feat: Add new LeetCode solutions

Author: Shamik07

2999-count-powerful-integers.dart

@@ -0,0 +1,91 @@
+import 'dart:math';
+
+class DigitCounter {
+  Map<String, BigInt> memo = {};
+  late String numStr;
+  late int digitLimit;
+
+  BigInt dp(int index, bool tight, bool isLeadingZero) {
+    if (index == numStr.length) {
+      return BigInt.one;
+    }
+    String key = "$index-$tight-$isLeadingZero";
+    if (memo.containsKey(key)) {
+      return memo[key]!;
+    }
+
+    BigInt ans = BigInt.zero;
+    int currentDigitLimit = tight ? int.parse(numStr[index]) : 9;
+    int upperBound = min(currentDigitLimit, digitLimit);
+
+    for (int digit = 0; digit <= upperBound; digit++) {
+      bool newTight = tight && (digit == currentDigitLimit);
+      ans += dp(index + 1, newTight, isLeadingZero && (digit == 0));
+    }
+
+    memo[key] = ans;
+    return ans;
+  }
+
+  BigInt count(BigInt n, int limit) {
+    if (n < BigInt.zero) {
+      return BigInt.zero;
+    }
+    numStr = n.toString();
+    digitLimit = limit;
+    memo.clear(); // new count.
+    return dp(0, true, true);
+  }
+}
+
+BigInt countUpTo(BigInt n, int limit) {
+  return DigitCounter().count(n, limit);
+}
+
+BigInt solve(BigInt n, int limit, String s) {
+  for (int i = 0; i < s.length; i++) {
+    if (int.parse(s[i]) > limit) {
+      return BigInt.zero;
+    }
+  }
+
+  BigInt sValue = BigInt.parse(s);
+  if (n < sValue) {
+    return BigInt.zero;
+  }
+
+  BigInt power = BigInt.from(10).pow(s.length);
+  // count of 'y' such that x = y * 10^L + s <= n.
+  BigInt nPrime = (n - sValue) ~/ power;
+
+  return countUpTo(nPrime, limit);
+}
+
+int countPowerfulIntegers(int start, int finish, int limit, String s) {
+  BigInt finishBig = BigInt.from(finish);
+  BigInt startMinusOneBig = BigInt.from(start) - BigInt.one;
+
+  BigInt countFinish = solve(finishBig, limit, s);
+  BigInt countStart = solve(startMinusOneBig, limit, s);
+
+  BigInt result = countFinish - countStart;
+  return result.toInt();
+}
+
+void main() {
+  // Example 1
+  int start1 = 1;
+  int finish1 = 6000;
+  int limit1 = 4;
+  String s1 = "124";
+  print("Expected: 5");
+  print("Output: ${countPowerfulIntegers(start1, finish1, limit1, s1)}");
+
+  // Example 2
+  int start2 = 15;
+  int finish2 = 215;
+  int limit2 = 6;
+  String s2 = "10";
+  print("Expected: 2");
+  print("Output: ${countPowerfulIntegers(start2, finish2, limit2, s2)}");
+}