Create maximum-number-of-ones.py

Author: kamyu104

Python/maximum-number-of-ones.py

@@ -0,0 +1,55 @@
+# Time:  O(1)
+# Space: O(1)
+
+class Solution(object):
+    def maximumNumberOfOnes(self, width, height, sideLength, maxOnes):
+        """
+        :type width: int
+        :type height: int
+        :type sideLength: int
+        :type maxOnes: int
+        :rtype: int
+        """
+        if width < height:
+            width, height = height, width
+
+        # 1. split matrix by SxS tiles
+        # 2. split each SxS tile into four parts
+        #    (r, c), (r, S-c), (S-r, c), (S-r, S-c)
+        # 3. for each count of tile part in matrix is
+        #    (R+1)*(C+1), (R+1)*C, R*(C+1), R*C (already in descending order)
+        # 4. fill one into matrix by tile part of which count is in descending order
+        #    until number of ones in a tile comes to maxOnes
+        # 
+        # ps. area of a tile and its count in matrix are as follows:
+        #
+        #  |<---- c ---->|<-- S-c -->|
+        #  ^             |           |
+        #  |             |           |
+        #  r (R+1)*(C+1) |  (R+1)*C  |
+        #  |             |           |
+        #  v             |           |
+        #  ---------------------------
+        #  ^             |           |
+        #  |             |           |
+        #  S-r  R*(C+1)  |   R*C     |
+        #  |             |           |
+        #  v             |           |
+        #  ---------------------------
+        #
+
+        R, r = divmod(height, sideLength)
+        C, c = divmod(width, sideLength)
+        assert(R <= C)
+        area_counts = [(r*c, (R+1)*(C+1)), \
+                       (r*(sideLength-c), (R+1)*C), \
+                       ((sideLength-r)*c, R*(C+1)), \
+                       ((sideLength-r)*(sideLength-c), R*C)]
+        result = 0
+        for area, count in area_counts:
+            area = min(maxOnes, area)
+            result += count*area
+            maxOnes -= area
+            if not maxOnes:
+                break
+        return result