给定一个正整数 n,你可以做如下操作:
1. 如果 n 是偶数,则用 n / 2替换 n。
2. 如果 n 是奇数,则可以用 n + 1或n - 1替换 n。
n 变为 1 所需的最小替换次数是多少?
思路:
1. 如果 n 是偶数,则用 n / 2替换 n。当为2的幂时,降幂是最快的选择;
2. 如果 n 是奇数,则可以用 n + 1或n - 1替换 n。选择n+1或者n-1取决于n+1或者n-1是2的幂次方;
3. 如果 n 是奇数,当n+1(n-1)之后,如果除以2任然是偶数,那么就选择n+1(n-1),因为奇数比偶数多一步的处理,如果两种操作后都是偶数,那么选择n-1;
4. 特殊数字3,当然是3-1最快;
public static int integerReplacement(long n){
if(n == 0 || n == 1){
return 0;
}
if(n == 2){
return 1;
}
if(n == 3){
return 2;
}
int count = 0;
boolean flage = true;
while(flage){
System.out.println("n: " + n + ", " + "count: " + count);
if(n == 0 || n == 1){//达到条件,结束循环
flage = false;
break;
}
if(n % 2 == 1){//为奇数
if(power2(n - 1)){//n-1为2的幂次方
n = n - 1;
count ++;
continue;
}
if(power2(n + 1)){//n+1为2的幂次方
n = n + 1;
count ++;
continue;
}
//如果 n 是奇数,当n+1(n-1)之后,如果除以2任然是偶数,那么就选择n+1(n-1)
n = select(n);
count ++;
System.out.println("n: " + n + ", " + "count: " + count);
}
count ++;
n = n / 2;
}
return count;
}
/**
* @Title: power2
* @Description: 判断一个数是否为2的幂次方
* @param num
* @return
* @author chenxy
* @date 2018-4-8 上午8:43:34
*/
public static boolean power2(long num){
if(num <= 0){
return false;
}
for(int i = 0; i <= 32; i++){
if(2<<i == num){
return true;
}
}
return false;
}
/**
* @Title: select
* @Description:
* @param num 如果 n 是奇数,当n+1(n-1)之后,如果除以2任然是偶数,那么就选择n+1(n-1),因为奇数比偶数多一步的处理;
* @return
* @author chenxy
* @date 2018-4-8 上午9:01:42
*/
public static long select(long num){
if(num == 3){
num = num - 1;
}
boolean flage1 = false;
boolean flage2 = false;
long temp = 0;
temp = (num - 1)/2;
if(temp % 2 == 0){
flage1 = true;
}
temp = (num + 1)/2;
if(temp % 2 == 0){
flage2 = true;
}
if(flage1){
num = num - 1;
return num;
}
if(flage2){
num = num + 1;
return num;
}
return num;
}
结果:
n = 2147483647
n: 2147483647, count: 0
n: 2147483648, count: 1
n: 1073741824, count: 2
n: 536870912, count: 3
n: 268435456, count: 4
n: 134217728, count: 5
n: 67108864, count: 6
n: 33554432, count: 7
n: 16777216, count: 8
n: 8388608, count: 9
n: 4194304, count: 10
n: 2097152, count: 11
n: 1048576, count: 12
n: 524288, count: 13
n: 262144, count: 14
n: 131072, count: 15
n: 65536, count: 16
n: 32768, count: 17
n: 16384, count: 18
n: 8192, count: 19
n: 4096, count: 20
n: 2048, count: 21
n: 1024, count: 22
n: 512, count: 23
n: 256, count: 24
n: 128, count: 25
n: 64, count: 26
n: 32, count: 27
n: 16, count: 28
n: 8, count: 29
n: 4, count: 30
n: 2, count: 31
n: 1, count: 32
n = 10000
1n: 10000, count: 0
1n: 5000, count: 1
1n: 2500, count: 2
1n: 1250, count: 3
1n: 625, count: 4
2n: 624, count: 5
1n: 312, count: 6
1n: 156, count: 7
1n: 78, count: 8
1n: 39, count: 9
2n: 40, count: 10
1n: 20, count: 11
1n: 10, count: 12
1n: 5, count: 13
1n: 4, count: 14
1n: 2, count: 15
1n: 1, count: 16