Create 3519-count-numbers-with-non-decreasing-digits.js

Author: everthis

3519-count-numbers-with-non-decreasing-digits.js

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+/**
+ * @param {string} l
+ * @param {string} r
+ * @param {number} b
+ * @return {number}
+ */
+var countNumbers = function (l, r, b) {
+  const mod = 1000000007
+
+  const bigL = BigInt(l)
+  const bigR = BigInt(r)
+
+  const rightCnt = helper(bigR, b)
+  const leftCnt = helper(bigL - 1n, b)
+  const ans = (rightCnt - leftCnt + BigInt(mod)) % BigInt(mod)
+  return Number(ans)
+  function helper(num, b) {
+    if (num < 0n) return 0n
+
+    // b base digits
+    const digits = Array.from(num.toString(b)).map((d) => BigInt(d) - 0n)
+    const n = digits.length
+
+    const seen = new Map()
+
+    function dfs(pos, last, started, tight) {
+      if (pos === n) return 1n
+
+      const key = `${pos}, ${last}, ${started}, ${tight}`
+      if (seen.has(key)) return seen.get(key)
+
+      const limit = tight ? digits[pos] : BigInt(b - 1)
+      let ways = 0n
+
+      for (let d = 0n; d <= limit; d++) {
+        if (started && d < last) continue
+
+        const nextStarted = started || d !== 0n
+        const nextLast = started || d !== 0n ? d : last
+
+        const nextTight = tight && d === limit
+        ways =
+          (ways + dfs(pos + 1, nextLast, nextStarted, nextTight)) % BigInt(mod)
+      }
+      seen.set(key, ways % BigInt(mod))
+      return ways
+    }
+
+    return dfs(0, 0n, false, true)
+  }
+}