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Merge pull request fnplus#646 from jaynilshah/master

Longest Increasing Subsequence

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Algorithms/Dynamic Programming/Longest Increasing Subsequence/CPP
- LongestIncreasingSubsequence.java

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	`1`	`+import java.util.ArrayList;`
	`2`	`+import java.util.List;`
	`3`	`+`
	`4`	`+public class LIS {`
	`5`	`+ public static int lowerBound(List<Integer> a, int low, int high, int element){`
	`6`	`+ while(low < high){`
	`7`	`+ int middle = low + (high - low)/2;`
	`8`	`+ if(element > a.get(middle))`
	`9`	`+ low = middle + 1;`
	`10`	`+ else`
	`11`	`+ high = middle;`
	`12`	`+ }`
	`13`	`+ return low;`
	`14`	`+ }`
	`15`	`+`
	`16`	`+ public static int upperBound(List<Integer> a, int low, int high, int element){`
	`17`	`+ while(low < high){`
	`18`	`+ int middle = low + (high - low)/2;`
	`19`	`+ if(a.get(middle) > element)`
	`20`	`+ high = middle;`
	`21`	`+ else`
	`22`	`+ low = middle + 1;`
	`23`	`+ }`
	`24`	`+ return low;`
	`25`	`+ }`
	`26`	`+`
	`27`	`+ public static int longestIncreasingSubsequence(List<Integer> a){`
	`28`	`+ //equals included then upperbound`
	`29`	`+ // else lower bound use as required`
	`30`	`+ ArrayList<Integer> ans = new ArrayList<>();`
	`31`	`+ for(int i=0;i<a.size();i++){`
	`32`	`+ int x = lowerBound(ans,0,ans.size(),a.get(i));`
	`33`	`+ if(x+1>ans.size()){`
	`34`	`+ ans.add(a.get(i));`
	`35`	`+ }`
	`36`	`+ else`
	`37`	`+ ans.set(x,a.get(i));`
	`38`	`+ }`
	`39`	`+ return ans.size();`
	`40`	`+ }`
	`41`	`+`
	`42`	`+}`

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