add

public/c/ch3/lcs/lcs1.c

@@ -0,0 +1,88 @@
+#include <stdio.h>
+#include <string.h> 
+#define MAX 100  
+int getLCS(char* text1, char* text2) {
+    int t1_len = strlen(text1);
+    int t2_len = strlen(text2);
+    int dp[MAX][MAX] = {0}; 
+    for (int i = 1; i <= t1_len; i++) {
+        for (int j = 1; j <= t2_len; j++) {
+            if (text1[i - 1] == text2[j - 1]) {
+                //找到一个 lcs 的元素，继续往前找
+                dp[i][j] = 1 + dp[i - 1][j - 1];
+            } else {//谁能让 lcs 最长，就取谁的值
+                dp[i][j] = (dp[i - 1][j] > dp[i][j - 1])?
+                           dp[i - 1][j] : dp[i][j - 1];
+            }
+        }
+    }
+    return dp[t1_len][t2_len];
+}
+
+void getLCSTable(int dp[MAX][MAX], char* text1, char* text2, char b[MAX][MAX]) {
+    int t1_len = strlen(text1);
+    int t2_len = strlen(text2);    
+    for (int i = 1; i <= t1_len; i++) {
+        for (int j = 1; j <= t2_len; j++) {
+            if (text1[i - 1] == text2[j - 1]) {
+                dp[i][j] = 1 + dp[i - 1][j - 1];
+                b[i][j] = 'X'; // LCS元素，使用 'X' 作为占位符
+            } else if (dp[i - 1][j] >= dp[i][j - 1]) {
+                dp[i][j] = dp[i - 1][j];
+                b[i][j] = '|'; // 取上面的值
+            } else {
+                dp[i][j] = dp[i][j - 1];
+                b[i][j] = '-'; // 取左边的值
+            }
+        }
+    }
+}
+
+void printLCSTable(char b[MAX][MAX], char* t1, char* t2, int l1, int l2) {
+    printf("\t");
+    for (int j = 0; j < l2; j++)  
+        printf("%c\t", t2[j]); 
+    printf("\n"); 
+    for (int i = 0; i <= l1; i++) {
+        printf("%c\t", (i == 0) ? ' ' : t1[i - 1]);
+        for (int j = 0; j <= l2; j++) {
+            if (i == 0 && j == 0) {
+                printf("\t");
+            } else {
+                printf("%c\t", b[i][j]);
+            }
+        }
+        printf("\n");
+    }
+}
+
+void printLCSString(char b[MAX][MAX], char* x, int i, int j) {
+    if (i == 0 || j == 0) return; 
+    if (b[i][j] == 'X') {
+        printLCSString(b, x, i - 1, j - 1);
+        // 打印当前字符
+        printf("%c", x[i - 1]);
+    } else if (b[i][j] == '|') {
+        printLCSString(b, x, i - 1, j);
+    } else {
+        printLCSString(b, x, i, j - 1);
+    }
+}
+
+int main() {
+    char t1[] = "ABCB";
+    char t2[] = "BDCA"; 
+    printf("字符串: %s 和字符串: %s 的 LCS 长度为: %d\n", t1, t2, getLCS(t1, t2));
+    printf("--------------------------------\n"); 
+    int dp[MAX][MAX] = {0};
+    char b[MAX][MAX] = {0};
+    getLCSTable(dp, t1, t2, b);
+    printLCSTable(b, t1, t2, strlen(t1), strlen(t2));
+    printf("-------------------------------\n");
+    
+    printf("LCS 字符串为: ");
+    printLCSString(b, t1, strlen(t1), strlen(t2));
+    printf("\n");
+
+    return 0;
+}