Merge pull request #1286 from Hitesh4278/find-the-n-th-value-after-k-seconds

Added the Solution of  Find the N-th Value After K Seconds - Issue No #1227

Author: ajay-dhangar

dsa-problems/leetcode-problems/3100-3199.md

@@ -417,6 +417,12 @@ export const problems = [
     "difficulty": "Medium",
     "leetCodeLink": "https://leetcode.com/problems/better-compression-of-string",
     "solutionLink": "#"
+  },
+   {
+    "problemName": "3179.Find the N-th Value After K Seconds",
+    "difficulty": "Medium",
+    "leetCodeLink": "https://leetcode.com/problems/find-the-n-th-value-after-k-seconds/",
+    "solutionLink": "/dsa-solutions/lc-solutions/3100-3189/find-the-n-th-value-after-k-seconds"
   }
 ];
 

dsa-solutions/lc-solutions/3100-3199/3179-find-the-n-th-value-after-k-seconds.md

@@ -0,0 +1,235 @@
+---
+id: find-the-n-th-value-after-k-seconds
+title:  Find the N-th Value After K Seconds
+sidebar_label: 3179. Find the N-th Value After K Seconds
+tags:
+- Array
+- Math
+- Simulation
+- Combinatorics
+- Prefix Sum
+description: "This is a solution to the Find the N-th Value After K Seconds problem on LeetCode."
+---
+
+## Problem Description
+You are given two integers n and k.
+
+Initially, you start with an array a of n integers where `a[i] = 1 for all 0 <= i <= n - 1`. After each second, you simultaneously update each element to be the sum of all its preceding elements plus the element itself. For example, after one second, a[0] remains the same, a[1] becomes a[0] + a[1], a[2] becomes a[0] + a[1] + a[2], and so on.
+
+Return the value of a[n - 1] after k seconds.
+
+Since the answer may be very large, return it modulo 109 + 7.
+
+### Examples
+
+**Example 1:**
+
+```
+Input: n = 4, k = 5
+
+Output: 56
+
+Explanation:
+
+Second	State After
+0	 [1,1,1,1]
+1	 [1,2,3,4]
+2	 [1,3,6,10]
+3	 [1,4,10,20]
+4	 [1,5,15,35]
+5	 [1,6,21,56]
+
+
+```
+
+**Example 2:**
+```
+Input: n = 5, k = 3
+
+Output: 35
+
+Explanation:
+
+Second	State After
+0	[1,1,1,1,1]
+1	[1,2,3,4,5]
+2	[1,3,6,10,15]
+3	[1,4,10,20,35]
+
+```
+
+### Constraints
+
+- `1 <= n, k <= 1000`
+
+## Solution for Find the N-th Value After K Seconds Problem
+### Approach 
+The problem essentially involves calculating the prefix sum of an array iteratively over a given number of seconds K. Each element in the array represents a value that is derived from summing up all previous elements in the array (including itself) from the previous iteration. The goal is to determine the value of the N-th element in the array after K seconds.
+### Steps
+-  Start with an array of size N where all elements are initialized to 1. This represents the array at time t=0.
+-  For each second from 1 to K, update the array by calculating the prefix sum for each element. This means that each element at position i (0-indexed) will be updated to the sum of all elements from position 0 to i of the previous iteration.
+- After K seconds, return the value of the N-th element in the array.
+
+<Tabs>
+  <TabItem value="Solution" label="Solution">
+
+    #### Implementation
+    ```jsx live
+    function Solution(arr) {
+       function valueAfterKSeconds(n, k) {
+        let arr = new Array(n).fill(1);
+        const mod = 1000000007;
+
+        for (let i = 1; i <= k; i++) {
+            let prefix = new Array(n).fill(0);
+            prefix[0] = arr[0] % mod;
+            for (let j = 1; j < n; j++) {
+                prefix[j] = (prefix[j - 1] + arr[j]) % mod;
+            }
+            arr = prefix;
+        }
+        return arr[n - 1];
+    }
+      const input = 4;
+      const  k = 5
+      const output = valueAfterKSeconds(input , k) ;
+      return (
+        <div>
