feat(geektime_algo): add 42 dynamic programming

edit_distance, longest_increasing_subsequence

rust/42_dynamic_programming/edit_distance.rs

@@ -0,0 +1,29 @@
+// leetcode 72 [edit_distance](https://leetcode.com/problems/edit-distance/)
+fn edit_distance(word1: &str, word2: &str) -> i32 {
+    let word1_chars: Vec<char> = word1.chars().collect();
+    let word2_chars: Vec<char> = word2.chars().collect();
+    let m = word1.len();
+    let n = word2.len();
+    let mut dp = vec![vec![0; m+1]; n+1];
+
+    // 初始化第一行
+    for i in 0..=m { dp[i][0] = i; }
+    // 初始化第一列
+    for j in 0..=n { dp[0][j] = j; }
+
+    for i in 1..=m {
+        for j in 1..=n {
+            let mut step = 0;
+            if word1_chars[i-1] != word2_chars[j-1] { step = 1; }
+            dp[i][j] = (dp[i][j-1] + 1).min(dp[i-1][j] + 1).min(dp[i-1][j-1] + step);
+        }
+    }
+
+    dp[m][n] as i32
+}
+fn main() {
+    let word1 = "mitcmu";
+    let word2 = "mtacnu";
+    let m = edit_distance(word1, word2);
+    println!("{:?}", m);
+}

rust/42_dynamic_programming/longest_increasing_subsequence.rs

@@ -0,0 +1,22 @@
+// leetcode 300 [longest_increasing_subsequence](https://leetcode.com/problems/longest-increasing-subsequence)
+fn longest_increasing_subsequence(nums: Vec<i32>) -> i32 {
+    if nums.len() <= 1 { return nums.len() as i32; }
+
+    let mut dp = vec![1; nums.len()];
+    let mut max_list = 1;
+
+    for i in 0..nums.len() {
+        for j in 0..i {
+            if nums[i] > nums[j] {
+                dp[i] = dp[i].max(dp[j]+1);
+            }
+        }
+        max_list = max_list.max(dp[i]);
+    }
+    max_list
+}
+fn main() {
+    let nums = vec![2, 9, 3, 6, 5, 1, 7];
+    let m = longest_increasing_subsequence(nums);
+    println!("{:?}", m);
+}