조합

arr : [1,2,3,4] 배열 
num: 3 4개 중 3개를 뽑음
function combination(arr, num) {
  let result = [];
  if(num == 1) return arr.map(e => [e]);
  
  arr.forEach((e,i,array) => {
    let rest = array.slice(i+1);
    let combinations = combination(rest,num-1);
    let combiArr = combinations.map(x => [e, ...x])
    result.push(...combiArr);
  }) 
  return result;
}
/* [ [ 1, 2, 3 ], [ 1, 2, 4 ],
   [ 1, 3, 4 ], [ 2, 3, 4 ] ] */

순열

function combination(arr, num) {
  let result = [];
  if(num == 1) return arr.map(e => [e]);
  
  arr.forEach((e,i,array) => {
    let rest = [...array.slice(0,i), ...array.slice(i+1)];
    let combinations = combination(rest,num-1);
    let combiArr = combinations.map(x => [e, ...x])
    result.push(...combiArr);
  }) 
  return result;
}
/* [
  [ 1, 2, 3 ], [ 1, 2, 4 ],
  [ 1, 3, 2 ], [ 1, 3, 4 ],
  [ 1, 4, 2 ], [ 1, 4, 3 ],
  [ 2, 1, 3 ], [ 2, 1, 4 ],
  [ 2, 3, 1 ], [ 2, 3, 4 ],
  [ 2, 4, 1 ], [ 2, 4, 3 ],
  [ 3, 1, 2 ], [ 3, 1, 4 ],
  [ 3, 2, 1 ], [ 3, 2, 4 ],
  [ 3, 4, 1 ], [ 3, 4, 2 ],
  [ 4, 1, 2 ], [ 4, 1, 3 ],
  [ 4, 2, 1 ], [ 4, 2, 3 ],
  [ 4, 3, 1 ], [ 4, 3, 2 ]
] */

부분집합

비트연산자 활용
let arr = [1,2,3,4];
let result = [];

for(let i = 1; i < (1 << arr.length); i++) {
  	result.push([]);
	for(let j = 0; j < arr.length; j++) {
    	if(i & (1 << j)) result[i-1].push(arr[j])
    }
}
 /* [
  [ 1 ],          [ 2 ],
  [ 1, 2 ],       [ 3 ],
  [ 1, 3 ],       [ 2, 3 ],
  [ 1, 2, 3 ],    [ 4 ],
  [ 1, 4 ],       [ 2, 4 ],
  [ 1, 2, 4 ],    [ 3, 4 ],
  [ 1, 3, 4 ],    [ 2, 3, 4 ],
  [ 1, 2, 3, 4 ]
] */

완전탐색

let set = new Set();
numOfCase([1,7],'')
function numOfCase(arr,str) {
	if(arr.length) {
    	for(let i = 0; i <arr.length; i++) {
        	let copy = [...arr];
          	copy.splice(i,1);
          	numOfCase(copy,str + arr[i])
        }
    }
  	if(str > 0) set.add(Number(str))
}
console.log(Array.from(set)) 
// [17,1,71,7]