Leetcode 2999. Count the Number of Powerful Integers | Python Digit DP Solution

In this Leetcode 2999 problem "Count the Number of Powerful Integers", we are given a range [start, finish], a digit limit, and a string suffix s. The goal is to count how many integers in this range have all digits less than or equal to the limit, except for the last digits matching exactly with the suffix s. This is a perfect digit-based counting problem, and we solve it using a custom digit-by-digit simulation approach that avoids brute force. We simulate the number as a string and intelligently skip entire branches using powers of (limit+1), similar to digit DP. This method is extremely efficient and handles edge cases gracefully. The code uses string manipulation, prefix-suffix logic, and powers to optimize the count. Ideal problem for mastering digit simulations and counting techniques in competitive programming or interviews. We also explain: Why simple iteration won’t work How to subtract results using prefix count String vs integer strategy Why we simulate digits as strings Power of (limit+1) logic Handling edge cases like leading digits exceeding the limit How we reuse the count function for range subtraction 🧠 Keywords count powerful integers powerful integers leetcode leetcode 2999 digit dp problems digit based counting suffix based filtering prefix simulation digit limit leetcode simulate integer digits powerful integer definition count with digit restrictions prefix + suffix number filter range digit count string based number count count valid numbers count numbers with suffix leetcode counting trick python digit manipulation efficient counting prefix math logic smart digit dp python digit dp count numbers in range limit digits in number simulate number with suffix suffix s in number avoid brute force efficient digit simulation range based counting count by digits powers of limit + 1 python suffix match prefix filter python math logic power of base system match number suffix count integers in range start to finish number count smart counting with strings prefix pruning skip digit branches count valid digit numbers matching string suffix simulate with string avoid TLE leetcode string suffix logic python logic based counting satisfy digit limit match last digits number filter with suffix build digit from left early break counting prune by digit digit dp inspiration math simulation problem digit string optimization interview problem competitive coding leetcode smart counting custom count function digit tree pruning suffix-based match suffix math trick suffix validation math based counting match digits from end simulate number ranges count matching numbers filtering with limit range-based digit filter math from start to finish simulate from left to right filter invalid digits avoid invalid prefixes count with suffix check suffix s check simulate up to finish subtract for range prefix mismatch skip limit digit range maximum valid digit only allowed digits smart counting logic skip large branches backtrack-like simulation early pruning logic string digit comparison substring match substring suffix convert int to str digit-wise check range counting technique count using power simulate all valid prefixes simulate valid numbers filter using suffix powerful numbers prefix suffix leetcode digit simulation trick math-based python leetcode digit problem interview suffix match smart string logic competitive suffix problem leetcode digit-based problem string manipulation logic efficient number count