Added Solutions to Leetcode 914

Author: shreyash3087

dsa-problems/leetcode-problems/0900-0999.md

@@ -99,7 +99,7 @@ export const problems = [
         problemName: "914. X of a Kind in a Deck of Cards",
         difficulty: "Easy",
         leetCodeLink: "https://leetcode.com/problems/x-of-a-kind-in-a-deck-of-cards",
-        solutionLink: "#"
+        solutionLink: "/dsa-solutions/lc-solutions/0900-0999/x-of-a-kind-in-a-deck-of-cards"
     },
     {
         problemName: "915. Partition Array into Disjoint Intervals",

dsa-solutions/lc-solutions/0900-0999/0914-x-of-a-kind-in-a-deck-of-cards.md

@@ -0,0 +1,264 @@
+---
+id: x-of-a-kind-in-a-deck-of-cards
+title: X of a Kind in a Deck of Cards
+sidebar_label: 0914 - X of a Kind in a Deck of Cards
+tags:
+  - Math
+  - Hash Table
+  - Array
+description: "This is a solution to the X of a Kind in a Deck of Cards problem on LeetCode."
+---
+
+## Problem Description
+
+You are given an integer array deck where `deck[i]` represents the number written on the $i^th$ card.
+
+Partition the cards into **one or more groups** such that:
+
+- Each group has **exactly** `x` cards where `x > 1`, and
+- All the cards in one group have the same integer written on them.
+
+Return `true` if such partition is possible, or `false` otherwise.
+
+
+### Examples
+
+**Example 1:**
+
+```
+Input: deck = [1,2,3,4,4,3,2,1]
+Output: true
+Explanation: Possible partition [1,1],[2,2],[3,3],[4,4].
+```
+**Example 2:**
+
+```
+Input: deck = [1,1,1,2,2,2,3,3]
+Output: false
+Explanation: No possible partition.
+```
+
+### Constraints
+
+- $1 \leq deck.length \leq 10^4$
+- $0 \leq deck[i] < 10^4$
+
+## Solution for X of a Kind in a Deck of Cards
+
+## Approach 1: Brute Force
+### Intuition
+
+We can try every possible `X`.
+
+### Algorithm
+
+Since we divide the deck of `N` cards into say, `K` piles of `X` cards each, we must have `N % X == 0`.
+
+Then, say the deck has `C_i` copies of cards with number `i`. Each group with number `i` has `X` copies, so we must have `C_i % X == 0`. These are necessary and sufficient conditions.
+
+### Code in Different Languages
+
+<Tabs>
+<TabItem value="cpp" label="C++">
+  <SolutionAuthor name="@Shreyash3087"/>
+
+```cpp
+class Solution {
+public:
+    bool hasGroupsSizeX(vector<int>& deck) {
+        int N = deck.size();
+        vector<int> count(10000, 0);
+        for (int c : deck)
+            count[c]++;
+
+        vector<int> values;
+        for (int i = 0; i < 10000; ++i)
+            if (count[i] > 0)
+                values.push_back(count[i]);
+
+        for (int X = 2; X <= N; ++X) {
+            if (N % X == 0) {
+                bool valid = true;
+                for (int v : values) {
+                    if (v % X != 0) {
+                        valid = false;
+                        break;
+                    }
+                }
+                if (valid)
+                    return true;
+            }
+        }
+
+        return false;
+    }
+};
+
+
+```
+</TabItem>
+<TabItem value="java" label="Java">
+  <SolutionAuthor name="@Shreyash3087"/>
+
+```java
+class Solution {
+    public boolean hasGroupsSizeX(int[] deck) {
+        int N = deck.length;
+        int[] count = new int[10000];
+        for (int c: deck)
+            count[c]++;
+
+        List<Integer> values = new ArrayList();
+        for (int i = 0; i < 10000; ++i)
+            if (count[i] > 0)
+                values.add(count[i]);
+
+        search: for (int X = 2; X <= N; ++X)
+            if (N % X == 0) {
+                for (int v: values)
+                    if (v % X != 0)
+                        continue search;
+                return true;
+            }
+
+        return false;
+    }
