Create 2518-number-of-great-partitions.js

Author: everthis

2518-number-of-great-partitions.js

@@ -0,0 +1,40 @@
+const ll = BigInt,
+  mod = 1e9 + 7,
+  bmod = ll(mod)
+const sm = (a) => a.reduce((x, y) => x + y, 0)
+const powmod = (a, b, mod) => {
+  let r = 1n
+  while (b > 0n) {
+    if (b % 2n == 1) r = (r * a) % mod
+    b >>= 1n
+    a = (a * a) % mod
+  }
+  return r
+}
+const minus_mod = (x, y, mod) => (((x - y) % mod) + mod) % mod
+const knapsack_01 = (a, k) => {
+  if (sm(a) < 2 * k) return 0
+  let dp = Array(k).fill(0)
+  dp[0] = 1
+  for (const x of a) {
+    for (let j = k - 1; j > x - 1; j--) {
+      dp[j] += dp[j - x]
+      dp[j] %= mod
+    }
+  }
+  let bad = ll(sm(dp) * 2),
+    tot = powmod(2n, ll(a.length), bmod),
+    good = minus_mod(tot, bad, bmod)
+  return good
+}
+/**
+ * @param {number[]} nums
+ * @param {number} k
+ * @return {number}
+ */
+const countPartitions = function(nums, k) {
+  return knapsack_01(nums, k)
+};
+
+
+