# Longest Common Subsequence

β 1143. Longest Common Subsequence

medium | Accept. 61% | εζ£δΈζη«

Given two strings `text1`

and `text2`

, return the length of their longest common subsequence.

A common subsequence of two strings is a subsequence that is common to both strings.

```
Example:
Input: text1 = "abcbdab", text2 = "bdcaba"
Output: 4
Explanation:
The longest common subsequence is "bcba" and its length is 4.
```

## Code

```
public int longestCommonSubsequence(String text1, String text2) {
int m = text1.length(), n = text2.length();
int[][] dp = new int[m + 1][n + 1];
for (int i = 1; i <= m; i++) {
char c1 = text1.charAt(i - 1);
for (int j = 1; j <= n; j++) {
char c2 = text2.charAt(j - 1);
if (c1 == c2) {
dp[i][j] = dp[i - 1][j - 1] + 1; } else {
dp[i][j] = Math.max(dp[i - 1][j], dp[i][j - 1]); }
}
}
return dp[m][n];
}
```

## State transition

$dp[i][j] = \begin{cases}
dp[i - 1][j - 1] + 1 & s[i] = s[j] \\
max(dp[i][j - 1], dp[i - 1][j]) & s[i] \not = s[j]
\end{cases}$

Try clicking on different values to see how they are calculated.

"" | o | b | d | c | a | b | a | |
---|---|---|---|---|---|---|---|---|

"" | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

a | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |

b | 0 | 0 | 1 | 1 | 1 | 1 | 2 | 2 |

c | 0 | 0 | 1 | 1 | 2 | 2 | 2 | 2 |

b | 0 | 0 | 1 | 1 | 2 | 2 | 3 | 3 |

d | 0 | 0 | 1 | 2 | 2 | 2 | 3 | 3 |

a | 0 | 0 | 1 | 2 | 2 | 3 | 3 | 4 |

b | 0 | 0 | 1 | 2 | 2 | 3 | 4 | 4 |