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巴斯卡三角形
Pascal's Triangle
0 1 0 0 0 0
0 1 1 0 0 0
0 1 2 1 0 0
0 1 3 3 1 0
0 1 4 6 4 1
計算原理：如上面文字所列
每一格的數值即是( x , y ) ，其中 y 是由上往下數
套入公式 ( x , y ) = ( x-1 , y -1 ) + ( x , y-1 )
使用陣列，馬上就能寫出來
Every number existed in the triangle can be expressed like ( x , y ) = ( x - 1 , y -1 ) + ( x , y - 1 )
Please notice that the " y " here , is counted from up to down.
( For example : ( 2 , 1 ) = 0 ( 2 , 2 ) = 1 ( 3 , 3 ) = 3 )
You can try to write a script to compute this triangle using the formula above. ( It's recommended to use array. )
在數學上的應用：
Usage of Pascal's Triangle in Mathematics
0 1 1 0 0 0
0 1 2 1 0 0
0 1 3 3 1 0
0 1 4 6 4 1
計算原理：如上面文字所列
每一格的數值即是( x , y ) ，其中 y 是由上往下數
套入公式 ( x , y ) = ( x-1 , y -1 ) + ( x , y-1 )
使用陣列，馬上就能寫出來
Every number existed in the triangle can be expressed like ( x , y ) = ( x - 1 , y -1 ) + ( x , y - 1 )
Please notice that the " y " here , is counted from up to down.
( For example : ( 2 , 1 ) = 0 ( 2 , 2 ) = 1 ( 3 , 3 ) = 3 )
You can try to write a script to compute this triangle using the formula above. ( It's recommended to use array. )
在數學上的應用：
Usage of Pascal's Triangle in Mathematics
原始碼 (使用最省記憶、最有效率的寫法)
#include<stdio.h>
#include<stdlib.h>
int main ()
{
int phase[34][2],counter,x,row,y;
printf(" 《楊輝三角形產生器》\n\n本程式可以輸出你輸入的列數\n\n任何時候都可以輸入-1離開\n\n(３２位元電腦只支援到34行)\n\n ");
while(x==x)/* 無限迴圈開始 */
{
for(x=0;x<=34;x++) /* 清空變數 */
{
for(y=0;y<=1;y++)
phase[x][y]=0;
}
printf("請輸入顯示列數 : ");
scanf("%d",&counter);
printf("\n");
if(counter>=35)
counter=34;
if(counter==-1) /* 使用者輸入 -1 離開 */
break;
phase[0][0]=1; /* 初始化計算用數值 */
row=1;
while(row<=counter) /* 程式跑到指定列數才結束 */
{
for(x=1;x<=counter-row;x++) /* 美化用的迴圈... */
printf(" ");
for(x=1;x<=row;x++) /* 計算並顯示數值 */
{
phase[x][1]=phase[x-1][0]+phase[x][0];
printf(" %d",phase[x][1]);
}
for(x=0;x<=row;x++) /* 放入這個迴圈的數值 讓下個迴圈計算 */
phase[x][0]=phase[x][1];
row++; /* 跑的列數 +1 */
printf("\n\n");
}
} /* 無限迴圈結束 */
printf("(c) NTPU CSIE 49571602\n\n");
system("pause");
return 0;
}
Pascal's Triangle Code. ( White Texts Hidden Below, for your reference. )
(Using the most efficient method, which saves most memory that I've ever tried.)
#include<stdio.h>
#include<stdlib.h>
int main ()
{
int phase[34][2],counter,x,row,y;
printf(" << Pascal's Triangle Computer >>\n\nThis program computes the number of line you requested.\n\nYou may exit any time by typing -1\n\n( A 32-bit computer is limited to display less than 34 lines. )\n\n ");
while(x==x)
{
for(x=0;x<=34;x++)
{
for(y=0;y<=1;y++)
phase[x][y]=0;
}
printf("For How many Lines would you like to Compute : ");
scanf("%d",&counter);
printf("\n");
if(counter>=35)
counter=34;
if(counter==-1)
break;
phase[0][0]=1;
row=1;
while(row<=counter)
{
for(x=1;x<=counter-row;x++)
printf(" ");
for(x=1;x<=row;x++) /* 計算並顯示數值 */
{
phase[x][1]=phase[x-1][0]+phase[x][0];
printf(" %d",phase[x][1]);
}
for(x=0;x<=row;x++)
phase[x][0]=phase[x][1];
row++;
printf("\n\n");
}
}
printf("(c) NTPU CSIE 49571602\n\n");
system("pause");
return 0;
}
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