c语言最长公共子序列自顶向下和自底向上代码

C语言中求解最长公共子序列可以使用动态规划算法，其中自顶向下和自底向上是两种不同的实现方式。

自顶向下的代码实现：

#include <stdio.h>
#include <string.h>

#define MAXLEN 100

int lcs(char *str1, char *str2, int m, int n, int memo[][MAXLEN]) {
    if (m == 0 || n == 0) {
        return 0;
    }
    if (memo[m-1] != -1) {
        return memo[m-1][n-1];
    }
    if (str1[m-1] == str2[n-1]) {
        memo[m-1][n-1] = 1 + lcs(str1, str2, m-1, n-1, memo);
    } else {
        memo[m-1][n-1] = (lcs(str1, str2, m, n-1, memo) > lcs(str1, str2, m-1, n, memo)) ? lcs(str1, str2, m, n-1, memo) : lcs(str1, str2, m-1, n, memo);
    }
    return memo[m-1][n-1];
}

int main() {
    char str1[MAXLEN], str2[MAXLEN];
    int m, n;
    scanf("%s", str1);
    scanf("%s", str2);
    m = strlen(str1);
    n = strlen(str2);
    int memo[MAXLEN][MAXLEN];
    memset(memo, -1, sizeof(memo));
    printf("The length of the longest common subsequence is %d\n", lcs(str1, str2, m, n, memo));
    return 0;
}

自底向上的代码实现：

#include <stdio.h>
#include <string.h>

#define MAXLEN 100

int lcs(char *str1, char *str2) {
    int m = strlen(str1);
    int n = strlen(str2);
    int memo[MAXLEN][MAXLEN];
    for (int i = 0; i <= m; i++) {
        for (int j = 0; j <= n; j++) {
            if (i == 0 || j == 0) {
                memo[i][j] = 0;
            } else if (str1[i-1] == str2[j-1]) {
                memo[i][j] = 1 + memo[i-1][j-1];
            } else {
                memo[i][j] = (memo[i][j-1] > memo[i-1][j]) ? memo[i][j-1] : memo[i-1][j];
            }
        }
    }
    return memo[m][n];
}

int main() {
    char str1[MAXLEN], str2[MAXLEN];
    scanf("%s", str1);
    scanf("%s", str2);
    printf("The length of the longest common subsequence is %d\n", lcs(str1, str2));
    return 0;
}