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Merge pull request fnplus#564 from nikhilgupta30/nikhil

Basic Dynamic Programming Problems

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	`1`	`+/* Dynamic Programming C++ implementation of Longest Common Subseq. problem */`
	`2`	`+#include<bits/stdc++.h>`
	`3`	`+using namespace std;`
	`4`	`+`
	`5`	`+int lcs(string X, string Y, int m, int n ) {`
	`6`	`+ int L[m + 1][n + 1];`
	`7`	`+ int i, j;`
	`8`	`+`
	`9`	`+ for (i = 0; i <= m; i++) {`
	`10`	`+ for (j = 0; j <= n; j++) {`
	`11`	`+ if (i == 0 \|\| j == 0)`
	`12`	`+ L[i][j] = 0;`
	`13`	`+`
	`14`	`+ else if (X[i - 1] == Y[j - 1])`
	`15`	`+ L[i][j] = L[i - 1][j - 1] + 1;`
	`16`	`+`
	`17`	`+ else`
	`18`	`+ L[i][j] = max(L[i - 1][j], L[i][j - 1]);`
	`19`	`+ }`
	`20`	`+ }`
	`21`	`+`
	`22`	`+ return L[m][n];`
	`23`	`+}`
	`24`	`+`
	`25`	`+// main function`
	`26`	`+int main(){`
	`27`	`+`
	`28`	`+ string X,Y;`
	`29`	`+ cout<<"enter first string: ";`
	`30`	`+ cin>>X;`
	`31`	`+ cout<<"\nenter second string: ";`
	`32`	`+ cin>>Y;`
	`33`	`+`
	`34`	`+ int m = X.size();`
	`35`	`+ int n = Y.size();`
	`36`	`+`
	`37`	`+ cout << "Length of LCS is "`
	`38`	`+ << lcs( X, Y, m, n );`
	`39`	`+`
	`40`	`+ return 0;`
	`41`	`+}`

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	`1`	`+/* Dynamic Programming C++ implementation of Longest commong substring problem */`
	`2`	`+#include<bits/stdc++.h>`
	`3`	`+using namespace std;`
	`4`	`+`
	`5`	`+int lcs(string X, string Y, int m, int n ) {`
	`6`	`+ int LCSuff[m + 1][n + 1];`
	`7`	`+ int result = 0;`
	`8`	`+`
	`9`	`+ for (int i = 0; i <= m; i++) {`
	`10`	`+ for (int j = 0; j <= n; j++) {`
	`11`	`+ if (i == 0 \|\| j == 0)`
	`12`	`+ LCSuff[i][j] = 0;`
	`13`	`+ else if (X[i-1] == Y[j-1]) {`
	`14`	`+ LCSuff[i][j] = LCSuff[i-1][j-1] + 1;`
	`15`	`+ result = max(result, LCSuff[i][j]);`
	`16`	`+ }`
	`17`	`+ else LCSuff[i][j] = 0;`
	`18`	`+ }`
	`19`	`+ }`
	`20`	`+`
	`21`	`+ return result;`
	`22`	`+}`
	`23`	`+`
	`24`	`+// main function`
	`25`	`+int main(){`
	`26`	`+`
	`27`	`+ string X,Y;`
	`28`	`+ cout<<"enter first string: ";`
	`29`	`+ cin>>X;`
	`30`	`+ cout<<"\nenter second string: ";`
	`31`	`+ cin>>Y;`
	`32`	`+`
	`33`	`+ int m = X.size();`
	`34`	`+ int n = Y.size();`
	`35`	`+`
	`36`	`+ cout << "Length of LCS is "`
	`37`	`+ << lcs( X, Y, m, n );`
	`38`	`+`
	`39`	`+ return 0;`
	`40`	`+}`

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	`1`	`+/* Dynamic Programming C++ implementation of LIS problem */`
	`2`	`+#include<bits/stdc++.h>`
	`3`	`+using namespace std;`
	`4`	`+`
	`5`	`+int lis( int arr[], int n ) {`
	`6`	`+ int lis[n];`
	`7`	`+`
	`8`	`+ lis[0] = 1;`
	`9`	`+`
	`10`	`+ for (int i = 1; i < n; i++ ) {`
	`11`	`+ lis[i] = 1;`
	`12`	`+ for (int j = 0; j < i; j++ )`
	`13`	`+ if ( arr[i] > arr[j] && lis[i] < lis[j] + 1)`
	`14`	`+ lis[i] = lis[j] + 1;`
	`15`	`+ }`
	`16`	`+`
	`17`	`+ return *max_element(lis, lis+n);`
	`18`	`+}`
	`19`	`+`
	`20`	`+// main function`
	`21`	`+int main() {`
	`22`	`+ int n;`
	`23`	`+ cout<<"enter size of array: ";`
	`24`	`+ cin>>n;`
	`25`	`+`
	`26`	`+ int arr[n];`
	`27`	`+ cout<<"enter elements: \n";`
	`28`	`+ for(int i=0;i<n;i++) cin>>arr[i];`
	`29`	`+`
	`30`	`+ printf("Length of lis is %d\n", lis( arr, n ) );`
	`31`	`+`
	`32`	`+ return 0;`
	`33`	`+}`

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