Balanced Numbers with Digit DP in Java

🔥 𝗛𝗼𝘄 𝗜 𝗦𝘁𝗼𝗽𝗽𝗲𝗱 𝗕𝗿𝘂𝘁𝗲 𝗙𝗼𝗿𝗰𝗶𝗻𝗴 𝗡𝘂𝗺𝗯𝗲𝗿𝘀 𝗮𝗻𝗱 𝗦𝘁𝗮𝗿𝘁𝗲𝗱 𝗧𝗵𝗶𝗻𝗸𝗶𝗻𝗴 𝗶𝗻 𝗗𝗶𝗴𝗶𝘁𝘀 Today’s problem looked simple: 𝗖𝗼𝘂𝗻𝘁 𝗵𝗼𝘄 𝗺𝗮𝗻𝘆 𝗻𝘂𝗺𝗯𝗲𝗿𝘀 𝗶𝗻 [𝗹𝗼𝘄, 𝗵𝗶𝗴𝗵] 𝗮𝗿𝗲 𝗕𝗮𝗹𝗮𝗻𝗰𝗲𝗱. A number is balanced if it has 𝗮𝘁 𝗹𝗲𝗮𝘀𝘁 𝘁𝘄𝗼 𝗱𝗶𝗴𝗶𝘁𝘀 and the 𝘀𝘂𝗺 𝗼𝗳 𝗱𝗶𝗴𝗶𝘁𝘀 𝗮𝘁 𝗼𝗱𝗱 𝗽𝗼𝘀𝗶𝘁𝗶𝗼𝗻𝘀 𝗲𝗾𝘂𝗮𝗹𝘀 𝘁𝗵𝗲 𝘀𝘂𝗺 𝗮𝘁 𝗲𝘃𝗲𝗻 𝗽𝗼𝘀𝗶𝘁𝗶𝗼𝗻𝘀. A brute force check over the range isn’t practical for large limits — this is where 𝗗𝗶𝗴𝗶𝘁 𝗗𝗣 comes in. 🧠 𝗧𝘂𝗿𝗻𝗶𝗻𝗴 𝗧𝘄𝗼 𝗦𝘂𝗺𝘀 𝗶𝗻𝘁𝗼 𝗢𝗻𝗲 𝗩𝗮𝗹𝘂𝗲 Instead of tracking two sums, I tracked: balance = (odd position sum) − (even position sum) If this balance becomes 0 at the end, the number is balanced. 🧩 𝗧𝗵𝗲 𝗖𝗹𝗮𝘀𝘀𝗶𝗰 𝗥𝗮𝗻𝗴𝗲 𝗧𝗿𝗶𝗰𝗸 answer = solve(high) − solve(low − 1) Now the task reduces to counting balanced numbers from 0 to a given number. ⚙️ 𝗕𝘂𝗶𝗹𝗱𝗶𝗻𝗴 𝘁𝗵𝗲 𝗡𝘂𝗺𝗯𝗲𝗿 𝗗𝗶𝗴𝗶𝘁 𝗯𝘆 𝗗𝗶𝗴𝗶𝘁 While forming the number left to right, I tracked: 1. digit index 2. current balance 3. whether we are under prefix restriction (tight) DP state: dp[idx][balance][tight] An OFFSET handles negative balances. 💡 𝗪𝗵𝗮𝘁 𝗧𝗵𝗶𝘀 𝗣𝗿𝗼𝗯𝗹𝗲𝗺 𝗧𝗮𝘂𝗴𝗵𝘁 𝗠𝗲 Converting conditions into a running state Thinking in terms of digit positions, not full numbers Understanding how the tight flag controls the search space Why Digit DP is powerful for large range constraints This problem helped me truly understand Digit DP by walking through the logic step by step. #DataStructures #Coding #Programming #Java #Recursion #Memoization #Tech #SoftwareEngineering #Developer #LearnInPublic #100DaysOfCode #CodeNewbie #CompetitiveCoding #CodeDaily #InterviewPrep #LeetCode #GeeksforGeeks #ComputerScience #ProblemSolvingSkills #CodingJourney

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