refine the window functions

docs/en/sql-reference/20-sql-functions/08-window-functions/cume-dist.md

@@ -1,65 +1,68 @@
----
-title: CUME_DIST
----
-import FunctionDescription from '@site/src/components/FunctionDescription';
-
-<FunctionDescription description="Introduced: v1.2.7"/>
-
-Returns the cumulative distribution of a given value in a set of values. It calculates the proportion of rows that have values less than or equal to the specified value, divided by the total number of rows. Please note that the resulting value falls between 0 and 1, inclusive.
-
-See also: [PERCENT_RANK](percent_rank.md)
-
-## Syntax
-
-```sql
-CUME_DIST() OVER (
-	PARTITION BY expr, ...
-	ORDER BY expr [ASC | DESC], ...
-)
-```
-
-## Examples
-
-This example retrieves the students' names, scores, grades, and the cumulative distribution values (cume_dist_val) within each grade using the CUME_DIST() window function.
-
-```sql
-CREATE TABLE students (
-    name VARCHAR(20),
-    score INT NOT NULL,
-    grade CHAR(1) NOT NULL
-);
-
-INSERT INTO students (name, score, grade)
-VALUES
-    ('Smith', 81, 'A'),
-    ('Jones', 55, 'C'),
-    ('Williams', 55, 'C'),
-    ('Taylor', 62, 'B'),
-    ('Brown', 62, 'B'),
-    ('Davies', 84, 'A'),
-    ('Evans', 87, 'A'),
-    ('Wilson', 72, 'B'),
-    ('Thomas', 72, 'B'),
-    ('Johnson', 100, 'A');
-
-SELECT
-    name,
-    score,
-    grade,
-    CUME_DIST() OVER (PARTITION BY grade ORDER BY score) AS cume_dist_val
-FROM
-    students;
-
-name    |score|grade|cume_dist_val|
---------+-----+-----+-------------+
-Smith   |   81|A    |         0.25|
-Davies  |   84|A    |          0.5|
-Evans   |   87|A    |         0.75|
-Johnson |  100|A    |          1.0|
-Taylor  |   62|B    |          0.5|
-Brown   |   62|B    |          0.5|
-Wilson  |   72|B    |          1.0|
-Thomas  |   72|B    |          1.0|
-Jones   |   55|C    |          1.0|
-Williams|   55|C    |          1.0|
-```
+---
+title: CUME_DIST
+---
+import FunctionDescription from '@site/src/components/FunctionDescription';
+
+<FunctionDescription description="Introduced: v1.2.7"/>
+
+Calculates the cumulative distribution of each row's value. Returns the fraction of rows with values less than or equal to the current row's value.
+
+See also: [PERCENT_RANK](percent_rank.md)
+
+## Syntax
+
+```sql
+CUME_DIST()
+OVER (
+    [ PARTITION BY partition_expression ]
+    ORDER BY sort_expression [ ASC | DESC ]
+)
+```
+
+**Arguments:**
+- `PARTITION BY`: Optional. Divides rows into partitions
+- `ORDER BY`: Required. Determines the distribution order
+- `ASC | DESC`: Optional. Sort direction (default: ASC)
+
+**Notes:**
+- Returns values between 0 and 1 (exclusive of 0, inclusive of 1)
+- Formula: (number of rows ≤ current value) / (total rows)
+- Always returns 1.0 for the highest value(s)
+- Useful for calculating percentiles and cumulative percentages
+
+## Examples
+
+```sql
+-- Create sample data
+CREATE TABLE scores (
+    student VARCHAR(20),
+    score INT
+);
+
+INSERT INTO scores VALUES
+    ('Alice', 95),
+    ('Bob', 87),
+    ('Charlie', 87),
+    ('David', 82),
+    ('Eve', 78);
+```
+
+**Calculate cumulative distribution (showing what percentage of students scored at or below each score):**
+
+```sql
+SELECT student, score,
+       CUME_DIST() OVER (ORDER BY score) AS cume_dist,
+       ROUND(CUME_DIST() OVER (ORDER BY score) * 100) AS cumulative_percent
+FROM scores
+ORDER BY score;
+```
+
+Result:
+```
+student | score | cume_dist | cumulative_percent
+--------+-------+-----------+-------------------
+Eve     |    78 |       0.2 |                20
+David   |    82 |       0.4 |                40
+Bob     |    87 |       0.8 |                80
+Charlie |    87 |       0.8 |                80
+Alice   |    95 |       1.0 |               100

docs/en/sql-reference/20-sql-functions/08-window-functions/dense-rank.md

@@ -2,59 +2,96 @@
 title: DENSE_RANK
 ---
 
-Returns the rank of a value within a group of values, without gaps in the ranks.
-
-The rank value starts at 1 and continues up sequentially.
-
-If two values are the same, they have the same rank.
+Assigns a rank to each row within a partition. Rows with equal values receive the same rank, with no gaps in subsequent rankings.
 
