【LeetCode】数学题

50. Pow(x, n)

题目：实现幂函数

思路：递归——注意超出最大值的判断

public class Solution {    public double myPow(double x, int n) {        if(n < 0){            x = 1/x;            n = ~n+1;        }        if(n == 0) return 1;        if(n == 1) return x;        if(x*x > Double.MAX_VALUE){            return 0.0;        }        if(n%2 == 0){            return myPow(x*x, n/2);        }        else{            return myPow(x*x, n/2)*x;        }    }}

69. Sqrt(x)

题目：实现开方函数

思路：二分——注意使用乘法，不要用除法，这样不会溢出。并且要求返回下取整。

public class Solution {    public int mySqrt(int x) {        if(x == 0) return 0;        if(x == 1) return 1;        int start = 0, end = x;        while(start <= end){            int mid = start+(end-start)/2;            if(mid == x/mid) return mid;            else if(mid < x/mid){                start = mid+1;            }            else{                end = mid-1;            }        }        return end;    }}

367. Valid Perfect Square

题目：判断一个整数是不是完全平方数

思路：二分法——注意要强制转换为浮点型

public class Solution {    public boolean isPerfectSquare(int num) {        int start = 0, end = num;        while(start <= end){            int mid = start + (end - start)/2;            if((double)mid == (double)num/mid) return true;            else if((double)mid > (double)num/mid){                end = mid - 1;            }            else{                start = mid + 1;            }        }        return false;    }}

还有一种牛顿方法

public boolean isPerfectSquare(int num) {        long x = num;        while (x * x > num) {            x = (x + num / x) >> 1;        }        return x * x == num;    }