Finding the number of ways to extract arrays with 7 elements from a larger array of 49 elements in Javascript

Question

Finding the number of ways to extract arrays with 7 elements from a larger array of 49 elements in Javascript

I have a task to create unique groups of 7 elements from an array of 49 and determine the number of possible outputs.

For example: [A,a,B,b,C,c,D,d,E,e,F,f,G,g,H,h,I,i,J,j,K,k,L,l,M,m,N,n,O,o,P,p,Q,q,R,r,S,s,T,t,U,u,V,v,W,w,X,x,Y]

The desired outputs are: [ [A,a,B,b,C,c,D], [a,B,b,C,c,D,d], [B,b,C,c,D,d,E], [b,C,c,D,d,E,e], . . . [A,C,c,D,d,E,e], [A,B,b,c,D,d,E], . . . ] How can I achieve this output? Below is my attempt based on advice received from stackoverflow:

let jar = ["A","a","B","b","C","c","D","d","E","e","F","f","G","g","H","h","I","i","J","j","K","k","L","l","M","m","N","n","O","o","P","p","Q","q","R","r","S","s","T","t","U","u","V","v","W","w","X","x","Y"];
 
const size = 7;

let result11 = [];

for(let i = 0; i <= (jar.length - size); i++){
     result11.push(jar.slice(i, size+i));
}
console.log(result11)

Each output should be unique without any repetition. For example, outputs like aaaaaaa, aaxxxYY, AAAAAAA, AABbcDe are not valid, but outputs like avWwXxY, bvWwXxY, cvWwXxY, among others, are acceptable.

javascript arrays

Answer 1

Answer №1

Here is a functional code snippet that generates unique combinations from an array. The starting point is the initial draw vector v. This vector should have the same number of elements as the desired draws and must be in ascending order. Using the function nextDraw(), the next possible combination is selected from the available numbers between 0 and n-1.

The snippet is limited to 1000 draws to avoid overwhelming you with all possible combinations, which would be too many to handle.

function nextDraw(v,n){
 // generate a new vector w by copying v
 // set k to point to the last element of w:
 let w=v.slice(0),l=w.length,k=l-1;
 while (true){ // unconditional loop
  // Is the k-th element of w lower than n-l+k?
  if (w[k]<n-l+k) {
   // increment w[k]
   w[k]++;
   // and, in case k<l-1:
   // initialise all following elements of w with an increasing sequence:
   for (let j=k+1;j<l;j++) {
    w[j]=w[j-1]+1;
   }
   // return a valid draw vector!
   return w;
  }
  else {
   // as long as there is still a smaller k index available: decrement k
   // and continue with the while loop
   if(k) k--
   // else: we have reached the end of the series! 
   else return false;
  }
 }
}
function allDraws(v,n){
 const res=[];
 res.push(v);
 while (res.length<1000 && (v=nextDraw(v,n))) res.push(v)
 return res;
}

// Show first 1000 and last 121 draws:
[[0,1,2,3,4,5,6],[38,43,44,45,46,47,48]].forEach(v=>{
  let res=allDraws(v,49);
  console.log(res.length,res.map(r=>r.join(",")));
});

Although the snippet works with index numbers instead of arbitrary elements, you can easily use the calculated index vectors to retrieve actual values from an array of length n.

Answer 2

Here is a functional code snippet that generates unique combinations from an array. The starting point is the initial draw vector v. This vector should have the same number of elements as the desired draws and must be in ascending order. Using the function nextDraw(), the next possible combination is selected from the available numbers between 0 and n-1.

The snippet is limited to 1000 draws to avoid overwhelming you with all possible combinations, which would be too many to handle.

function nextDraw(v,n){
 // generate a new vector w by copying v
 // set k to point to the last element of w:
 let w=v.slice(0),l=w.length,k=l-1;
 while (true){ // unconditional loop
  // Is the k-th element of w lower than n-l+k?
  if (w[k]<n-l+k) {
   // increment w[k]
   w[k]++;
   // and, in case k<l-1:
   // initialise all following elements of w with an increasing sequence:
   for (let j=k+1;j<l;j++) {
    w[j]=w[j-1]+1;
   }
   // return a valid draw vector!
   return w;
  }
  else {
   // as long as there is still a smaller k index available: decrement k
   // and continue with the while loop
   if(k) k--
   // else: we have reached the end of the series! 
   else return false;
  }
 }
}
function allDraws(v,n){
 const res=[];
 res.push(v);
 while (res.length<1000 && (v=nextDraw(v,n))) res.push(v)
 return res;
}

// Show first 1000 and last 121 draws:
[[0,1,2,3,4,5,6],[38,43,44,45,46,47,48]].forEach(v=>{
  let res=allDraws(v,49);
  console.log(res.length,res.map(r=>r.join(",")));
});

Although the snippet works with index numbers instead of arbitrary elements, you can easily use the calculated index vectors to retrieve actual values from an array of length n.

Finding the number of ways to extract arrays with 7 elements from a larger array of 49 elements in Javascript

Answer №1

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