在给定的 2D 模式中找到第 R 行和第 C 列的元素

原文:https://www . geeksforgeeks . org/find-the-element-at-rth-row-cth-column-in-given-a-2d-pattern/

给定两个整数 R 和 C ，任务是找到 R 第行和 C 第列的元素。 图案:

  • The first element I , line = \frac{i*(i-1)}{2} + 1
  • Each element is a arithmetic progression incremental difference, where the tolerance is 1.
  • Initial difference term = i + 1

例:

输入: R = 4，C = 4 输出: 25 解释: 大小为 4 * 4 的图案为– 1 3 6 10 2 5 9 14 4 8 13 19 7 12 18 25 因此，Pat[4][4] = 25 处的元素输入: R = 3， C = 3 输出: 13 解释: 大小为 3 * 3 的图案为– 1 3 6 2 5 9 4 8 13 因此，帕特[3][3] = 13

天真方法:一个简单的解决方案是生成大小为 R * C 的模式矩阵，然后最终返回 R 第行和 C 第列的元素。 时间复杂度: O(RC)* 辅助空间: O(RC) 高效方法:*思路是利用公式\frac{R*(R+1)}{2} 找到 R 第行的第一项，然后借助循环最终计算出该列的 C 第项。 以下是上述方法的实施:

C++

// C++ implementation to compute the
// R'th row and C'th column of the
// given pattern

#include <bits/stdc++.h>
using namespace std;

// Function to compute the
// R'th row and C'th column of the
// given pattern
int findValue(int R, int C)
{

    // First element of a given row
    int k = (R * (R - 1)) / 2 + 1;

    int diff = R + 1;

    // Element in the given column
    for (int i = 1; i < C; i++) {
        k = (k + diff);
        diff++;
    }

    return k;
}

// Driver Code
int main()
{
    int R = 4;
    int C = 4;

    // Function call
    int k = findValue(R, C);

    cout << k;

    return 0;
}

Java 语言(一种计算机语言，尤用于创建网站)

// Java implementation to compute the
// R'th row and C'th column of the
// given pattern
import java.io.*;

class GFG{

// Function to compute the R'th
// row and C'th column of the
// given pattern
static int findValue(int R, int C)
{

    // First element of a given row
    int k = (R * (R - 1)) / 2 + 1;

    int diff = R + 1;

    // Element in the given column
    for(int i = 1; i < C; i++)
    {
       k = (k + diff);
       diff++;
    }
    return k;
}

// Driver code
public static void main (String[] args)
{
    int R = 4;
    int C = 4;

    // Function call
    int k = findValue(R, C);

    System.out.println(k);
}
}

// This code is contributed by mohit kumar 29

Python 3

# Python3 implementation to find the
# R'th row and C'th column value in
# the given pattern

# Function to find the
# R'th row and C'th column value in
# the given pattern
def findValue(R, C):

    # First element of a given row
    k = (R*(R-1))//2 + 1

    diff = R + 1

    # Element in the given column
    for i in range(1, C):
        k = (k + diff)
        diff+= 1

    return k

# Driver Code
if __name__ == "__main__":
    R = 4
    C = 4

    k = findValue(R, C)
    print(k)

C

// C# implementation to compute the
// R'th row and C'th column of the
// given pattern
using System;
class GFG{

// Function to compute the R'th
// row and C'th column of the
// given pattern
static int findValue(int R, int C)
{

    // First element of a given row
    int k = (R * (R - 1)) / 2 + 1;

    int diff = R + 1;

    // Element in the given column
    for(int i = 1; i < C; i++)
    {
        k = (k + diff);
        diff++;
    }
    return k;
}

// Driver code
public static void Main()
{
    int R = 4;
    int C = 4;

    // Function call
    int k = findValue(R, C);

    Console.Write(k);
}
}

// This code is contributed by Code_Mech

java 描述语言

<script>
// Javascript implementation to compute the
// R'th row and C'th column of the
// given pattern

// Function to compute the R'th
// row and C'th column of the
// given pattern
function findValue(R, C)
{

    // First element of a given row
    let k = (R * (R - 1)) / 2 + 1;

    let diff = R + 1;

    // Element in the given column
    for(let i = 1; i < C; i++)
    {
       k = (k + diff);
       diff++;
    }
    return k;
}

  // Driver Code

    let R = 4;
    let C = 4;

    // Function call
    let k = findValue(R, C);

     document.write(k);

</script>

Output: 

25

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