// Name(s):
// Email id(s):

import java.util.*;
import java.awt.*;

public class EditDistance {


	public static void main( String[] args ) {
		
		Solution solution = solve( "TAAGGTCA", "AACAGTTACC" );
			
		System.out.println( solution );
			
		System.out.println( solution.validate() );
	}

	public static Solution solve ( String s1, String s2 ) {

		int n1 = s1.length();
		int n2 = s2.length();

		int[][] optimal = new int [ n1+1 ] [ n2+1 ];

		for ( int i = 0; i < n1; ++i ) {
			optimal[ i ][ n2 ] = 2 * ( n1 - i );
		}

		for ( int j = 0; j < n2; ++j ) {
			optimal[ n1 ][ j ] = 2 * ( n2 - j );
		}

		for ( int i = n1 - 1; 0 <= i; --i ) {
			for ( int j = n2 - 1; 0 <= j; --j ) {
				int[] poss = new int[ 3 ];

				poss[ 0 ] =  optimal[ i+1 ] [ j+1 ] + ( s1.charAt( i ) == s2.charAt( j ) ? 0 : 1 );
				poss[ 1 ] =  optimal[ i ] [ j+1 ] + 2;
				poss[ 2 ] =  optimal[ i+1 ] [ j ] + 2;
				
				Arrays.sort( poss );
				
				optimal[ i ][ j ] = poss[ 0 ];
			}
		}
		
		String t1 = "";
		String t2 = "";
		String penalty = "";
				
		int j = 0;
		int i = 0;
		int k = 0;
		while ( j < s2.length() && i < s1.length() ) {
			if ( s1.charAt(i) == s2.charAt(j) && optimal[ i ][ j ] == optimal[ i+1 ][ j+1 ]) {
				t1 += s1.charAt(i);
				t2 += s2.charAt(j);
				penalty += 0;
				++i;
				++j;
			}
			else if ( ( optimal[ i ][ j ] - optimal[ i+1 ][ j+1 ] ) == 1 ) {
				t1 += s1.charAt(i);
				t2 += s2.charAt(j);
				penalty += 1;
				++i;
				++j;
			}
			else if ( optimal[ i ][ j ] == optimal[ i+1 ][ j ] + 2 ) {
				t1 += s1.charAt(i);
				t2 += "-";
				penalty += 2;
				++i;
			}
			else if ( optimal[ i ][ j ] == optimal[ i ][ j+1 ] + 2 ) {
				t1 += "-";
				t2 += s2.charAt(j);
				penalty += 2;
				++j;
			}
		}
		while ( i < s1.length() ) {
			t1 += s1.charAt( i ) ;
			t2 += "-";
			penalty += 2;
			++i;
		}
		while ( j < s2.length() ) {
			t1 += "-" ;
			t2 += s2.charAt( j );
			penalty += 2;
			++j;
		}

		return new Solution(s1, s2, optimal, t1, t2, penalty);
	}
}


class Solution {
	String s1;
	String s2;
	int[][] optimal;
	String t1;
	String t2;
	String penalty;

	public Solution(String s1, String s2, int[][] optimal, String t1, String t2, String penalty) {
		this.s1 = s1;
		this.s2 = s2;
		this.optimal = optimal;
		this.t1 = t1;
		this.t2 = t2;
		this.penalty = penalty;
	}
	
	public String toString() {
		String result = "";
		for (int i = 0; i < optimal.length; ++i ) {
			for (int j = 0; j < optimal[i].length; ++j ) {
				result += String.format( "%3d ", optimal[i][j] );
			}
			result += "\n";
		}
		
		result += "\n";
	
		result += s1 + "\n" + s2 + "\n\n" + t1 + "\n" + t2 + "\n" + penalty;
		
		return result;
	}
	
	public boolean validate() {
		int n = t1.length();

		// check to see if solution is nonsensible
		if ( ( n != t2.length() ) || ( n != penalty.length() ) ) {
			System.out.println( "Penalty and edit strings have conflicting sizes" );
			return false;
		}
		// does t1 and t2 track s1 and s2
	
		for ( int k = 0, i = 0, j = 0; i < s1.length(); ++k ) {
			char b = s1.charAt(i);
			char c = t1.charAt(j);
			char d = t2.charAt(k);

			if ( ( c != '-' ) && ( b == c ) ) {
				++i; 
				++j;
			}
			else if ( ( c == '-' ) ) {
				++j;
			}
			else {
				System.out.println( "Edits nonsensible for first string" );
				return false;
			}
		}

		for ( int k = 0, i = 0, j = 0; j < s2.length(); ++k ) {
			char b = s2.charAt(i);
			char c = t2.charAt(j);
			char d = t1.charAt(k);

			if ( ( c != '-' ) && ( b == c ) ) {
				++i; 
				++j;
			}
			else if ( ( c == '-' ) ) {
				++j;
			}
			else {
				System.out.println( "Edits nonsensible for second string" );
				return false;
			}
		}
		
		// does penalty make sense
		int sum = 0;
		for ( int i = 0; i < n; ++i ) {
			char c1 = t1.charAt(i);
			char c2 = t2.charAt(i);
			char p  = penalty.charAt(i);
			if ( (c1 == c2) && (c1 != '-') && (p == '0' ) ) {
				sum += 0;
				continue;
			}
			else if ( (c1 != c2) && (p == '1' )) {
				sum += 1;
				continue;
			}
			else if ( (c1 == '-') && (c2 != '-') && (p == '2') ) {
				sum += 2; 
				continue;		
			}
			else if ( (c1 != '-') && (c2 == '-') && (p == '2') ) {
				sum += 2;
				continue;		
			}
			
			System.out.println( "Penalties do not correspond with edits" );
			return false;
		}
		
		// left to check the penalty match the score
		
		if ( sum == optimal[0][0] )  {
			return true;
		}
		else {
			System.out.println( "Penalties do not sum to score" );
			return false;
		}
	}
}