 1 Mixing Milk](https://thealphajas.github.io/fun/usaco/problem-1-mixing-milk.md): USACO Bronze solution in C++ - [Problem 1 Reflection](https://thealphajas.github.io/fun/usaco/problem-1-reflection.md): USACO Bronze solution in C++ - [Problem 1 Shell Game](https://thealphajas.github.io/fun/usaco/problem-1-shell-game.md): USACO Bronze solution in C++ - [Problem 1 Sleepy Cow Herding](https://thealphajas.github.io/fun/usaco/problem-1-sleepy-cow-herding.md): USACO Bronze solution in C++ - [Problem 1 Team Tic Tac Toe](https://thealphajas.github.io/fun/usaco/problem-1-team-tic-tac-toe.md): USACO Bronze solution in C++ - [Problem 1 The Lost Cow](https://thealphajas.github.io/fun/usaco/problem-1-the-lost-cow.md): USACO Bronze solution in C++ - [Problem 2 Block Game](https://thealphajas.github.io/fun/usaco/problem-2-block-game.md): USACO Bronze solution in C++ - [Problem 2 Bovine Genomics](https://thealphajas.github.io/fun/usaco/problem-2-bovine-genomics.md): USACO Bronze solution in C++ - [Problem 2 Circular Barn](https://thealphajas.github.io/fun/usaco/problem-2-circular-barn.md): USACO Bronze solution in C++ - [Problem 2 Counting Liars](https://thealphajas.github.io/fun/usaco/problem-2-counting-liars.md): USACO Bronze solution in C++ - [Problem 2 Daisy Chains](https://thealphajas.github.io/fun/usaco/problem-2-daisy-chains.md): USACO Bronze solution in C++ - [Problem 2 Speeding Ticket](https://thealphajas.github.io/fun/usaco/problem-2-speeding-ticket.md): USACO Bronze solution in C++ - [Problem 2 The Bovine Shuffle](https://thealphajas.github.io/fun/usaco/problem-2-the-bovine-shuffle.md): USACO Bronze solution in C++ - [Problem 2 The Bucket List](https://thealphajas.github.io/fun/usaco/problem-2-the-bucket-list.md): USACO Bronze solution in C++ - [Problem 3 Cow Tipping](https://thealphajas.github.io/fun/usaco/problem-3-cow-tipping.md): USACO Bronze solution in C++ - [Problem 3 Load Balancing](https://thealphajas.github.io/fun/usaco/problem-3-load-balancing.md): USACO Bronze solution in C++ - [Problem 3 Measuring Traffic](https://thealphajas.github.io/fun/usaco/problem-3-measuring-traffic.md): USACO Bronze solution in C++ - [Problem 3 Milk Measurement](https://thealphajas.github.io/fun/usaco/problem-3-milk-measurement.md): USACO Bronze solution in C++ - [Problem 3 Mowing The Field](https://thealphajas.github.io/fun/usaco/problem-3-mowing-the-field.md): USACO Bronze solution in C++ - [Problem 3 Stuck In A Rut](https://thealphajas.github.io/fun/usaco/problem-3-stuck-in-a-rut.md): USACO Bronze solution in C++ - [Problem 3 The Cow Signal](https://thealphajas.github.io/fun/usaco/problem-3-the-cow-signal.md): USACO Bronze solution in C++ - [Problem 3 Watching Mooloo](https://thealphajas.github.io/fun/usaco/problem-3-watching-mooloo.md): USACO Bronze solution in C++ ## Optional - [All writeups in one file](https://thealphajas.github.io/llms-full.txt): the full Markdown of every post above, concatenated - [RSS feed](https://thealphajas.github.io/rss.xml): blog posts and probability writeups - [Sitemap](https://thealphajas.github.io/sitemap-index.xml)