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start divide and conquer

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`@@ -183,8 +183,12 @@ include::chapters/greedy-algorithms--knapsack-problem.adoc[]`
`183`	`183`
`184`	`184`	`= Divide and Conquer Algorithms`
`185`	`185`
	`186`	`+include::chapters/divide-and-conquer--intro.adoc[]`
	`187`	`+`
	`188`	`+`
`186`	`189`	`:leveloffset: +1`
`187`	`190`
	`191`	`+`
`188`	`192`	`:leveloffset: -1`
`189`	`193`
`190`	`194`	`= Backtracking Algorithms`

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`@@ -48,3 +48,7 @@ Let's implement this algorithm!`
`48`	`48`	`----`
`49`	`49`	`include::{codedir}/algorithms/knapsack-fractional.js[tag=snippet,indent=0]`
`50`	`50`	`----`
	`51`	`+`
	`52`	`+What's the runtime of this algorithm?`
	`53`	`+`
	`54`	`+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.`

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`@@ -75,6 +75,10 @@ BigInt allows to operate beyond the maximum safe limit of integers (Number.MAX_S`
`75`	`75`	`- <<Adaptive>>: [big]#✅# Yes`
`76`	`76`	`- Time Complexity: [big]#⛔️# <<Quadratic>> _O(n^2^)_`
`77`	`77`
	`78`	`+.How to explain dynamic programming to kids? 👶`
	`79`	`+----`
	`80`	`+test [big]🤯`
	`81`	`+----`
`78`	`82`
`79`	`83`	`== Images`
`80`	`84`

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`@@ -1,6 +1,7 @@`
`1`	`1`	`// tag::snippet[]`
`2`	`2`	`/**`
`3`		`- *`
	`3`	`+ * Solves Bounded Knapsack Problem (BKP)`
	`4`	`+ * You can take fractions or whole part of items.`
`4`	`5`	`* @param {Array} input array of objects with the shape {value, weight}`
`5`	`6`	`* @param {Number} max maximum weight for knapsack`
`6`	`7`	`*/`
`@@ -16,25 +17,17 @@ function solveFractionalKnapsack(input, max) {`
`16`	`17`	`const bestRatioItem = input.pop();`
`17`	`18`
`18`	`19`	`if (weight + bestRatioItem.weight <= max) {`
`19`		`- // take item as a whole`
`20`		`- bestRatioItem.proportion = 1;`
`21`		`- items.push(bestRatioItem);`
`22`		`- weight += bestRatioItem.weight;`
`23`		`- value += bestRatioItem.value;`
`24`		`- } else {`
`25`		`- // take a fraction of the item`
	`20`	`+ bestRatioItem.proportion = 1; // take item as a whole`
	`21`	`+ } else { // take a fraction of the item`
`26`	`22`	`bestRatioItem.proportion = (max - weight) / bestRatioItem.weight;`
`27`		`- items.push(bestRatioItem);`
`28`		`- weight += bestRatioItem.proportion * bestRatioItem.weight;`
`29`		`- value += bestRatioItem.proportion * bestRatioItem.value;`
`30`	`23`	`}`
	`24`	`+`
	`25`	`+ items.push(bestRatioItem);`
	`26`	`+ weight += bestRatioItem.proportion * bestRatioItem.weight;`
	`27`	`+ value += bestRatioItem.proportion * bestRatioItem.value;`
`31`	`28`	`}`
`32`	`29`
`33`		`- return {`
`34`		`- weight,`
`35`		`- value,`
`36`		`- items,`
`37`		`- };`
	`30`	`+ return { weight, value, items };`
`38`	`31`	`}`
`39`	`32`	`// end::snippet[]`
`40`	`33`

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