start divide and conquer

Author: amejiarosario

book/book.adoc

@@ -183,8 +183,12 @@ include::chapters/greedy-algorithms--knapsack-problem.adoc[]
 
 = Divide and Conquer Algorithms
 
+include::chapters/divide-and-conquer--intro.adoc[]
+
+
 :leveloffset: +1
 
+
 :leveloffset: -1
 
 = Backtracking Algorithms

book/chapters/greedy-algorithms--knapsack-problem.adoc

@@ -48,3 +48,7 @@ Let's implement this algorithm!
 ----
 include::{codedir}/algorithms/knapsack-fractional.js[tag=snippet,indent=0]
 ----
+
+What's the runtime of this algorithm?
+
+We have to sort the array based on value/weight ratio. Sorting runtime is O(n log n). The rest is linear operations, so we the answer is _O(n log n)_ for our greedy algorithm.

book/chapters/sample.adoc

@@ -75,6 +75,10 @@ BigInt allows to operate beyond the maximum safe limit of integers (Number.MAX_S
 - <<Adaptive>>: [big]#✅# Yes
 - Time Complexity: [big]#⛔️# <<Quadratic>> _O(n^2^)_
 
+.How to explain dynamic programming to kids? 👶
+----
+test [big]*🤯*
+----
 
 == Images
 

src/algorithms/knapsack-fractional.js

@@ -1,6 +1,7 @@
 // tag::snippet[]
 /**
- *
+ * Solves Bounded Knapsack Problem (BKP)
+ *  You can take fractions or whole part of items.
  * @param {Array} input array of objects with the shape {value, weight}
  * @param {Number} max maximum weight for knapsack
  */
@@ -16,25 +17,17 @@ function solveFractionalKnapsack(input, max) {
     const bestRatioItem = input.pop();
 
     if (weight + bestRatioItem.weight <= max) {
-      // take item as a whole
-      bestRatioItem.proportion = 1;
-      items.push(bestRatioItem);
-      weight += bestRatioItem.weight;
-      value += bestRatioItem.value;
-    } else {
-      // take a fraction of the item
+      bestRatioItem.proportion = 1; // take item as a whole
+    } else { // take a fraction of the item
       bestRatioItem.proportion = (max - weight) / bestRatioItem.weight;
-      items.push(bestRatioItem);
-      weight += bestRatioItem.proportion * bestRatioItem.weight;
-      value += bestRatioItem.proportion * bestRatioItem.value;
     }
+
+    items.push(bestRatioItem);
+    weight += bestRatioItem.proportion * bestRatioItem.weight;
+    value += bestRatioItem.proportion * bestRatioItem.value;
   }
 
-  return {
-    weight,
-    value,
-    items,
-  };
+  return { weight, value, items };
 }
 // end::snippet[]