Get Target Number Using Single Number and Operations *+-/

document.write(JSON.stringify(getCombinations(26, 3)));

/*
 * For example, if target=26 and singleNum=3,
 * the answer is 3*3*3 - 3/3
 */
function getCombinations(target, singleNum) {
  var queue = [];
  var visited = {};
  queue.push({curVal: singleNum, last: singleNum, operators: []});

  while (queue.length > 0) {
    var node = queue.shift();
    // can't use curVal because for target=8 (3*3-3/3) the loop
    // will stop at 3*3-3=6 because 6 was visited by 3+3 earlier
    var visitedKey = node.curVal + '_' + node.last;
    if (visited[visitedKey]) {
        continue;
    }
    visited[visitedKey] = true;

    if (node.curVal == target) {
      return node.operators;
    }
    // maybe there is a better condition to stop the search
    // but this works
    if (node.curVal < 0 || node.curVal > target * singleNum) {
      continue;
    }

    // check * operator
    queue.push({
      curVal: node.curVal - node.last + node.last * singleNum,
      last: node.last * singleNum,
      operators: node.operators.concat(['*'])
    });
    // check + operator
    queue.push({
      curVal: node.curVal + singleNum,
      last: singleNum,
      operators: node.operators.concat(['+'])
    });
    // check - operator
    queue.push({
      curVal: node.curVal - singleNum,
      last: -singleNum,
      operators: node.operators.concat(['-'])
    });
    // check / operator
    if (node.last % singleNum == 0) {
      queue.push({
        curVal: node.curVal - node.last + node.last / singleNum,
        last: node.last / singleNum,
        operators: node.operators.concat(['/'])
      });
    }
  }
  return [];
}