added Max with Min Altitudes

Author: minhyeong-joe

DynamicProgramming/MaxWithMinAltitudes/README.md

@@ -0,0 +1,39 @@
+# Max Of Min Altitudes
+
+[Leetcode Link](https://leetcode.com/discuss/interview-question/383669/)
+
+## Problem:
+
+Given a matrix with r rows and c columns, find the maximum score of a path starting at [0, 0] and ending at [r-1, c-1]. The score of a path is the minimum value in that path. For example, the score of the path 8 → 4 → 5 → 9 is 4.
+
+Don't include the first or final entry. You can only move either down or right at any point in time.
+
+## Example:
+
+```
+Input:
+[[5, 1],
+ [4, 5]]
+
+Output: 4
+Explanation:
+Possible paths:
+5 → 1 → 5 => min value is 1
+5 → 4 → 5 => min value is 4
+Return the max value among minimum values => max(4, 1) = 4.
+```
+
+```
+Input:
+[[1, 2, 3]
+ [4, 5, 1]]
+
+Output: 4
+Explanation:
+Possible paths:
+1-> 2 -> 3 -> 1
+1-> 2 -> 5 -> 1
+1-> 4 -> 5 -> 1
+So min of all the paths = [2, 2, 4]. Note that we don't include the first and final entry.
+Return the max of that, so 4.
+```

DynamicProgramming/MaxWithMinAltitudes/solution.py

@@ -0,0 +1,18 @@
+def maxScore(grid):
+    dp = [[None for _ in range(len(grid))] for _ in range(len(grid))]
+    # top and left borders have 1 unique path, so the score is minimum of previous col or row
+    for j in range(1, len(dp[0])):
+        dp[0][j] = grid[0][j] if j == 1 else min(dp[0][j-1], grid[0][j])
+    for i in range(1, len(dp)):
+        dp[i][0] = grid[i][0] if i == 1 else min(dp[i-1][0], grid[i][0])
+    # score will be based on either route is from top or left, we want to take max score out of two paths
+    for i in range(1, len(dp)):
+        for j in range(1, len(dp[i])):
+            fromTop = min(dp[i-1][j], grid[i][j])
+            fromLeft = min(dp[i][j-1], grid[i][j])
+            dp[i][j] = max(fromTop, fromLeft)
+    return max(dp[-2][-1], dp[-1][-2])
+
+
+print(maxScore([[1, 2, 3], [4, 5, 1]]))
+print(maxScore([[8, 4, 5], [3, 2, 7], [1, 6, 9]]))

README.md

@@ -63,6 +63,7 @@ Languages used: Java and Python
 - [Longest Increasing Subsequence](DynamicProgramming/LongestIncreasingSubsequence)
 - [Longest Palindromic Substring](DynamicProgramming/LongestPalindromicSubstring)
 - [Maximum Length Pair Chain](DynamicProgramming/MaximumLengthPairChain)
+- [Max with Min Altitudes](DynamicProgramming/MaxWithMinAltitudes)
 - [Number Of Islands](DynamicProgramming/NumberOfIslands)
 - [Palindromic Substrings](DynamicProgramming/PalindromicSubstrings)
 - [Predict Winner](DynamicProgramming/PredictWinner)