Create 07. Kth Smallest Element in a Sorted Matrix.py

11_Binary-Search/07. Kth Smallest Element in a Sorted Matrix.py

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+# https://leetcode.com/problems/kth-smallest-element-in-a-sorted-matrix/
+
+class Solution:
+    def kthSmallest(self, matrix: List[List[int]], k: int) -> int:
+        row = len(matrix); col = len(matrix[0])
+        def isValid(num):  
+            count = 1
+            for i in range(row):
+                l = 0; r = col-1
+                while l <= r:     # bisect.bisect_left(matrix[i], num)
+                    mid = l + (r - l) // 2
+                    if matrix[i][mid] <= num:
+                        l = mid + 1
+                    else:
+                        r = mid - 1
+                count += l
+            return count <= k
+
+        mini = matrix[0][0]; maxi = matrix[0][-1]
+        for i in range(row):
+            mini = min(mini, matrix[i][0])
+            maxi = max(maxi, matrix[i][-1])
+
+        l = mini; r = maxi
+        while l <= r:
+            mid = l + (r - l) // 2
+            if isValid(mid):
+                l = mid + 1
+            else: 
+                r = mid - 1
+
+        return l
+
+
+# Time: O(log(maxi) * row * log(col))
+# Space: O(1)