【leetcode】1237. Find Positive Integer Solution for a Given Equation
题目如下:
Given a function
f(x, y)
and a valuez
, return all positive integer pairsx
andy
wheref(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 targetz
as input, wherefunction_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 1:
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 + yExample 2:
Input: function_id = 2, z = 5
Output: [[1,5],[5,1]]
Explanation: function_id = 2 means that f(x, y) = x * yConstraints:
1 <= function_id <= 9
1 <= z <= 100
- It's guaranteed that the solutions of
f(x, y) == z
will be on the range1 <= x, y <= 1000
- It's also guaranteed that
f(x, y)
will fit in 32 bit signed integer if1 <= x, y <= 1000
解题思路:看到1 <= x, y <= 1000时,就可以意识到O(n^2)的复杂度是可以接受的,那么两层循环计算一下吧。
代码如下:
"""
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(object):
def findSolution(self, customfunction, z):
"""
:type num: int
:type z: int
:rtype: List[List[int]]
"""
res = []
for x in range(1,1001):
for y in range(1,1001):
if customfunction.f(x,y) == z:
res.append([x,y])
elif customfunction.f(x,y) > z:
break
return res
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