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Create LCS_Top_Down.java

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	`1`	`+// solving lcs with top down approch`
	`2`	`+`
	`3`	`+public class HelloWorld{`
	`4`	`+`
	`5`	`+ public static void main(String []args){`
	`6`	`+ String a = "aeiou";`
	`7`	`+ String b = "asdertiop";`
	`8`	`+ int lena = a.length();`
	`9`	`+ int lenb = b.length();`
	`10`	`+`
	`11`	`+ int[][] arr = new int[lena + 1][lenb + 1];`
	`12`	`+ int i ,j;`
	`13`	`+ for (i =0;i<=lena;i++)`
	`14`	`+ {`
	`15`	`+ for(j =0;j<=lenb;j++)`
	`16`	`+ {`
	`17`	`+ if(i==0 \|\| j == 0)`
	`18`	`+ {`
	`19`	`+ arr[i][j] = 0;`
	`20`	`+ }`
	`21`	`+ }`
	`22`	`+ }`
	`23`	`+`
	`24`	`+ for(i = 1; i<=lena;i++)`
	`25`	`+ {`
	`26`	`+ for (j = 1; j<=lenb; j++)`
	`27`	`+ {`
	`28`	`+ if(a.charAt(i-1) == b.charAt(j-1))`
	`29`	`+ {`
	`30`	`+ arr[i][j] = 1 + arr[i-1][j-1];`
	`31`	`+ }`
	`32`	`+ else`
	`33`	`+ {`
	`34`	`+ arr[i][j] = Math.max(arr[i-1][j] , arr[i][j-1]);`
	`35`	`+ }`
	`36`	`+ }`
	`37`	`+ }`
	`38`	`+`
	`39`	`+ System.out.println(arr[lena][lenb]);`
	`40`	`+ }`
	`41`	`+}`

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