arrays - How to convert an index into N coordinates? -

in 1 dimensional space:

x = 

in 2 dimensional space (of size sx, sy):

x = / sx y = % sx 

in 3 dimensional space (of size sx, sy, sz):

x = / (sy*sz) y = (i/sz) % sy z = % sz 

how deal n dimensional space? how can these formulas generalized?

what inverse conversion?

(x1, x2, ..., xn) --> 

note: variables integer.

i guess common formulas looks like:

to check formulas used programs , looks works.

#include <iostream> #include <string> #include <string.h>   #define sz1 2 #define sz2 3 #define sz3 4 #define sz4 5   using namespace std;  int main() {     int a[sz4][sz3][sz2][sz1];     int i,j,k,l,n,x1,x2,x3,x4,s1,s2,s3,s4;     s1=sz1;s2=sz2;s3=sz3,s4=sz4;      memset(a,0,sizeof(a));      (i=0;i<s1*s2*s3*s4;i++){         x4= i/(s1*s2*s3);         x3 = / (s1*s2) % s3;         x2 = (i/s1) % s2;         x1 = % s1;          a[x4][x3][x2][x1]=i;     }      (l=0;l<sz4;l++) {         (i=0;i<sz3;i++) {             for(j=0;j<sz2;j++) {                 for(k=0;k<sz1;k++) {                     n=s1*s2*s3*l+s1*s2*i+s1*j+k;//inverse convertion                     cout<<a[l][i][j][k]<<"{"<<n<<"} ";                 }                 cout<<"|";             }             cout<<endl;         }         cout<<endl<<endl;     }     return 0; }