auto commit

notes/算法.md

@@ -104,17 +104,21 @@ public class ThreeSumSlow implements ThreeSum {
     public int count(int[] nums) {
         int N = nums.length;
         int cnt = 0;
-        for (int i = 0; i < N; i++)
-            for (int j = i + 1; j < N; j++)
-                for (int k = j + 1; k < N; k++)
-                    if (nums[i] + nums[j] + nums[k] == 0)
+        for (int i = 0; i < N; i++) {
+            for (int j = i + 1; j < N; j++) {
+                for (int k = j + 1; k < N; k++) {
+                    if (nums[i] + nums[j] + nums[k] == 0) {
                         cnt++;
+                    }
+                }
+            }
+        }
         return cnt;
     }
 }
 ```
 
-### 2. ThreeSumFast
+### 2. ThreeSumBinarySearch
 
 通过将数组先排序，对两个元素求和，并用二分查找方法查找是否存在该和的相反数，如果存在，就说明存在三元组的和为 0。
 
@@ -123,19 +127,23 @@ public class ThreeSumSlow implements ThreeSum {
 该方法可以将 ThreeSum 算法增长数量级降低为 O(N<sup>2</sup>logN)。
 
 ```java
-public class ThreeSumFast {
-    public static int count(int[] nums) {
+public class ThreeSumBinarySearch implements ThreeSum {
+
+    @Override
+    public int count(int[] nums) {
         Arrays.sort(nums);
         int N = nums.length;
         int cnt = 0;
-        for (int i = 0; i < N; i++)
+        for (int i = 0; i < N; i++) {
             for (int j = i + 1; j < N; j++) {
                 int target = -nums[i] - nums[j];
                 int index = BinarySearch.search(nums, target);
                 // 应该注意这里的下标必须大于 j，否则会重复统计。
-                if (index > j)
+                if (index > j) {
                     cnt++;
+                }
             }
+        }
         return cnt;
     }
 }
@@ -143,22 +151,59 @@ public class ThreeSumFast {
 
 ```java
 public class BinarySearch {
+
     public static int search(int[] nums, int target) {
         int l = 0, h = nums.length - 1;
         while (l <= h) {
             int m = l + (h - l) / 2;
-            if (target == nums[m])
+            if (target == nums[m]) {
                 return m;
-            else if (target > nums[m])
+            } else if (target > nums[m]) {
                 l = m + 1;
-            else
+            } else {
                 h = m - 1;
+            }
         }
         return -1;
     }
 }
 ```
 
+### 3. ThreeSumTwoPointer
+
+更有效的方法是先将数组排序，然后使用双指针进行查找，时间复杂度为 O(N<sup>2</sup>)。
+
+```java
+public class ThreeSumTwoPointer implements ThreeSum {
+
+    @Override
+    public int count(int[] nums) {
+        int N = nums.length;
+        int cnt = 0;
+        Arrays.sort(nums);
+        for (int i = 0; i < N - 2; i++) {
+            int l = i + 1, h = N - 1, target = -nums[i];
+            if (i > 0 && nums[i] == nums[i - 1]) continue;
+            while (l < h) {
+                int sum = nums[l] + nums[h];
+                if (sum == target) {
+                    cnt++;
+                    while (l < h && nums[l] == nums[l + 1]) l++;
+                    while (l < h && nums[h] == nums[h - 1]) h--;
+                    l++;
+                    h--;
+                } else if (sum < target) {
+                    l++;
+                } else {
+                    h--;
+                }
+            }
+        }
+        return cnt;
+    }
+}
+```
+
 ## 倍率实验
 
 如果 T(N) \~ aN<sup>b</sup>logN，那么 T(2N)/T(N) \~ 2<sup>b</sup>。
@@ -180,29 +225,20 @@ public class BinarySearch {
 public class RatioTest {
 
     public static void main(String[] args) {
-
         int N = 500;
         int loopTimes = 7;
         double preTime = -1;
-
         while (loopTimes-- > 0) {
-
             int[] nums = new int[N];
-
             StopWatch.start();
-
             ThreeSum threeSum = new ThreeSumSlow();
-
             int cnt = threeSum.count(nums);
             System.out.println(cnt);
-
             double elapsedTime = StopWatch.elapsedTime();
             double ratio = preTime == -1 ? 0 : elapsedTime / preTime;
             System.out.println(N + "  " + elapsedTime + "  " + ratio);
-
             preTime = elapsedTime;
             N *= 2;
-
         }
     }
 }