 ## Syntax
 
 ```sql
-DENSE_RANK() OVER ( [ PARTITION BY <expr1> ] ORDER BY <expr2> [ ASC | DESC ] [ <window_frame> ] )
+DENSE_RANK() 
+OVER (
+    [ PARTITION BY partition_expression ]
+    ORDER BY sort_expression [ ASC | DESC ]
+)
 ```
 
+**Arguments:**
+- `PARTITION BY`: Optional. Divides rows into partitions
+- `ORDER BY`: Required. Determines the ranking order
+- `ASC | DESC`: Optional. Sort direction (default: ASC)
+
+**Notes:**
+- Ranks start from 1
+- Equal values get the same rank
+- No gaps in ranking sequence after ties
+- Example: 1, 2, 2, 3, 4 (not 1, 2, 2, 4, 5 like RANK)
+
 ## Examples
 
-**Create the table**
 ```sql
-CREATE TABLE employees (
-  employee_id INT,
-  first_name VARCHAR,
-  last_name VARCHAR,
-  department VARCHAR,
-  salary INT
+-- Create sample data
+CREATE TABLE scores (
+    student VARCHAR(20),
+    subject VARCHAR(20),
+    score INT
 );
+
+INSERT INTO scores VALUES
+    ('Alice', 'Math', 95),
+    ('Alice', 'English', 87),
+    ('Alice', 'Science', 92),
+    ('Bob', 'Math', 85),
+    ('Bob', 'English', 85),
+    ('Bob', 'Science', 80),
+    ('Charlie', 'Math', 88),
+    ('Charlie', 'English', 85),
+    ('Charlie', 'Science', 85);
 ```
 
-**Insert data**
+**Dense rank all scores (showing no gaps after ties):**
+
 ```sql
-INSERT INTO employees (employee_id, first_name, last_name, department, salary) VALUES
-  (1, 'John', 'Doe', 'IT', 90000),
-  (2, 'Jane', 'Smith', 'HR', 85000),
-  (3, 'Mike', 'Johnson', 'IT', 82000),
-  (4, 'Sara', 'Williams', 'Sales', 77000),
-  (5, 'Tom', 'Brown', 'HR', 75000);
+SELECT student, subject, score,
+       DENSE_RANK() OVER (ORDER BY score DESC) AS dense_rank
+FROM scores
+ORDER BY score DESC, student, subject;
 ```
 
-**Calculating the total salary per department using DENSE_RANK**
+Result:
+```
+student | subject | score | dense_rank
+--------+---------+-------+-----------
+Alice   | Math    |    95 | 1
+Alice   | Science |    92 | 2
+Charlie | Math    |    88 | 3
+Alice   | English |    87 | 4
+Bob     | English |    85 | 5
+Bob     | Math    |    85 | 5
+Charlie | English |    85 | 5
+Charlie | Science |    85 | 5
+Bob     | Science |    80 | 6
+```
+
+**Dense rank scores within each student:**
 
 ```sql
-SELECT
-    department,
-    SUM(salary) AS total_salary,
-    DENSE_RANK() OVER (ORDER BY SUM(salary) DESC) AS dense_rank
-FROM
-    employees
-GROUP BY
-    department;
+SELECT student, subject, score,
+       DENSE_RANK() OVER (PARTITION BY student ORDER BY score DESC) AS subject_dense_rank
+FROM scores
+ORDER BY student, score DESC, subject;
 ```
 
 Result:
-
-| department | total_salary | dense_rank |
-|------------|--------------|------------|
-| IT         | 172000       | 1          |
-| HR         | 160000       | 2          |
-| Sales      | 77000        | 3          |
+```
+student | subject | score | subject_dense_rank
+--------+---------+-------+-------------------
+Alice   | Math    |    95 | 1
+Alice   | Science |    92 | 2
+Alice   | English |    87 | 3
+Bob     | English |    85 | 1
+Bob     | Math    |    85 | 1
+Bob     | Science |    80 | 2
+Charlie | Math    |    88 | 1
+Charlie | English |    85 | 2
+Charlie | Science |    85 | 2
+```