feat(geektime_algo): add 40 dynamic programming

bag, knapsack, triangle

rust/40_dynamic_programming/bag.rs

@@ -0,0 +1,42 @@
+fn knapsack(items: Vec<i32>, capacity: i32) -> i32 {
+    let mut states = vec![vec![false; (capacity + 1) as usize]; items.len()];
+    let mut result = vec![];
+    states[0][0] = true;
+    if items[0] <= capacity { states[0][items[0] as usize] = true; }
+    for i in 1..items.len() {
+        for j in 0..=capacity as usize {
+            if states[i-1][j] { states[i][j] = true; }
+        }
+
+        for j in 0..=(capacity - items[i]) as usize {
+            if states[i-1][j] { states[i][j + items[i] as usize] = true; }
+        }
+    }
+
+    let mut idx = capacity;
+    while idx <= capacity {
+       if states[items.len()-1][idx as usize] { break; }
+       idx += 1;
+    }
+    for i in (1..items.len()).rev() {
+        if idx - items[i] >= 0 && states[i-1][(idx-items[i]) as usize] {
+            idx -= items[i];
+            result.push(items[i]);
+        }
+    }
+
+    if idx != 0 { result.push(items[0]); }
+    println!("{:?}", result);
+
+    for i in (0..=capacity as usize).rev() {
+        if states[items.len()-1][i] { return i as i32; }
+    }
+    0
+}
+
+fn main() {
+    let items = vec![2, 2, 4, 6, 3];
+    let capacity = 9;
+    let m = knapsack(items, capacity);
+    println!("{}", m);
+}

rust/40_dynamic_programming/knapsack.rs

@@ -0,0 +1,32 @@
+fn knapsack(items: Vec<(i32, i32)>, capacity: i32) -> i32 {
+    let mut states = vec![-1; (capacity + 1) as usize];
+    let mut result = vec![];
+    states[0] = 0;
+    if items[0].0 <= capacity { states[items[0].0 as usize] = items[0].1; }
+    for i in 1..items.len() {
+        for j in 0..=(capacity - items[i].0) as usize {
+            if states[j] >= 0 {
+                let value = states[j] + items[i].1;
+                if value > states[j+items[i].0 as usize] {
+                    states[j+items[i].0 as usize] = value;
+                    result.push(items[i].0);
+                }
+            }
+        }
+    }
+
+    let mut max_value = -1;
+    for i in (0..=capacity as usize).rev() {
+        if states[i] >= max_value {
+            max_value = states[i];
+        }
+    }
+    max_value
+}
+
+fn main() {
+    let items = vec![(2, 3), (2, 4), (4, 8), (6, 9), (3, 6)];
+    let capacity = 9;
+    let m = knapsack(items, capacity);
+    println!("{}", m);
+}

rust/40_dynamic_programming/triangle.rs

@@ -0,0 +1,23 @@
+# leetcode [minimum_total](https://leetcode.com/problems/triangle/)
+
+pub fn minimum_total(mut triangle: Vec<Vec<i32>>) -> i32 {
+    if triangle.len() == 0 { return 0; }
+
+    for i in (0..triangle.len() - 1).rev() {
+        for j in 0..triangle[i].len() {
+            triangle[i][j] = triangle[i+1][j].min(triangle[i+1][j+1]) + triangle[i][j];
+        }
+    }
+    triangle[0][0]
+}
+
+fn main() {
+    let triangle = vec![
+        vec![2],
+        vec![3, 4],
+        vec![6, 5, 7],
+        vec![4, 1, 8, 3],
+    ];
+
+    println!("{:?}", minimum_total(triangle));
+}