build

chapter_dynamic_programming/edit_distance_problem.md

@@ -213,7 +213,32 @@ $$
 === "Swift"
 
     ```swift title="edit_distance.swift"
-    [class]{}-[func]{editDistanceDP}
+    /* 编辑距离：动态规划 */
+    func editDistanceDP(s: String, t: String) -> Int {
+        let n = s.utf8CString.count
+        let m = t.utf8CString.count
+        var dp = Array(repeating: Array(repeating: 0, count: m + 1), count: n + 1)
+        // 状态转移：首行首列
+        for i in stride(from: 1, through: n, by: 1) {
+            dp[i][0] = i
+        }
+        for j in stride(from: 1, through: m, by: 1) {
+            dp[0][j] = j
+        }
+        // 状态转移：其余行列
+        for i in stride(from: 1, through: n, by: 1) {
+            for j in stride(from: 1, through: m, by: 1) {
+                if s.utf8CString[i - 1] == t.utf8CString[j - 1] {
+                    // 若两字符相等，则直接跳过此两字符
+                    dp[i][j] = dp[i - 1][j - 1]
+                } else {
+                    // 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1
+                    dp[i][j] = min(min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1
+                }
+            }
+        }
+        return dp[n][m]
+    }
     ```
 
 === "Zig"
@@ -458,7 +483,35 @@ $$
 === "Swift"
 
     ```swift title="edit_distance.swift"
-    [class]{}-[func]{editDistanceDPComp}
+    /* 编辑距离：状态压缩后的动态规划 */
+    func editDistanceDPComp(s: String, t: String) -> Int {
+        let n = s.utf8CString.count
+        let m = t.utf8CString.count
+        var dp = Array(repeating: 0, count: m + 1)
+        // 状态转移：首行
+        for j in stride(from: 1, through: m, by: 1) {
+            dp[j] = j
+        }
+        // 状态转移：其余行
+        for i in stride(from: 1, through: n, by: 1) {
+            // 状态转移：首列
+            var leftup = dp[0] // 暂存 dp[i-1, j-1]
+            dp[0] = i
+            // 状态转移：其余列
+            for j in stride(from: 1, through: m, by: 1) {
+                let temp = dp[j]
+                if s.utf8CString[i - 1] == t.utf8CString[j - 1] {
+                    // 若两字符相等，则直接跳过此两字符
+                    dp[j] = leftup
+                } else {
+                    // 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1
+                    dp[j] = min(min(dp[j - 1], dp[j]), leftup) + 1
+                }
+                leftup = temp // 更新为下一轮的 dp[i-1, j-1]
+            }
+        }
+        return dp[m]
+    }
     ```
 
 === "Zig"