feat(geektime_algo): add 38 divide and conquer

Author: caitlingao

rust/38_divide_and_conquer/merge_sort_count.rs

@@ -0,0 +1,57 @@
+fn merge_sort_count(mut nums: Vec<i32>) -> i32 {
+    let mut count = 0;
+    let n = nums.len() - 1;
+    merge_sort(&mut nums, 0, n, &mut count);
+    count
+}
+
+fn merge_sort(nums: &mut Vec<i32>, low: usize, high: usize, count: &mut i32) {
+    if low >= high { return; }
+
+    let middle = low + ((high - low) >> 1);
+    merge_sort(nums, low, middle, count);
+    merge_sort(nums, middle+1, high, count);
+
+    merge(nums, low, middle, high, count);
+}
+
+fn merge(nums:   &mut Vec<i32>,
+         low:    usize,
+         middle: usize,
+         high:   usize,
+         count:  &mut i32) {
+    let mut i = low;
+    let mut j = middle + 1;
+    let mut tmp = vec![];
+
+    while i <= middle && j <= high {
+        if nums[i] <= nums[j] {
+            tmp.push(nums[i]);
+            i += 1;
+        } else {
+            // count += &(middle - i + 1);
+            *count += (middle - i + 1) as i32;
+            tmp.push(nums[j]);
+            j += 1;
+        }
+    }
+
+    while i <= middle {
+        tmp.push(nums[i]);
+        i += 1;
+    }
+
+    while j <= high {
+        tmp.push(nums[j]);
+        j += 1;
+    }
+
+   for i in 0..=(high-low) {
+       nums[low+1] = tmp[i];
+   }
+}
+fn main() {
+    let nums = vec![1, 5, 6, 2, 3, 4];
+    let m = merge_sort_count(nums);
+    println!("{:?}", m);
+}