Create 3352-count-k-reducible-numbers-less-than-n.js

Author: everthis

3352-count-k-reducible-numbers-less-than-n.js

@@ -0,0 +1,58 @@
+const ll = BigInt,
+  mod = ll(1e9 + 7),
+  N = 1e4 + 15
+let fact = Array(N).fill(0),
+  ifact = Array(N).fill(0),
+  inv = Array(N).fill(0)
+const hcomb = (p, q) => (p == 0 && q == 0 ? 1 : comb(p + q - 1, q))
+const comb_init = () => {
+  fact[0] = ifact[0] = inv[1] = 1n // factorial, inverse factorial
+  for (let i = 2; i < N; i++)
+    inv[i] = ((mod - mod / ll(i)) * inv[mod % ll(i)]) % mod
+  for (let i = 1; i < N; i++) {
+    fact[i] = (fact[i - 1] * ll(i)) % mod
+    ifact[i] = (ifact[i - 1] * inv[i]) % mod
+  }
+}
+
+// combination mod pick k from n
+const comb = (n, k) => {
+  if (n < k || k < 0) return 0
+  return (((fact[n] * ifact[k]) % mod) * ifact[n - k]) % mod
+}
+
+/**
+ * @param {string} s
+ * @param {number} k
+ * @return {number}
+ */
+var countKReducibleNumbers = function (s, k) {
+  let dp = new Array(1000).fill(0)
+  for (let i = 2; i < 1000; i++) {
+    dp[i] = dp[bitCnt(i)] + 1
+  }
+  let c1 = 0
+  let n = s.length
+  let res = 0n
+  comb_init()
+  for (let i = 0; i < n; i++) {
+    if (s[i] === "1") {
+      for (let c2 = 0; c2 < n - i; c2++) {
+        if (c1 + c2 > 0 && dp[c1 + c2] + 1 <= k) {
+          res = res + comb(n - i - 1, c2)
+        }
+      }
+      c1++
+    }
+  }
+  return Number(res % mod)
+
+  function bitCnt(num) {
+    let cnt = 0
+    while (num) {
+      cnt += num & 1
+      num >>= 1
+    }
+    return cnt
+  }
+}