+          <p>
+            <b>Input: </b>
+            {JSON.stringify(input)}
+          </p>
+          <p>
+            <b>Output:</b> {output.toString()}
+          </p>
+        </div>
+      );
+    }
+    ```
+
+    #### Complexity Analysis
+
+    - Time Complexity: $ O(N*K) $ because of Nested Loops
+    - Space Complexity: $ O(N) $  because of prefix array
+
+   ## Code in Different Languages
+   <Tabs>
+  <TabItem value="JavaScript" label="JavaScript">
+  <SolutionAuthor name="@hiteshgahanolia"/>
+   ```javascript
+    function valueAfterKSeconds(n, k) {
+        let arr = new Array(n).fill(1);
+        const mod = 1000000007;
+
+        for (let i = 1; i <= k; i++) {
+            let prefix = new Array(n).fill(0);
+            prefix[0] = arr[0] % mod;
+            for (let j = 1; j < n; j++) {
+                prefix[j] = (prefix[j - 1] + arr[j]) % mod;
+            }
+            arr = prefix;
+        }
+        return arr[n - 1];
+    }
+   
+    ```
+
+  </TabItem>
+  <TabItem value="TypeScript" label="TypeScript">
+  <SolutionAuthor name="@hiteshgahanolia"/> 
+   ```typescript
+   class Solution {
+    valueAfterKSeconds(n: number, k: number): number {
+        let arr: number[] = new Array(n).fill(1);
+        const mod: number = 1000000007;
+
+        for (let i = 1; i <= k; i++) {
+            let prefix: number[] = new Array(n).fill(0);
+            prefix[0] = arr[0] % mod;
+            for (let j = 1; j < n; j++) {
+                prefix[j] = (prefix[j - 1] + arr[j]) % mod;
+            }
+            arr = prefix;
+        }
+        return arr[n - 1];
+    }
+}
+
+    ```
+  </TabItem>
+  <TabItem value="Python" label="Python">
+  <SolutionAuthor name="@hiteshgahanolia"/>
+   ```python
+   class Solution:
+    def value_after_k_seconds(self, n: int, k: int) -> int:
+        arr = [1] * n
+        mod = 10**9 + 7
+
+        for i in range(1, k + 1):
+            prefix = [0] * n
+            prefix[0] = arr[0] % mod
+            for j in range(1, n):
+                prefix[j] = (prefix[j - 1] + arr[j]) % mod
+            arr = prefix
+        
+        return arr[n - 1]
+   ```
+  </TabItem>
+  <TabItem value="Java" label="Java">
+  <SolutionAuthor name="@hiteshgahanolia"/>
+   ```java
+   import java.util.Arrays;
+
+public class Solution {
+    public int valueAfterKSeconds(int n, int k) {
+        int[] arr = new int[n];
+        Arrays.fill(arr, 1);
+        int mod = 1000000007;
+
+        for (int i = 1; i <= k; i++) {
+            int[] prefix = new int[n];
+            prefix[0] = arr[0] % mod;
+            for (int j = 1; j < n; j++) {
+                prefix[j] = (prefix[j - 1] + arr[j]) % mod;
+            }
+            arr = prefix;
+        }
+        return arr[n - 1];
+    }
+}
+
+    ```
+
+  </TabItem>
+  <TabItem value="C++" label="C++">
+  <SolutionAuthor name="@hiteshgahanolia"/>
+   ```cpp
+   class Solution {
+public:
+    int valueAfterKSeconds(int n, int k) {
+        vector<int> arr(n, 1);
+        int mod = 1e9 + 7;
+        for (int i = 1; i <= k; i++) {
+            vector<int> prefix(n, 0);
+            prefix[0] = arr[0]%mod;
+            for (int j = 1; j < n; j++) {
+                prefix[j] = (prefix[j - 1] + arr[j]) % mod;
+            }
+            arr = prefix;
+        }
+        return arr[n-1];
+    }
+};
+    ```
+</TabItem>
+</Tabs>
+
+  </TabItem>
+</Tabs>
+
+## References
+
+- **LeetCode Problem**: [Find the N-th Value After K Seconds](https://leetcode.com/problems/find-the-n-th-value-after-k-seconds/)
+
+- **Solution Link**: [LeetCode Solution](https://leetcode.com/problems/find-the-n-th-value-after-k-seconds/solutions)
+