chapter 1 sorted matrix search v1

Chapter 10 Sorting and searching/10.9. sorted_matrix_search.md

@@ -0,0 +1,44 @@
+# 10.9. Sorted matrix search
+
+## Given an M x N matrix in which each row and each column is sorted in ascending order, write a method to find an element
+
+> example
+
+```python
+A = [[1,2,4,5,7],
+     [2,3,5,6,8],
+     [3,6,7,8,10],
+     [4,7,8,9,11]]
+
+num = 3
+```
+
+## First idea
+
+If A[0][3] < num and A[3][0] < num, if A[3][3] < num, return -1. Otherwise it must be in the matrix.
+
+If A[0][3] => num or A[3][0] => num, Iterate through the last column, find first row where `A[row][3] > num`. Then iterate that row from the back. If not found, iterate through the last row, do the same. This should take O(N+M) in the worst case.
+
+```python
+def search_sorted_matrix(M, N, A, num):
+    if num < A[0][0] or num > A[M][N]:
+        return 0
+    if num == A[0][0] or num == A[M][N]:
+        return 1
+    if num < A[0][N]:
+        initidx = 0
+        maxidx = N
+        while True:
+            i = maxidx // 2
+            if A[0][i] == num:
+                return 1
+            elif A[0][i] > num:
+                maxidx = i
+            elif A[0][i] < num:
+                initidx = i
+
+            if A[0][initidx] < num and A[0][initidx+1] > num:
+                break
+
+
+```

Chapter 10 Sorting and searching/10.9. sorted_matrix_search.py

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+import unittest
+
+M = 5 - 1
+N = 5 - 1
+
+def search_sorted_matrix(A, num):
+    if num < A[0][0] or num > A[M][N]:
+        return 0
+    if num == A[0][0] or num == A[M][N]:
+        return 1
+    if num < A[0][N]:
+        initidx = 0
+        maxidx = N
+        while True:
+            i = maxidx // 2
+            if A[0][i] == num:
+                return 1
+            elif A[0][i] > num:
+                maxidx = i
+            elif A[0][i] < num:
+                initidx = i
+
+            if A[0][initidx] < num and A[0][initidx+1] > num:
+                break
+    return 0
+
+class Test(unittest.TestCase):
+    data = [
+        ([
+            [0, 1, 3, 4, 6],
+            [6, 7, 8, 9, 10],
+            [11, 12, 13, 14, 15],
+            [16, 17, 18, 19, 20],
+            [21, 22, 23, 24, 25]
+        ], 2, 1)
+    ]
+
+    def test_rotate_matrix(self):
+        for test_matrix, num, expected in self.data:
+            actual = search_sorted_matrix(test_matrix, num)
+            self.assertEqual(actual, expected)
+
+if __name__ == "__main__":
+    unittest.main()

README.md

@@ -24,3 +24,7 @@
 ## Chapter 8 Recursion
 
 * Magic index
+
+## Chapter 10 Sorting and searching
+
+* Sorted matrix search