1237. 找出给定方程的正整数解
给出一个函数 f(x, y) 和一个目标结果 z,请你计算方程 f(x,y) == z 所有可能的正整数 数对 x 和 y。
给定函数是严格单调的,也就是说:
f(x, y) < f(x + 1, y)
f(x, y) < f(x, y + 1)
函数接口定义如下:
interface CustomFunction {
public:
// Returns positive integer f(x, y) for any given positive integer x and y.
int f(int x, int y);
};
如果你想自定义测试,你可以输入整数 function_id 和一个目标结果 z 作为输入,其中 function_id 表示一个隐藏函数列表中的一个函数编号,题目只会告诉你列表中的 2 个函数。
你可以将满足条件的 结果数对 按任意顺序返回。
示例 1:
输入:function_id = 1, z = 5
输出:[[1,4],[2,3],[3,2],[4,1]]
解释:function_id = 1 表示 f(x, y) = x + y
示例 2:
输入:function_id = 2, z = 5
输出:[[1,5],[5,1]]
解释:function_id = 2 表示 f(x, y) = x * y
提示:
1 <= function_id <= 9
1 <= z <= 100
题目保证 f(x, y) == z 的解处于 1 <= x, y <= 1000 的范围内。
在 1 <= x, y <= 1000 的前提下,题目保证 f(x, y) 是一个 32 位有符号整数。
来源:力扣(LeetCode)
链接:https://leetcode-cn.com/problems/find-positive-integer-solution-for-a-given-equation
暴力
""" 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]]: res=[] for i in range(1,z+1): for j in range(1,z+1): if customfunction.f(i,j)==z: res.append([i,j]) return res
二分
""" 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]]: res=[] for i in range(1,z+1): l=1 r=z while l<=r: mid=(l+r)>>1 fun=customfunction.f(i,mid) if fun==z: res.append([i,mid]) break elif fun<z: l=mid+1 else: r=mid-1 return res
利用单调性
""" 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]]: y=z for x in range(1,z+1): while y: if customfunction.f(x,y)<=z: if customfunction.f(x,y)==z: yield [x,y] break y-=1