Create 1237.FindPositiveIntegerSolutionforaGivenEquation.py

Easy/1237.FindPositiveIntegerSolutionforaGivenEquation.py

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+'''
+    Given a function  f(x, y) and a value z, return all 
+    positive integer pairs x and y where f(x,y) == z.
+
+    The function is constantly increasing, i.e.:
+        - f(x, y) < f(x + 1, y)
+        - f(x, y) < f(x, y + 1)
+
+    The function interface is defined like this: 
+
+        interface CustomFunction {
+        public:
+            // Returns positive integer f(x, y) for any  
+            // given positive integer x and y.
+            int f(int x, int y);
+        };
+
+    For custom testing purposes you're given an integer 
+    function_id and a target z as input, where function_id 
+    represent one function from an secret internal list, on 
+    the examples you'll know only two functions from the list.  
+
+    You may return the solutions in any order.
+
+    Example:
+    Input: function_id = 1, z = 5
+    Output: [[1,4],[2,3],[3,2],[4,1]]
+    Explanation: function_id = 1 means that f(x, y) = x + y
+
+    Example:
+    Input: function_id = 2, z = 5
+    Output: [[1,5],[5,1]]
+    Explanation: function_id = 2 means that f(x, y) = x * y
+
+    Constraints:
+        - 1 <= function_id <= 9
+        - 1 <= z <= 100
+        - It's guaranteed that the solutions of f(x, y) == z 
+          will be on the range 1 <= x, y <= 1000
+        - It's also guaranteed that f(x, y) will fit in 32 bit 
+          signed integer if 1 <= x, y <= 1000
+'''
+#Difficulty: Easy
+#45 / 45 test cases passed.
+#Runtime: 40 ms
+#Memory Usage: 14.1 MB
+
+#Runtime: 40 ms, faster than 71.52% of Python3 online submissions for Find Positive Integer Solution for a Given Equation.
+#Memory Usage: 14.1 MB, less than 75.13% of Python3 online submissions for Find Positive Integer Solution for a Given Equation.
+
+"""
+   This is the custom function interface.
+   You should not implement it, or speculate about its 
+   implementation
+   class CustomFunction:
+       # Returns f(x, y) for any given positive integers 
+       # x and y.
+       # Note that f(x, y) is increasing with respect to 
+       # both x and y.
+       # i.e. f(x, y) < f(x + 1, y), f(x, y) < f(x, y + 1)
+       def f(self, x, y):
+  
+"""
+
+class Solution:
+
+    def findSolution(self, customfunction: 'CustomFunction', z: int) -> List[List[int]]:
+        result = []
+        for x in range(1, z+1):
+            y = self.binarySearch(customfunction, x, z)
+            if y:
+                result.append([x, y])
+        return result
+
+    def binarySearch(self, customfunction: 'CustomFunction', x: int, z: int) -> int:
+        lo = 1
+        hi = 1000
+        while lo <= hi:
+            mid = (lo+hi) // 2
+            if customfunction.f(x, mid) == z:
+                return mid
+            elif customfunction.f(x, mid) > z:
+                hi = mid - 1
+            else:
+                lo = mid + 1