+}
+```
+
+</TabItem>
+<TabItem value="python" label="Python">
+  <SolutionAuthor name="@Shreyash3087"/>
+
+```python
+class Solution(object):
+    def hasGroupsSizeX(self, deck):
+        count = collections.Counter(deck)
+        N = len(deck)
+        for X in xrange(2, N+1):
+            if N % X == 0:
+                if all(v % X == 0 for v in count.values()):
+                    return True
+        return False
+```
+</TabItem>
+</Tabs>
+
+### Complexity Analysis
+
+#### Time Complexity: $O(N^2log(logN))$
+
+> **Reason**: where N is the number of cards. It is outside the scope of this article to prove that the number of divisors of N is bounded by $O(Nlog(⁡log⁡N))$.
+
+#### Space Complexity: $O(N)$ 
+
+> **Reason**: The space needed to store the counts of each card type in the `values` list.
+
+## Approach 2: Greatest Common Divisor
+### Intuition and Algorithm
+
+Again, say there are `C_i` cards of number `i`. These must be broken down into piles of `X` cards each, ie. `C_i % X == 0` for all `i`.
+
+Thus, `X` must divide the greatest common divisor of `C_i`. If this greatest common divisor `g` is greater than `1`, then `X = g` will satisfy. Otherwise, it won't.
+
+### Code in Different Languages
+
+<Tabs>
+<TabItem value="cpp" label="C++">
+  <SolutionAuthor name="@Shreyash3087"/>
+
+```cpp
+class Solution {
+public:
+    bool hasGroupsSizeX(vector<int>& deck) {
+        vector<int> count(10000, 0);
+        for (int c : deck)
+            count[c]++;
+
+        int g = -1;
+        for (int i = 0; i < 10000; ++i)
+            if (count[i] > 0) {
+                if (g == -1)
+                    g = count[i];
+                else
+                    g = gcd(g, count[i]);
+            }
+
+        return g >= 2;
+    }
+
+    int gcd(int x, int y) {
+        return x == 0 ? y : gcd(y % x, x);
+    }
+};
+
+```
+</TabItem>
+<TabItem value="java" label="Java">
+  <SolutionAuthor name="@Shreyash3087"/>
+
+```java
+class Solution {
+    public boolean hasGroupsSizeX(int[] deck) {
+        int[] count = new int[10000];
+        for (int c: deck)
+            count[c]++;
+
+        int g = -1;
+        for (int i = 0; i < 10000; ++i)
+            if (count[i] > 0) {
+                if (g == -1)
+                    g = count[i];
+                else
+                    g = gcd(g, count[i]);
+            }
+
+        return g >= 2;
+    }
+
+    public int gcd(int x, int y) {
+        return x == 0 ? y : gcd(y%x, x);
+    }
+}
+```
+
+</TabItem>
+<TabItem value="python" label="Python">
+  <SolutionAuthor name="@Shreyash3087"/>
+
+```python
+class Solution(object):
+    def hasGroupsSizeX(self, deck):
+        from fractions import gcd
+        vals = collections.Counter(deck).values()
+        return reduce(gcd, vals) >= 2
+```
+</TabItem>
+</Tabs>
+
+### Complexity Analysis
+
+#### Time Complexity: $O(Nlog^2(N))$
+
+> **Reason**: where N is the number of votes. If there are $C_i$ cards with number i, then each gcd operation is naively $O(\log^2 C_i)$. Better bounds exist, but are outside the scope of this article to develop
+
+#### Space Complexity: $O(N)$ 
+
+> **Reason**: The space needed to store the counts of each card type in the `values` list.
+
+
+
+## Video Solution 
+
+<LiteYouTubeEmbed
+    id="wN_BIEB73Jc"
+    params="autoplay=1&autohide=1&showinfo=0&rel=0"
+    title="LeetCode 914. X of a Kind in a Deck of Cards"
+    poster="hqdefault"
+    webp />
+
+## References
+
+- **LeetCode Problem**: [X of a Kind in a Deck of Cards](https://leetcode.com/problems/x-of-a-kind-in-a-deck-of-cards/description/)
+
+- **Solution Link**: [X of a Kind in a Deck of Cards](https://leetcode.com/problems/x-of-a-kind-in-a-deck-of-cards/solutions/)