给定两个整数S和N,任务是找到可以放置在堆栈中的N 个整数的最大可能平方和,以满足以下属性:
- 堆栈顶部的整数不应小于其正下方的元素。
- 所有堆栈元素都应在[1, 9]范围内。
- 堆栈元素的总和应该完全等于S 。
如果不可能获得这样的安排,则打印-1 。
例子:
Input: S = 12, N = 3
Output: 86
Explanation:
Stack arrangement [9, 2, 1] generates the sum 12 (= S), thus, satisfying the properties.
Therefore, maximum possible sum of squares = 9 * 9 + 2 * 2 + 1 * 1= 81 + 4 + 1 = 86
Input: S = 11, N = 1
Output: -1
处理方法:按照以下步骤解决问题:
- 检查S是否有效,即它是否在[N, 9 * N]范围内。
- 初始化一个变量,比如res来存储堆栈元素的最大平方和。
- 栈中整数的最小值可以是1,所以用1初始化所有栈元素。因此,从S中减去N。
- 现在,检查值大于 1 的整数的数量。为此,将 8(如果可能)添加到从堆栈底部开始的整数,并继续添加直到S > 0 。
- 最后,将S % 8添加到当前整数并用 1 填充所有剩余的堆栈元素。
- 最后,添加堆栈元素的平方和。
下面是上述方法的实现:
C++
// C++ Program to implement
// the above approach
#include
using namespace std;
// Function to find the maximum
// sum of squares of stack elements
void maxSumOfSquares(int N,
int S)
{
// Stores the sum ofsquares
// of stack elements
int res = 0;
// Check if sum is valid
if (S < N || S > 9 * N)
{
cout << (-1);
return;
}
// Initialize all stack
// elements with 1
S = S - N;
// Stores the count the
// number of stack elements
// not equal to 1
int c = 0;
// Add the sum of squares
// of stack elements not
// equal to 1
while (S > 0)
{
c++;
if (S / 8 > 0)
{
res += 9 * 9;
S -= 8;
}
else
{
res += (S + 1) *
(S + 1);
break;
}
}
// Add 1 * 1 to res as the
// remaining stack elements
// are 1
res = res + (N - c);
// Print the result
cout << (res);
}
// Driver Code
int main()
{
int N = 3;
int S = 12;
// Function call
maxSumOfSquares(N, S);
}
// This code is contributed by 29AjayKumar
Java
// Java program to implement
// the above approach
import java.io.*;
import java.util.*;
class GFG {
// Function to find the maximum
// sum of squares of stack elements
public static void maxSumOfSquares(
int N, int S)
{
// Stores the sum ofsquares
// of stack elements
int res = 0;
// Check if sum is valid
if (S < N || S > 9 * N) {
System.out.println(-1);
return;
}
// Initialize all stack
// elements with 1
S = S - N;
// Stores the count the
// number of stack elements
// not equal to 1
int c = 0;
// Add the sum of squares of
// stack elements not equal to 1
while (S > 0) {
c++;
if (S / 8 > 0) {
res += 9 * 9;
S -= 8;
}
else {
res += (S + 1)
* (S + 1);
break;
}
}
// Add 1 * 1 to res as the
// remaining stack elements are 1
res = res + (N - c);
// Print the result
System.out.println(res);
}
// Driver Code
public static void main(String args[])
{
int N = 3;
int S = 12;
// Function call
maxSumOfSquares(N, S);
}
}
Python3
# Python3 program to implement
# the above approach
# Function to find the maximum
# sum of squares of stack elements
def maxSumOfSquares(N, S):
# Stores the sum ofsquares
# of stack elements
res = 0
# Check if sum is valid
if (S < N or S > 9 * N):
cout << -1;
return
# Initialize all stack
# elements with 1
S = S - N
# Stores the count the
# number of stack elements
# not equal to 1
c = 0
# Add the sum of squares of
# stack elements not equal to 1
while (S > 0):
c += 1
if (S // 8 > 0):
res += 9 * 9
S -= 8
else:
res += (S + 1) * (S + 1)
break
# Add 1 * 1 to res as the
# remaining stack elements are 1
res = res + (N - c)
# Print the result
print(res)
# Driver Code
if __name__ == '__main__':
N = 3
S = 12
# Function call
maxSumOfSquares(N, S)
# This code is contributed by mohit kumar 29
C#
// C# program to implement
// the above approach
using System;
class GFG{
// Function to find the maximum
// sum of squares of stack elements
public static void maxSumOfSquares(int N,
int S)
{
// Stores the sum ofsquares
// of stack elements
int res = 0;
// Check if sum is valid
if (S < N || S > 9 * N)
{
Console.WriteLine(-1);
return;
}
// Initialize all stack
// elements with 1
S = S - N;
// Stores the count the
// number of stack elements
// not equal to 1
int c = 0;
// Add the sum of squares of
// stack elements not equal to 1
while (S > 0)
{
c++;
if (S / 8 > 0)
{
res += 9 * 9;
S -= 8;
}
else
{
res += (S + 1) *
(S + 1);
break;
}
}
// Add 1 * 1 to res
// as the remaining
// stack elements are 1
res = res + (N - c);
// Print the result
Console.WriteLine(res);
}
// Driver Code
public static void Main(String []args)
{
int N = 3;
int S = 12;
// Function call
maxSumOfSquares(N, S);
}
}
// This code is contributed by shikhasingrajput
Javascript
输出:
86
时间复杂度:O(N)
辅助空间: O(1)