Merge pull request royalpranjal#28 from khannagautam/patch-1

Adding solution for Ways to form Max Heap

Author: Sahil

Heaps-and-Maps/WaysToFormMaxHeap.cpp

@@ -0,0 +1,47 @@
+long long dp[105];
+long long comb[105][105];
+#define MOD 1000000007
+int rec(int n)
+{
+    if(n<=1)
+        return 1;
+    if(dp[n] != -1)
+        return dp[n];
+    int i;
+    int fill = 0;
+    int pw = 2;
+    int left,right;
+    left = right = 0;
+    
+    while(fill+pw < n-1)
+    {
+        fill += pw;
+        left += pw/2;
+        right += pw/2;
+        pw *= 2;
+    }
+    int rem = n-1-fill;
+    if(rem > pw/2)
+    {
+        left += pw/2;
+        right += (rem-pw/2);
+    }
+    else
+        left += rem;
+
+    return dp[n] = (((rec(left)*1LL*rec(right))%MOD)*1LL*comb[n-1][left])%MOD;
+}
+int Solution::solve(int A)
+{
+    int i,j;
+    for(i=0;i<=100;i++)
+        dp[i] = -1;
+    comb[0][0] = 1;
+    for(i=1;i<=100;i++)
+    {
+        comb[i][0] = comb[i][i] = 1;
+        for(j=1;j<i;j++)
+            comb[i][j] = (comb[i-1][j-1]+comb[i-1][j])%MOD;
+    }
+    return rec(A);
+}