[Programming question] The longest Public String

56. The longest Public String (algorithm, string ).
Question: If all the characters in string 1 appear in the order of the strings in another string,
Then, string 1 is called a substring of string 2.
Note that the character of a substring (string 1) must appear in string 2 consecutively.
Compile a function, enter two strings, calculate their longest public substrings, and print the longest public substrings.
For example, input two strings: bdcaba and abcbdab. The strings bcba and bdab are both the most
Long Public substrings are output with a length of 4 and any substring is printed.

 

Typical dynamic planning questions.

# Include <stdio. h> # include <stdlib. h> # include <string. h> void printlcs (char * X, int M, int N, int I, Int J, char * B) {if (I <0 | j <0) {return;} Char B = * (B + I * n + J); If (B = 'y') {printlcs (x, M, N, I-1, j-1, B); printf ("% C", X [I]); // obtain the following common letters first, it should be printed later} else if (B = 'U') {printlcs (x, M, N, I-1, J, B );} else {printlcs (x, M, N, I, j-1, B) ;}} int LCS (char * X, char * Y, int M, int N, char * & B) // returns the maximum length of Public substrings {int * c = (int *) malloc (m + 1) * (n + 1) * sizeof (INT); // records the longest common subsequence of each subproblem 0-m 0-n B = (char *) malloc (M * n * sizeof (char); // mark 1-m 1-N memset (C, 0, (m + 1) * (n + 1) * sizeof (INT); // Initialization is all 0 for (INT I = 0; I <m; I ++) {int * crow_1 = C + I * (n + 1 ); // note that in C, I = 1 j = 1 corresponds to X [0] of X and Y [0] int * crow = C + (I + 1) of Y) * (n + 1); char * brow = B + I * N; // note that in B, I = 0 J = 0 corresponds to X [0] of X and Y [0] For (Int J = 0; j <N; j ++) {If (X [I] = Y [J]) {crow [J + 1] = crow_1 [J] + 1; brow [J] = 'y';} else {crow [J + 1] = (crow_1 [J + 1]> crow [J])? Crow_1 [J + 1]: crow [J]; brow [J] = (crow_1 [J + 1]> crow [J])? 'U': 'l' ;}} printlcs (x, m, n, m-1, n-1, B ); int maxlen = * (C + M * (n + 1) + n); free (c); free (B); Return maxlen;} int main () {char X [7] = {'A', 'B', 'C', 'B', 'D', 'A', 'B '}; char y [6] = {'B', 'D', 'C', 'A', 'B', 'A'}; char * B = NULL; int L = LCS (X, Y, 7, 6, B); Return 0 ;}