连续楼层函数的值：F(x) = F(floor(x/2)) + x

给定一个正整数数组。对于数组的每个元素 x，我们需要找到定义为F(x) = F(floor(x/2)) + x的连续楼层函数的值，其中 F(0) = 0。
例子 ：-

Input : arr[] = {6, 8}
Output : 10 15

Explanation : F(6) = 6 + F(3)
                   = 6 + 3 + F(1)
                   = 6 + 3 + 1 + F(0)
                   = 10
Similarly F(8) = 15

基本方法：对于给定的 x 值，我们可以使用简单的递归函数计算 F(x)：

int func(int x)
{
    if (x == 0) 
        return 0;
    return (x + func(floor(x/2)));
}

在这种方法中，如果我们有 n 个查询，那么每个查询元素都需要 O(x)
一种有效的方法是使用记忆化我们构造一个数组，该数组保存 x 的每个可能值的 F(x) 值。如果尚未计算，我们计算该值。否则我们返回值。

C++

// C++ program for finding value
// of continuous floor function
#include 
 
#define max 10000
using namespace std;
 
int dp[max];
 
void initDP()
    {
         for (int i = 0; i < max; i++)
             dp[i] = -1;
    }
 
// function to return value of F(n)
int func(int x)
    {
        if (x == 0)
            return 0;
        if (dp[x] == -1)
            dp[x] = x + func(x / 2);
 
        return dp[x];
    }
 
void printFloor(int arr[], int n)
    {
        for (int i = 0; i < n; i++)
            cout << func(arr[i]) << " ";
    }
 
// Driver code
int main()
    {
        // call the initDP() to fill DP array
        initDP();
 
        int arr[] = { 8, 6 };
        int n = sizeof(arr) / sizeof(arr[0]);
 
        printFloor(arr, n);
 
        return 0;
    }

Java

// Java program for finding value
// of continuous floor function
class GFG
{
    static final int max = 10000;
    static int dp[] = new int[max];
     
    static void initDP()
    {
        for (int i = 0; i < max; i++)
            dp[i] = -1;
    }
     
    // function to return value of F(n)
    static int func(int x)
    {
        if (x == 0)
            return 0;
        if (dp[x] == -1)
            dp[x] = x + func(x / 2);
     
        return dp[x];
    }
     
    static void printFloor(int arr[], int n)
    {
        for (int i = 0; i < n; i++)
            System.out.print(func(arr[i]) + " ");
    }
     
    // Driver code
    public static void main(String[] args)
    {
         
        // call the initDP() to fill DP array
        initDP();
     
        int arr[] = {8, 6};
        int n = arr.length;
     
        printFloor(arr, n);
    }
}
 
// This code is contributed by Anant Agarwal.

Python3

# Python3 program for finding value
# of continuous floor function
 
max = 10000
 
dp = [0] * max
 
# function to initialize the DP array
def initDP() :
     
        for i in range(max) :
                dp[i] = -1
     
# function to return value of F(n)
def func(x) :
 
    if (x == 0) :
        return 0
         
    if (dp[x] == -1) :
        dp[x] = x + func(x // 2)
 
    return dp[x]
     
def printFloor(arr, n) :
     
    for i in range(n) :
                 
        print(func(arr[i]), end = " ")
 
# Driver Code
if __name__ == "__main__" :
 
        # call the initDP() to
        # fill DP array        
        initDP()
 
        arr = [8, 6]
        n = len(arr)
 
        printFloor(arr, n)
 
# This code is contributed by Ryuga

C#

// C# program for finding value
// of continuous floor function
using System;
 
class GFG
{
    static int max = 10000;
    static int []dp = new int[max];
     
    static void initDP()
    {
        for (int i = 0; i < max; i++)
            dp[i] = -1;
    }
     
    // function to return value of F(n)
    static int func(int x)
    {
        if (x == 0)
            return 0;
        if (dp[x] == -1)
            dp[x] = x + func(x / 2);
     
        return dp[x];
    }
     
    static void printFloor(int []arr, int n)
    {
        for (int i = 0; i < n; i++)
            Console.Write(func(arr[i]) + " ");
    }
     
    // Driver code
    public static void Main()
    {
         
        // call the initDP() to fill DP array
        initDP();
     
        int []arr = {8, 6};
        int n = arr.Length;
     
        printFloor(arr, n);
    }
}
 
// This code is contributed by nitin mittal

Javascript

// Javascript program for finding value
// of continuous floor function
    let max = 10000;
    let dp = Array.from({length: max}, (_, i) => 0);
       
    function initDP()
    {
        for (let i = 0; i < max; i++)
            dp[i] = -1;
    }
       
    // function to return value of F(n)
    function func(x)
    {
        if (x == 0)
            return 0;
        if (dp[x] == -1)
            dp[x] = x + func(Math.floor(x / 2));
       
        return dp[x];
    }
       
    function prletFloor(arr, n)
    {
        for (let i = 0; i < n; i++)
            document.write(func(arr[i]) + " ");
    }
     
// driver function
 
        // call the initDP() to fill DP array
        initDP();
       
        let arr = [8, 6];
        let n = arr.length;
       
        prletFloor(arr, n);
    
   // This code is contributed by code_hunt.

输出：

15 10

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