Create Sum OR Explanation.txt

Author: MathProgrammer

Contests/Starters/84/Explanations/Sum OR Explanation.txt

@@ -0,0 +1,29 @@
+Each bit is set in at most 1 integer. 
+
+Let us use simple Mathematics to count the number of ways to distribute b bits into 3 sets 
+
+1. 3^b 
+2. There are 3 x 2^b ways in which one of the two integers are empty 
+3. There are 3 ways to distribute in which two of the three integers are empty 
+
+Answer = 3^b - 3 x 2^b + 3
+
+-----
+
+void solve()
+{
+    long long n;
+    cin >> n;
+    
+    int bit_count = no_of_ones(n);
+    
+    const int MOD = 1e9 + 7;
+    long long all_three = power(3, bit_count, MOD);
+    long long only_two = (3*power(2, bit_count, MOD))%MOD;
+    long long only_one = 3;
+    
+    long long answer = all_three - only_two + only_one + MOD;
+    answer %= MOD;
+    
+    cout << answer << "\n";
+}