Solved problem Lazy Sorting HackerRank

Author: AliOsm

Hackerrank/Lazy Sorting.cpp

@@ -0,0 +1,48 @@
+/*
+  - Idea:
+    - If the array if sorted then the expected value is 0.
+    - Otherwise declare fr_i to be the frequency of the i_th element
+      in the array, so we can sort the array in `all` = (fr_1! * fr_2! * ... * fr_n!)
+      ways, then the probability to sort the array after shuffling is `all/N!`,
+      finally the expected value if `1/(all/N!)` which is equal to `N!/all`.
+*/
+
+#include <bits/stdc++.h>
+
+using namespace std;
+
+int n, a[18], b[18], fr[101];
+
+long long fact(int x) {
+  long long ret = 1;
+  for(int i = 2; i <= x; ++i)
+    ret *= i;
+  return ret;
+}
+
+int main() {
+  scanf("%d", &n);
+  for(int i = 0; i < n; ++i)
+    scanf("%d", a + i), b[i] = a[i], ++fr[a[i]];
+
+  sort(b, b + n);
+
+  bool ok = true;
+  for(int i = 0; i < n; ++i)
+    if(a[i] != b[i])
+      ok = false;
+
+  if(ok) {
+    puts("0");
+    return 0;
+  }
+
+  long long all = fact(n);
+
+  for(int i = 0; i <= 100; ++i)
+    all /= fact(fr[i]);
+
+  printf("%lld\n", all);
+
+  return 0;
+}

Hackerrank/README.md

@@ -30,6 +30,7 @@
 - [Jack goes to Rapture](https://www.hackerrank.com/challenges/jack-goes-to-rapture)
 - [Journey to the Moon](https://www.hackerrank.com/challenges/journey-to-the-moon)
 - [Jumping on the Clouds](https://www.hackerrank.com/challenges/jumping-on-the-clouds)
+- [Lazy Sorting](https://www.hackerrank.com/challenges/lazy-sorting)
 - [Little Ashish's Huge Donation](https://www.hackerrank.com/challenges/little-chammys-huge-donation)
 - [Maximizing XOR](https://www.hackerrank.com/challenges/maximizing-xor)
 - [Maximum Draws](https://www.hackerrank.com/challenges/maximum-draws)