3160. Find the Number of Distinct Colors Among the Balls
Description
You are given an integer limit
and a 2D array queries
of size n x 2
.
There are limit + 1
balls with distinct labels in the range [0, limit]
. Initially, all balls are uncolored. For every query in queries
that is of the form [x, y]
, you mark ball x
with the color y
. After each query, you need to find the number of distinct colors among the balls.
Return an array result
of length n
, where result[i]
denotes the number of distinct colors after ith
query.
Note that when answering a query, lack of a color will not be considered as a color.
Example 1:
Input: limit = 4, queries = [[1,4],[2,5],[1,3],[3,4]]
Output: [1,2,2,3]
Explanation:
- After query 0, ball 1 has color 4.
- After query 1, ball 1 has color 4, and ball 2 has color 5.
- After query 2, ball 1 has color 3, and ball 2 has color 5.
- After query 3, ball 1 has color 3, ball 2 has color 5, and ball 3 has color 4.
Example 2:
Input: limit = 4, queries = [[0,1],[1,2],[2,2],[3,4],[4,5]]
Output: [1,2,2,3,4]
Explanation:
- After query 0, ball 0 has color 1.
- After query 1, ball 0 has color 1, and ball 1 has color 2.
- After query 2, ball 0 has color 1, and balls 1 and 2 have color 2.
- After query 3, ball 0 has color 1, balls 1 and 2 have color 2, and ball 3 has color 4.
- After query 4, ball 0 has color 1, balls 1 and 2 have color 2, ball 3 has color 4, and ball 4 has color 5.
Constraints:
1 <= limit <= 109
1 <= n == queries.length <= 105
queries[i].length == 2
0 <= queries[i][0] <= limit
1 <= queries[i][1] <= 109
Solutions
Solution 1: Double Hash Tables
We use a hash table g
to record the color of each ball, and another hash table cnt
to record the count of each color.
Next, we traverse the array queries
. For each query $(x, y)$, we increase the count of color $y$ by $1$, then check whether ball $x$ has been colored. If it has, we decrease the count of the color of ball $x$ by $1$. If the count drops to $0$, we remove it from the hash table cnt
. Then, we update the color of ball $x$ to $y$, and add the current size of the hash table cnt
to the answer array.
After the traversal, we return the answer array.
The time complexity is $O(m)$, and the space complexity is $O(m)$, where $m$ is the length of the array queries
.
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