Word Break Problem: Dynamic Programming Solution
The word break problem is deceptively simple to state: given a string s and a dictionary of words, determine whether s can be segmented into a sequence of one or more dictionary words. For…
Problem
Unbounded Knapsack: Complete Knapsack Problem
The unbounded knapsack problem, also called the complete knapsack problem, removes the single-use constraint from its 0/1 cousin. You have a knapsack with capacity W and n item types, each with a…
Read more →Travelling Salesman Problem: Exact and Approximate Solutions
The Travelling Salesman Problem asks a deceptively simple question: given a set of cities and distances between them, what’s the shortest route that visits each city exactly once and returns to the…
Read more →Subset Sum Problem: DP and Backtracking Solutions
The subset sum problem asks a deceptively simple question: given a set of integers and a target sum, does any subset of those integers add up exactly to the target? Despite its straightforward…
Read more →Staircase Problem: Number of Ways to Climb
You’re standing at the bottom of a staircase with n steps. You can climb either 1 or 2 steps at a time. How many distinct ways can you reach the top?
Rod Cutting Problem: Maximum Revenue DP
You have a steel rod of length n inches. Your supplier buys rod pieces at different prices depending on their length. The question: how should you cut the rod to maximize revenue?
Read more →Partition Problem: Equal Subset Sum
The partition problem asks a deceptively simple question: given a set of positive integers, can you split them into two subsets such that both subsets have equal sums? Despite its straightforward…
Read more →Paint House Problem: Minimum Cost Coloring
The Paint House problem is a classic dynamic programming challenge that appears frequently in technical interviews and competitive programming. Here’s the setup: you have N houses arranged in a row,…
Read more →Knapsack Problem: 0/1 and Unbounded Variants
You have a backpack with limited capacity. You’re staring at a pile of items, each with a weight and a value. Which items do you take to maximize value without exceeding capacity?
Read more →Hungarian Algorithm: Assignment Problem
You have five developers and five features to build. Each developer has different skills, so the time to complete each feature varies by who’s assigned to it. Your goal: assign each developer to…
Read more →How to Solve Birthday Problem Probability
The birthday problem stands as one of probability theory’s most counterintuitive puzzles. Ask someone how many people need to be in a room before there’s a 50% chance that two share a birthday, and…
Read more →How to Apply the Gambler's Ruin Problem
The Gambler’s Ruin problem is deceptively simple: two players bet against each other repeatedly until one runs out of money. Player A starts with capital a, Player B starts with capital b, and…
Egg Drop Problem: Minimum Trials DP
The egg drop problem is a classic dynamic programming challenge that appears in technical interviews and competitive programming. Here’s the setup: you have n identical eggs and a building with k…
Coin Change Problem: Minimum Coins DP Solution
The coin change problem asks a deceptively simple question: given a set of coin denominations and a target amount, what’s the minimum number of coins needed to make exact change?
Read more →Burst Balloons: Interval DP Problem
LeetCode 312 - Burst Balloons presents a deceptively simple premise: you have n balloons with values, and bursting balloon i gives you nums[i-1] * nums[i] * nums[i+1] coins. After bursting,…
Branch and Bound: Optimization Problem Solving
Branch and bound (B&B) is an algorithmic paradigm for solving combinatorial optimization problems where you need the provably optimal solution, not just a good one. It’s the workhorse behind integer…
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