使用最后一项 N
打印三角形图案
原文:https://www . geesforgeks . org/printing-the-triangle-pattern-use-last-term-n/
给定一个数字 N，它代表三角形模式的最后一项。任务是打印从 1 到 N 的三角形图案，这样每行就完成了。 三角形图案如下:
1
2 3
4 5 6
7 8 9 10
.
.
例:
Input: N = 3
Output:
1
2 3
Input: N = 7
Output:
1
2 3
4 5 6
7 will not be printed as
it would result in an incomplete row
进场:
- 从给定的最后一项 n 中找出完整的行数
- As: 对于最大高度= 1，最后一项为 1 对于最大高度= 2，最后一项为 3 对于最大高度= 3，最后一项为 6
- 所以最后一项形成了一个模式: 1，3，6，10，15，…
- 因此，数列 1、3、6、10、15 的第 n 项，……T2【A(n)= 1+2+3+4……+(n–1)+n = n(n+1)/2 即 A(n)是前 n 个自然数之和。
- 所以在
A(n) = n(n + 1) / 2
A(n) represents the last term (as per our problem),
and n represents the max height of the Triangle
- 因此，这可以看作:
Last term = height (height + 1) / 2
- 因此，
height = (-1 + sqrt(1 + 8*lastTerm)) / 2
- 找到最大高度后，就可以轻松打印三角形图案了。
以下是上述方法的实现:
C++
// C++ code for printing the
// Triangle Pattern using last term N
#include <bits/stdc++.h>
using namespace std;
// Function to demonstrate printing pattern
void triangle(int n)
{
// number of spaces
int k = 2 * n - 2;
// character to be printed
int ch = 1;
// outer loop to handle number of rows
// n in this case
for (int i = 0; i < n; i++) {
// inner loop to handle number spaces
// values changing acc. to requirement
for (int j = 0; j < k; j++)
cout << " ";
// decrementing k after each loop
k = k - 1;
// inner loop to handle number of columns
// values changing acc. to outer loop
for (int j = 0; j <= i; j++) {
// printing stars
cout << ch++ << " ";
}
// ending line after each row
cout << endl;
}
}
// Function to find the max height
// or the number of lines
// in the triangle pattern
int maxHeight(int n)
{
return (((int)sqrt(1 + 8.0 * n)) - 1) / 2;
}
// Driver Function
int main()
{
int N = 9;
triangle(maxHeight(N));
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java code for printing the
// Triangle Pattern using last term N
import java.util.*;
class GFG
{
// Function to demonstrate printing pattern
static void triangle(int n)
{
// number of spaces
int k = 2 * n - 2;
// character to be printed
int ch = 1;
// outer loop to handle number of rows
// n in this case
for (int i = 0; i < n; i++)
{
// inner loop to handle number spaces
// values changing acc. to requirement
for (int j = 0; j < k; j++)
System.out.print(" ");
// decrementing k after each loop
k = k - 1;
// inner loop to handle number of columns
// values changing acc. to outer loop
for (int j = 0; j <= i; j++)
{
// printing stars
System.out.print(ch++ + " ");
}
// ending line after each row
System.out.println();
}
}
// Function to find the max height
// or the number of lines
// in the triangle pattern
static int maxHeight(int n)
{
return (((int)Math.sqrt(1 + 8.0 * n)) - 1) / 2;
}
// Driver Code
public static void main(String[] args)
{
int N = 9;
triangle(maxHeight(N));
}
}
// This code is contributed by PrinciRaj1992
Python 3
# Python3 code for printing the
# Triangle Pattern using last term N
from math import sqrt
# Function to demonstrate printing pattern
def triangle(n) :
# number of spaces
k = 2 * n - 2;
# character to be printed
ch = 1;
# outer loop to handle number of rows
# n in this case
for i in range(n) :
# inner loop to handle number spaces
# values changing acc. to requirement
for j in range(k) :
print(" ", end = "");
# decrementing k after each loop
k = k - 1;
# inner loop to handle number of columns
# values changing acc. to outer loop
for j in range(i + 1) :
# printing stars
print(ch, end = " ");
ch += 1;
# ending line after each row
print()
# Function to find the max height
# or the number of lines
# in the triangle pattern
def maxHeight(n) :
ans = (sqrt(1 + 8.0 * n) - 1) // 2;
return int(ans);
# Driver Code
if __name__ == "__main__" :
N = 9;
triangle(maxHeight(N));
# This code is contributed by AnkitRai01
C
// C# code for printing the
// Triangle Pattern using last term N
using System;
class GFG
{
// Function to demonstrate printing pattern
static void triangle(int n)
{
// number of spaces
int k = 2 * n - 2;
// character to be printed
int ch = 1;
// outer loop to handle number of rows
// n in this case
for (int i = 0; i < n; i++)
{
// inner loop to handle number spaces
// values changing acc. to requirement
for (int j = 0; j < k; j++)
Console.Write(" ");
// decrementing k after each loop
k = k - 1;
// inner loop to handle number of columns
// values changing acc. to outer loop
for (int j = 0; j <= i; j++)
{
// printing stars
Console.Write(ch++ + " ");
}
// ending line after each row
Console.WriteLine();
}
}
// Function to find the max height
// or the number of lines
// in the triangle pattern
static int maxHeight(int n)
{
return (((int)Math.Sqrt(1 + 8.0 * n)) - 1) / 2;
}
// Driver Code
public static void Main(String[] args)
{
int N = 9;
triangle(maxHeight(N));
}
}
// This code is contributed by Princi Singh
java 描述语言
<script>
// Javascript code for printing the
// Triangle Pattern using last term N
// Function to demonstrate printing pattern
function triangle(n)
{
// number of spaces
var k = 2 * n - 2;
// character to be printed
var ch = 1;
// outer loop to handle number of rows
// n in this case
for (var i = 0; i < n; i++) {
// inner loop to handle number spaces
// values changing acc. to requirement
for (var j = 0; j < k; j++)
document.write(" ");
// decrementing k after each loop
k = k - 1;
// inner loop to handle number of columns
// values changing acc. to outer loop
for (var j = 0; j <= i; j++) {
// printing stars
document.write(ch++ + " ");
}
// ending line after each row
document.write("<br>");
}
}
// Function to find the max height
// or the number of lines
// in the triangle pattern
function maxHeight(n)
{
return parseInt(((parseInt(Math.sqrt(1 + 8.0 * n))) - 1) / 2);
}
// Driver Function
var N = 9;
triangle(maxHeight(N));
// This code is contributed by noob2000.
</script>
Output:
1
2 3
4 5 6
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