Common Child


Problem Statement :


A string is said to be a child of a another string if it can be formed by deleting 0 or more characters from the other string. Given two strings of equal length, what's the longest string that can be constructed such that it is a child of both?

For example, ABCD and ABDC have two children with maximum length 3, ABC and ABD. They can be formed by eliminating either the D or C from both strings. Note that we will not consider ABCD as a common child because we can't rearrange characters and ABCD  ABDC.

Function Description

Complete the commonChild function in the editor below. It should return the longest string which is a common child of the input strings.

commonChild has the following parameter(s):

s1, s2: two equal length strings
Input Format

There is one line with two space-separated strings, s1 and s2.

Constraints

1  <=   | s1 | , | s2 |  <=  5000
All characters are upper case in the range ascii[A-Z].
Output Format

Print the length of the longest string s, such that  is a child of both s1 and s2.


Solution :



title-img 


                            Solution in C :

In  C++ :




#include <cmath>
#include <cstdio>
#include <vector>
#include <string>
#include <iostream>
#include <algorithm>
using namespace std;

int dp[5005][5005];

int main() {
    string a, b;
    cin >> a >> b;
    
    for(int i = 0; i < a.size(); ++i)
        for(int j = 0; j < b.size(); ++j)
            if(a[i] == b[j])
                dp[i + 1][j + 1] = dp[i][j] + 1;
            else
                dp[i + 1][j + 1] = max(dp[i][j + 1], dp[i + 1][j]);
    
    cout << dp[a.size()][b.size()];
    return 0;
}







In   Java ;





import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class Solution {

    public static void main(String[] args) {
    	Scanner s = new Scanner(System.in);
		String s1 = s.nextLine();
		String s2 = s.nextLine();
		int[][] lengths = new int[s1.length()+1][s2.length()+1];
		
		for (int i = 1; i < lengths.length; i++) {
			for (int j = 1; j < lengths.length; j++) {
				if (s1.charAt(i-1) == s2.charAt(j-1)) {
					lengths[i][j] = lengths[i-1][j-1] + 1;
				}
				else if (lengths[i][j-1] > lengths[i-1][j]) {
					lengths[i][j] = lengths[i][j-1];
				}
				else {
					lengths[i][j] = lengths[i-1][j];
				}
			}
		}
		System.out.println(lengths[lengths.length-1][lengths.length-1]);
    }
}







In  C :




#include<stdio.h>
#include<string.h>
char str1[5005],str2[5005];
int c[5005][5005];
int main()
{
  int i,j,m,n;
  scanf("%s %s",str1+1,str2+1);
  m=strlen(str1+1);
  n=strlen(str2+1);
  for(i=1;i<=m;i++)c[i][0]=0;
  for(j=0;j<=n;j++)c[0][j]=0;
  for(i=1;i<=m;i++)
    for(j=1;j<=n;j++)
      {
	if(str1[i]==str2[j])
	  c[i][j]=c[i-1][j-1]+1;
	else if(c[i-1][j]>=c[i][j-1])
	  c[i][j]=c[i-1][j];
	else
	  c[i][j]=c[i][j-1];
      }
  printf("%d\n",c[m][n]);
  return 0;
}








In  Python3 :






def llis(a, b):
    m = len(a)
    n = len(b)
    prev = [0 for x in range(n + 1)]
    for i in range(1, m + 1):
        curr = [0 for x in range(n + 1)]
        for j in range(1, n + 1):
            curr[j] = max(prev[j], curr[j - 1])
            if a[i - 1] == b[j - 1]:
                curr[j] = max(curr[j], prev[j - 1] + 1)
        prev = curr
    return curr[n]
    
if __name__ == '__main__':
    a = input().strip()
    b = input().strip()
    c = set(a) & set(b)
    a = "".join([x for x in a if x in c])
    b = "".join([x for x in b if x in c])
    print(llis(a, b))








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