Merge pull request #68 from InflixOP/patch1

Create #2338. Count the Number of Ideal Arrays.cpp

Author: InflixOP

#2338. Count the Number of Ideal Arrays.cpp

@@ -0,0 +1,34 @@
+const int mod = 1e9 + 7;
+int factMemo[100000] = {};
+int dp[100000][15];
+using ll = long long;
+class Solution {
+public:
+ll power(ll a, ll b, ll m = mod) {ll res = 1;while (b > 0) {if (b & 1)res = (res * a) % m;a = (a * a) % m;b = b >> 1;}return res;}
+    ll fact(ll n) {
+        if (n == 0) return 1;
+        if (factMemo[n]) return factMemo[n];
+        factMemo[n] = (n * fact(n - 1)) % mod;
+        return factMemo[n];
+    }
+    ll mod_inv(ll a, ll b) {
+        return (((fact(a) * power(fact(b), mod - 2)) % mod) * power(fact(a - b), mod - 2)) % mod;
+    }
+
+    int idealArrays(int n, int maxi) {
+        for (int i = 1; i <= maxi; i++)
+            for (int j = 1; j <= min(n, 14); j++)
+                dp[i][j] = 0;
+        for (int i = 1; i <= maxi; i++) {
+            dp[i][1] = 1;
+            for (int j = 2; j * i <= maxi; j++)
+                for (int k = 1; k < min(n, 14); k++)
+                    dp[i*j][k+1] += dp[i][k];
+        }
+        ll res = 0;
+        for (int i = 1; i <= maxi; i++)
+            for (int j = 1; j <= min(n, 14); j++)
+                res = (res + mod_inv(n - 1, n - j) * dp[i][j]) % mod;
+        return res;
+    } 
+};