diff --git a/Cargo.lock b/Cargo.lock
index 4f75e37..9e49a6e 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -4,6 +4,10 @@
 name = "binary_tree_postorder_traversal"
 version = "0.1.0"
 
+[[package]]
+name = "edit_distance"
+version = "0.1.0"
+
 [[package]]
 name = "implement_queue_using_stacks"
 version = "0.1.0"
diff --git a/Cargo.toml b/Cargo.toml
index 9eb1a88..f5961ca 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -11,4 +11,5 @@ members = [
     "intersection_of_two_arrays",
     "longest_palindromic_substring",
     "reverse_words_in_a_string_iii",
+    "edit_distance",
 ]
diff --git a/README.md b/README.md
index d0e4792..ce9b0c4 100644
--- a/README.md
+++ b/README.md
@@ -11,6 +11,7 @@ Resolving problems of LeetCode in RustLang.
 * [5. Longest Palindromic Substring](./longest_palindromic_substring/lib.rs)
 * [7. Reverse Integer](./reverse_integer/src/lib.rs)
 * [15. 3 Sum](./three_sum/src/lib.rs)
+* [72. Edit Distance](./edit_distance/src/lib.rs)
 * [88. Merge Sorted Array](./merge_sorted_array/src/lib.rs)
 * [145. Binary Tree Postorder Traversal](./binary_tree_postorder_traversal/src/lib.rs)
 * [215. Kth Largest Element in an Array](./kth_largest/src/lib.rs)
diff --git a/edit_distance/Cargo.toml b/edit_distance/Cargo.toml
new file mode 100644
index 0000000..dec118e
--- /dev/null
+++ b/edit_distance/Cargo.toml
@@ -0,0 +1,9 @@
+[package]
+name = "edit_distance"
+version = "0.1.0"
+authors = ["Ryan Li <conbas2019@gmail.com>"]
+edition = "2018"
+
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[dependencies]
diff --git a/edit_distance/src/lib.rs b/edit_distance/src/lib.rs
new file mode 100644
index 0000000..7dcee63
--- /dev/null
+++ b/edit_distance/src/lib.rs
@@ -0,0 +1,77 @@
+/*!
+ * # 72. Edit Distance
+ *
+ * [Problem link](https://leetcode.com/problems/edit-distance/)
+ */
+
+#![allow(dead_code)]
+
+struct Solution {}
+
+// ----------------------------------------------------------------------------
+
+use std::collections::HashMap;
+
+impl Solution {
+    pub fn reduce_min_distance(
+        word1: &str,
+        word2: &str,
+        cache: &mut HashMap<(String, String), usize>,
+    ) -> usize {
+        if let Some(&min) = cache.get(&(word1.to_string(), word2.to_string())) {
+            return min;
+        };
+        let (length1, length2) = (word1.len(), word2.len());
+        if length1 == 0 || length2 == 0 {
+            let min = length1.max(length2);
+            cache.insert((word1.to_string(), word2.to_string()), min);
+            return min;
+        }
+        let word1_slice = word1[1..].to_string();
+        let word2_slice = word2[1..].to_string();
+        if word1.chars().next().unwrap() == word2.chars().next().unwrap() {
+            return Solution::reduce_min_distance(&word1_slice, &word2_slice, cache);
+        }
+        let insert = 1 + Solution::reduce_min_distance(word1, &word2_slice, cache); // insert the first char of word2 in front of word1
+        let delete = 1 + Solution::reduce_min_distance(&word1_slice, word2, cache); // delete the first char of word1
+        let edit = 1 + Solution::reduce_min_distance(&word1_slice, &word2_slice, cache); // change from the first char of word1 to the one of word2
+        let min = *[insert, delete, edit].iter().min().unwrap();
+        cache.insert((word1.to_string(), word2.to_string()), min);
+        min
+    }
+
+    pub fn min_distance(word1: String, word2: String) -> i32 {
+        let mut cache = HashMap::new();
+        Self::reduce_min_distance(&word1, &word2, &mut cache) as i32
+    }
+}
+
+// ----------------------------------------------------------------------------
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn accept(word1: &str, word2: &str, expected: i32) {
+        assert_eq!(
+            Solution::min_distance(word1.to_string(), word2.to_string()),
+            expected
+        );
+    }
+
+    #[test]
+    fn test_example_1() {
+        let word1 = "horse";
+        let word2 = "ros";
+        let expected = 3;
+        accept(word1, word2, expected);
+    }
+
+    #[test]
+    fn test_example_2() {
+        let word1 = "intention";
+        let word2 = "execution";
+        let expected = 5;
+        accept(word1, word2, expected);
+    }
+}