CodingGyan

Longest Common Substring

medium Strings

Problem

Two words are given. Print the length of the longest continuous part that appears in both words. (A substring is continuous, unlike a subsequence.) If they share no letter, print 0.

Constraints

  • 1 <= length <= 1000
  • lowercase letters

Examples

Input

abcdxyz xyzabcd

Output

4

Solutions

Best approachTime O(n m)Space O(m)

If a[i] equals b[j], the common part that ends here is one longer than the common part that ended at (i - 1, j - 1). If they differ, it is 0. The best value seen is the answer. O(n m) time, O(m) memory.

Same code works in Java810172125Basic features only, so nothing changes between versions.
/*
 * Problem : Longest common part.
 * Input   : Two words.
 * Output  : The length.
 * Approach: DP with one row
 * Time    : O(n m)
 * Space   : O(m)
 * Java    : 8 or newer.
 */
import java.util.Scanner;

public class Main {
    // This method solves the task. It receives the input and returns the answer.
    static int solve(String a, String b) {
        // Step 1: run[j] is the length of the common ending of a[0..i] and b[0..j-1]. One row is enough.
        int[] run = new int[b.length() + 1];
        int best = 0;
        for (int i = 1; i <= a.length(); i++) {
            // Step 2: Go from right to left, so run[j - 1] still holds the value of the previous row.
            for (int j = b.length(); j >= 1; j--) {
                if (a.charAt(i - 1) == b.charAt(j - 1)) {
                    run[j] = run[j - 1] + 1;
                    best = Math.max(best, run[j]);
                } else {
                    // Step 3: A different letter breaks the common part.
                    run[j] = 0;
                }
            }
        }
        return best;
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        String a = scanner.next();
        String b = scanner.next();
        System.out.println(solve(a, b));
    }
}
Hints (2)
  1. Why does a mismatch give 0?
  2. Why go from right to left?

Try these next