The power of an integer x is defined as the number of steps needed to transform x into 1 using the following steps:
if x is even then x = x / 2
if x is odd then x = 3 * x + 1
For example, the power of x = 3 is 7 because 3 needs 7 steps to become 1 (3 --> 10 --> 5 --> 16 --> 8 --> 4 --> 2 --> 1).
Given three integers lo, hi and k. The task is to sort all integers in the interval [lo, hi] by the power value in ascending order , if two or more integers have the same power value sort them by ascending order.
Return the kth integer in the range [lo, hi] sorted by the power value.
Notice that for any integer x(lo <= x <= hi) it is guaranteed that x will transform into 1 using these steps and that the power of x is will fit in a 32-bit signed integer.
Input: lo =12, hi =15, k =2Output: 13Explanation: The power of 12is9(12-->6-->3-->10-->5-->16-->8-->4-->2-->1)The power of 13is9The power of 14is17The power of 15is17The interval sorted by the power value [12,13,14,15]. For k =2 answer is the second element which is13.Notice that 12 and 13 have the same power value and we sorted them in ascending order. Same for14 and 15.
Input: lo =7, hi =11, k =4Output: 7Explanation: The power array corresponding to the interval [7,8,9,10,11]is[16,3,19,6,14].The interval sorted by power is[8,10,11,7,9].The fourth number in the sorted array is7.
Calculate the power (Collatz conjecture steps) for each number in the range using memoization to avoid recomputation, then sort by power value with number as tiebreaker.
#include<vector>#include<algorithm>#include<unordered_map>usingnamespace std;
classSolution {
private: unordered_map<int, int> memo;
intgetPower(int x) {
if (x ==1) return0;
if (memo.find(x) != memo.end()) return memo[x];
int original = x;
int steps =0;
while (x !=1&& memo.find(x) == memo.end()) {
if (x %2==0) {
x = x /2;
} else {
x =3* x +1;
}
steps++;
}
// x is either 1 or found in memo
int totalSteps = steps + (x ==1?0: memo[x]);
// Backtrack and memoize
x = original;
for (int i = steps; i >0; i--) {
memo[x] = totalSteps - (steps - i);
if (x %2==0) {
x = x /2;
} else {
x =3* x +1;
}
}
return memo[original];
}
public:int getKth(int lo, int hi, int k) {
vector<pair<int, int>> nums;
for (int i = lo; i <= hi; i++) {
nums.push_back({getPower(i), i});
}
sort(nums.begin(), nums.end());
return nums[k -1].second;
}
};
classSolution {
privateval memo = mutableMapOf<Int, Int>()
privatefungetPower(x: Int): Int {
if (x ==1) return0if (memo.containsKey(x)) return memo[x]!!val original = x
var current = x
var steps = 0while (current !=1&& !memo.containsKey(current)) {
current = if (current % 2==0) {
current / 2 } else {
3 * current + 1 }
steps++ }
val totalSteps = steps + if (current ==1) 0else memo[current]!!// Backtrack and memoize
current = original
for (i in steps downTo 1) {
memo[current] = totalSteps - (steps - i)
current = if (current % 2==0) {
current / 2 } else {
3 * current + 1 }
}
return memo[original]!! }
fungetKth(lo: Int, hi: Int, k: Int): Int {
val nums = mutableListOf<Pair<Int, Int>>()
for (i in lo..hi) {
nums.add(Pair(getPower(i), i))
}
nums.sortWith { a, b ->when {
a.first != b.first -> a.first.compareTo(b.first)
else-> a.second.compareTo(b.second)
}
}
return nums[k - 1].second
}
}
defgetKth(lo: int, hi: int, k: int) -> int:
memo = {}
defget_power(x):
if x ==1:
return0if x in memo:
return memo[x]
original = x
steps =0while x !=1and x notin memo:
if x %2==0:
x = x //2else:
x =3* x +1 steps +=1 total_steps = steps + (0if x ==1else memo[x])
# Backtrack and memoize x = original
for i in range(steps, 0, -1):
memo[x] = total_steps - (steps - i)
if x %2==0:
x = x //2else:
x =3* x +1return memo[original]
nums = []
for i in range(lo, hi +1):
nums.append((get_power(i), i))
nums.sort()
return nums[k -1][1]
use std::collections::HashMap;
pubfnget_kth(lo: i32, hi: i32, k: i32) -> i32 {
letmut memo: HashMap<i32, i32>= HashMap::new();
fnget_power(x: i32, memo: &mut HashMap<i32, i32>) -> i32 {
if x ==1 {
return0;
}
iflet Some(&power) = memo.get(&x) {
return power;
}
let original = x;
letmut current = x;
letmut steps =0;
while current !=1&&!memo.contains_key(¤t) {
if current %2==0 {
current = current /2;
} else {
current =3* current +1;
}
steps +=1;
}
let total_steps = steps +if current ==1 { 0 } else { memo[¤t] };
// Backtrack and memoize
current = original;
for i in (1..=steps).rev() {
memo.insert(current, total_steps - (steps - i));
if current %2==0 {
current = current /2;
} else {
current =3* current +1;
}
}
memo[&original]
}
letmut nums = Vec::new();
for i in lo..=hi {
nums.push((get_power(i, &mut memo), i));
}
nums.sort();
nums[(k -1) asusize].1}