2D Dynamic Programming & Knapsack

def longest_common_subsequence(text1: str, text2: str) -> int:
    m, n = len(text1), len(text2)
    # dp[i][j] = LCS length between text1[:i] and text2[:j]
    dp = [[0] * (n + 1) for _ in range(m + 1)]
    
    for i in range(1, m + 1):
        for j in range(1, n + 1):
            if text1[i - 1] == text2[j - 1]:
                # Characters match: extend diagonal subsequence
                dp[i][j] = 1 + dp[i - 1][j - 1]
            else:
                # Discard either char from text1 or text2
                dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])
                
    return dp[m][n]