给定一个由N 个整数组成的数组,任务是找到整数K ,它需要最少的移动次数才能将给定的数组转换为 K 的幂序列,即{K 0 , K 1 , K 2 , ……. , K N – 1 } 。在每次移动中,将数组元素增加或减少 1。
例子:
Input: arr[] = {1, 2, 3}
Output: 2
Explanation: By incrementing arr[2] by 1 modifies to {1, 2, 4} which is equal to {20, 21, 22}. Therefore, K = 2.
Input: arr[] = {1, 9, 27}
Output: 5
Explanation: Modifying array to {1, 5, 25} requires minimum number of moves. Therefore, K = 5.
方法:这个想法是检查从1开始的所有数字,直到一个数字的幂超过最大值,即 10 10 (假设)。请按照以下步骤解决问题:
- 检查从1到x 的所有数字,直到x的值N – 1 < max_element of array + move 需要转换为 1 的幂。
- 计算在该元素的幂中制作数组所需的移动。
- 如果需要的移动比前一个值小,则更新K和min move 的值。
- 打印K的值。
下面是上述方法的实现。
C++
// C++ program for the above approach
#include
using namespace std;
#define ll long long
// Function to find the value of K such
// that it takes minimum number of moves
// to convert the array in its power
ll findMinCostInteger(vector& a)
{
// Size of the array
int n = a.size();
// Finding tha sum of the array
ll sum = accumulate(a.begin(),
a.end(), 0);
ll K = 0, minmove = LLONG_MAX;
// Find K for which the count
// of moves will become minimum
for (int i = 1;; ++i) {
ll power = 1, count = 0;
for (ll j = 0; j < n; ++j) {
count += abs(a[j] - power);
if (j != n - 1)
power = power * (ll)i;
// If exceeds maximum value
if (power >= 1e10)
break;
}
if (power >= (1e10)
|| power > (ll)(sum - n)
+ a[n - 1])
break;
// Update minimum moves
if (minmove > count) {
minmove = count;
K = i;
}
}
// Print K corresponds to minimum
// number of moves
cout << K;
}
// Driver Code
int main()
{
// Given vector
vector a = { 1, 9, 27 };
// Function Call
findMinCostInteger(a);
return 0;
}
Java
// Java program for the above approach
import java.util.*;
class GFG{
// Function to find the value of K such
// that it takes minimum number of moves
// to convert the array in its power
static void findMinCostInteger(int a[], int n)
{
// Finding tha sum of the array
int sum = 0;
for(int i = 0; i < n; i++)
sum += a[i];
int K = 0, minmove = Integer.MAX_VALUE;
// Find K for which the count
// of moves will become minimum
for(int i = 1;; ++i)
{
int power = 1, count = 0;
for(int j = 0; j < n; ++j)
{
count += Math.abs(a[j] - power);
if (j != n - 1)
power = power * i;
// If exceeds maximum value
if (power >= 1e10)
break;
}
if (power >= (1e10) ||
power > (sum - n) + a[n - 1])
break;
// Update minimum moves
if (minmove > count)
{
minmove = count;
K = i;
}
}
// Print K corresponds to minimum
// number of moves
System.out.println(K);
}
// Driver Code
public static void main(String args[])
{
// Given vector
int []a = { 1, 9, 27 };
// Function Call
findMinCostInteger(a, 3);
}
}
// This code is contributed by bgangwar59
Python3
# Python3 program for the above approach
import sys
# Function to find the value of K such
# that it takes minimum number of moves
# to convert the array in its power
def findMinCostInteger(a):
# Size of the array
n = len(a)
# Finding tha sm of the array
sm = sum(a)
K = 0
minmove = sys.maxsize
# Find K for which the count
# of moves will become minimum
i = 1
while(1):
power = 1
count = 0
for j in range(n):
count += abs(a[j] - power)
if (j != n - 1):
power = power * i
# If exceeds maximum value
if (power >= 1e10):
break
if (power >= (1e10) or
power > (sm - n) + a[n - 1]):
break
# Update minimum moves
if (minmove > count):
minmove = count
K = i
i += 1
# Print K corresponds to minimum
# number of moves
print(K)
# Driver Code
if __name__ == '__main__':
# Given vector
a = [ 1, 9, 27 ]
# Function Call
findMinCostInteger(a)
# This code is contributed by SURENDRA_GANGWAR
C#
// C# program for the
// above approach
using System;
class GFG{
// Function to find the value
// of K such that it takes
// minimum number of moves
// to convert the array in
// its power
static void findMinCostint(int []a,
int n)
{
// Finding tha sum of the array
int sum = 0;
for(int i = 0; i < n; i++)
sum += a[i];
int K = 0, minmove = int.MaxValue;
// Find K for which the count
// of moves will become minimum
for(int i = 1;; ++i)
{
int power = 1, count = 0;
for(int j = 0; j < n; ++j)
{
count += Math.Abs(a[j] - power);
if (j != n - 1)
power = power * i;
// If exceeds maximum value
if (power >= 1e10)
break;
}
if (power >= (1e10) ||
power > (sum - n) +
a[n - 1])
break;
// Update minimum moves
if (minmove > count)
{
minmove = count;
K = i;
}
}
// Print K corresponds to
// minimum number of moves
Console.WriteLine(K);
}
// Driver Code
public static void Main(String []args)
{
// Given vector
int []a = {1, 9, 27};
// Function Call
findMinCostint(a, 3);
}
}
// This code is contributed by gauravrajput1
Javascript
输出
5
时间复杂度: O(N * max(x))
辅助空间: O(1)
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