Kth multiple of 3,5,7

Author: sonugiri1043

17-Hard/9-Kth-Multiple.cpp

@@ -0,0 +1,46 @@
+/*
+  Kth Multiple: Design an algorithm to find the kth number such that the only prime factors are 3, 5,
+  and 7. Note that 3,5, and 7 do not have to be factors, but it should not have any other prime factors.
+  For example, the first several multiples would be (in order) 1,3, 5, 7, 9, 15, 21.
+ */
+
+#include <iostream>
+#include <queue>
+
+using std::cout;
+using std::endl;
+using std::queue;
+
+int getKthMultiple( int x, int y, int z, int k ) {
+  queue<int> qX, qY, qZ;
+  qX.push(1);
+  qX.push(x);
+  qY.push(y);
+  qZ.push(z);
+  int min;
+  for( int i=0; i < k; i++ ) {
+    min = qX.front() < qY.front() ? ( qX.front() < qZ.front() ? qX.front() : qZ.front() ) : (qY.front() < qZ.front() ? qY.front() : qZ.front() );
+    if( min == qX.front() ) {
+      qX.pop();
+      qX.push( min * x );
+      qY.push( min * y );
+      qZ.push( min * z );
+    }
+    if( min == qY.front() ) {
+      qY.pop();
+      qY.push( min * y );
+      qZ.push( min * z );
+    }
+    if( min == qZ.front() ) {
+      qZ.pop();
+      qZ.push( min * z ); 
+    }
+  }
+  return min;
+}
+
+int main() {
+  int k = 10;
+  int x = 3, y = 5, z = 7;
+  cout<< getKthMultiple( x, y, z, 10 ) << endl;
+}