From cb9bc3c3865dc0f779c836aaac90e7ad80ae0b85 Mon Sep 17 00:00:00 2001
From: Sanket Kale <sanket9k@gmail.com>
Date: Sun, 21 Jun 2026 10:45:55 -0500
Subject: [PATCH] Completed DP-3

---
 Problem1.py | 45 +++++++++++++++++++++++++++++++++++++++++++++
 Problem2.py | 33 +++++++++++++++++++++++++++++++++
 2 files changed, 78 insertions(+)
 create mode 100644 Problem1.py
 create mode 100644 Problem2.py

diff --git a/Problem1.py b/Problem1.py
new file mode 100644
index 00000000..3c64a985
--- /dev/null
+++ b/Problem1.py
@@ -0,0 +1,45 @@
+## Problem1: (https://leetcode.com/problems/delete-and-earn/)
+class Solution:
+    def deleteAndEarn(self, nums: List[int]) -> int:
+        """
+        Calculates the maximum points you can earn by deleting elements.
+        
+        Time Complexity: O(N + M)
+        - N is the number of elements in `nums`.
+        - M is the maximum value in `nums`.
+        Finding the max takes O(N). Initializing and iterating through the 
+        `sumOfFreq` array takes O(M). Populating it takes O(N). 
+        Total Time = O(N) + O(M) + O(N) + O(M) = O(N + M).
+        
+        Space Complexity: O(M)
+        - We create an array `sumOfFreq` of size M + 1. 
+        - The DP variables (previous, current, temp) only use O(1) space.
+        Total Space = O(M).
+        """
+        # Time: O(N) to find the maximum element
+        maxInArr = max(nums)
+        
+        # Space: O(M) for an array of size maxInArr + 1
+        # Time: O(M) to initialize
+        sumOfFreq = [0 for _ in range(maxInArr + 1)]
+        
+        # Time: O(N) to iterate through nums and populate the frequency sum
+        for n in nums:
+            sumOfFreq[n] += n
+            
+        n = len(sumOfFreq)
+        
+        if n == 2:
+            return sumOfFreq[1]
+            
+        previous = sumOfFreq[0] 
+        current = max(previous, sumOfFreq[1])
+        
+        # Time: O(M) to iterate through the sumOfFreq array
+        for i in range(2, n):
+            # Space: O(1) for temporary variables
+            temp = max(current, sumOfFreq[i] + previous)
+            previous = current
+            current = temp
+            
+        return current
\ No newline at end of file
diff --git a/Problem2.py b/Problem2.py
new file mode 100644
index 00000000..f964df3b
--- /dev/null
+++ b/Problem2.py
@@ -0,0 +1,33 @@
+## Problem2 (https://leetcode.com/problems/minimum-falling-path-sum/)
+class Solution:
+    def minFallingPathSum(self, matrix: List[List[int]]) -> int:
+        """
+        Time Complexity: O(N^2), where N is the number of rows (and columns) in the matrix.
+                         We iterate through almost every cell in the NxN matrix exactly once.
+        Space Complexity: O(1) auxiliary space. We modify the input matrix in-place to store 
+                          our intermediate results, so no extra proportional memory is allocated.
+        """
+        rows = len(matrix)
+        
+        # We start from the second row (index 1) because the minimum falling path sum 
+        # to reach any cell in the first row is just the value of the cell itself.
+        for r in range(1, rows):
+            for c in range(rows):
+                
+                # Fetch the three possible paths from the row directly above:
+                # 1. Left diagonal (check bounds to ensure we don't wrap around)
+                left = matrix[r - 1][c - 1] if c > 0 else float('inf')
+                
+                # 2. Directly above
+                mid = matrix[r - 1][c]
+                
+                # 3. Right diagonal (check bounds)
+                right = matrix[r - 1][c + 1] if c < rows - 1 else float('inf')
+                
+                # Update the current cell to store the minimum sum required to reach it.
+                # This builds our optimal substructure moving downwards.
+                matrix[r][c] = matrix[r][c] + min(left, mid, right)
+        
+        # After processing all rows, the last row contains the minimum path sums 
+        # ending at each respective column. The answer is simply the smallest one.
+        return min(matrix[-1])
\ No newline at end of file