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RNA Secondary structure

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13.Dynamic-programming/RNA Secondary structure
- RNASecondaryStructureTopDown.cpp

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	`1`	`+/* Amit Bansal - @amitbansal7 */`
	`2`	`+#include <bits/stdc++.h>`
	`3`	`+using namespace std;`
	`4`	`+// RNA Secondary structure problem (RNA folding)`
	`5`	`+// OPT(i,j) = max(OPT(i,j-1), (for all t)max(1 + OPT(i,t-1) + OPT(t+1,j-1)));`
	`6`	`+// All characters in the string are from set {A, U, C, G}`
	`7`	`+// One blank character at s[0] because we use 1 based indexing.`
	`8`	`+// Running time of this algorithm is O(n^3)`
	`9`	`+`
	`10`	`+string s = " ACCGGUAGU";`
	`11`	`+`
	`12`	`+int DP[100][100];`
	`13`	`+`
	`14`	`+int OPT(int i, int j)`
	`15`	`+{`
	`16`	`+ if (DP[i][j] != -1)`
	`17`	`+ return DP[i][j];`
	`18`	`+`
	`19`	`+ if (i <= j - 4)`
	`20`	`+ {`
	`21`	`+ int a = OPT(i, j - 1);`
	`22`	`+ int b = INT_MIN;`
	`23`	`+ for (int t = i; t < j; t++)`
	`24`	`+ if ((s[t] == 'A' && s[j] == 'U') \|\| ((s[t] == 'C') && s[j] == 'G'))`
	`25`	`+ b = max(b, 1 + OPT(i, t - 1) + OPT(t + 1, j - 1));`
	`26`	`+`
	`27`	`+ return DP[i][j] = max(a, b);`
	`28`	`+ }`
	`29`	`+ else`
	`30`	`+ return DP[i][j] = 0;`
	`31`	`+}`
	`32`	`+`
	`33`	`+int main()`
	`34`	`+{`
	`35`	`+ memset(DP, -1, sizeof(DP));`
	`36`	`+ printf("%d\n", OPT(1, s.length() - 1));`
	`37`	`+}`

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