Как пересечь два массива диапазонов?

идея, предложенная @Ted Hopp может быть реализован в меньшем количестве строк кода следующим образом:

var A = [[1, 3], [7, 9], [12, 18]];
var B = [[2, 3], [4, 5], [6, 8], [13, 14], [16, 17]];

var result = [];
var ai = 0, alength = A.length, ax, ay;
var bi = 0, blength = B.length, bx, by;
while (ai < alength && bi < blength) {
  ax = A[ai][0];
  ay = A[ai][1];
  bx = B[bi][0];
  by = B[bi][1];
  if (ay < bx) {
    // a ends before b
    ai++;
  } else if (by < ax) {
    // b ends before a
    bi++;
  } else {
    // a overlaps b
    result.push([ax > bx ? ax : bx, ay < by ? ay : by]);
    // the smaller range is considered processed
    if (ay < by) {
      ai++;
    } else {
      bi++;
    }
  }
}
console.log(result);

Ниже приведен комплексный тест с большими массивами:

var A = [];
var B = [];
var R = [];
(function(rangeArray1, rangeArray2, bruteForceResult) {
  // create random, non-overlapping, sorted ranges
  var i, n, x, y;
  for (i = 0, n = 0; i < 1000; i++) {
    x = n += Math.floor(Math.random() * 100) + 1;
    y = n += Math.floor(Math.random() * 100);
    rangeArray1.push([x, y]);
  }
  for (i = 0, n = 0; i < 1000; i++) {
    x = n += Math.floor(Math.random() * 100) + 1;
    y = n += Math.floor(Math.random() * 100);
    rangeArray2.push([x, y]);
  }
  // calculate intersections using brute force
  rangeArray1.forEach(function(a) {
    rangeArray2.forEach(function(b) {
      if (b[1] >= a[0] && a[1] >= b[0]) {
        bruteForceResult.push([Math.max(a[0], b[0]), Math.min(a[1], b[1])]);
      }
    });
  });
})(A, B, R);

var result = [];
var ai = 0, alength = A.length, ax, ay;
var bi = 0, blength = B.length, bx, by;
while (ai < alength && bi < blength) {
  ax = A[ai][0];
  ay = A[ai][1];
  bx = B[bi][0];
  by = B[bi][1];
  if (ay < bx) {
    // a ends before b
    ai++;
  } else if (by < ax) {
    // b ends before a
    bi++;
  } else {
    // a overlaps b
    result.push([ax > bx ? ax : bx, ay < by ? ay : by]);
    // the smaller range is considered processed
    if (ay < by) {
      ai++;
    } else {
      bi++;
    }
  }
}
console.log(JSON.stringify(R) === JSON.stringify(result) ? "test passed" : "test failed");

довольно просто, просто приличное количество кода для записи. Сплющить a и b в отдельные элементы вместо диапазонов найдите их пересечение и снова превратите его в массив диапазонов.

const a = [[1, 3], [7, 9], [12, 18]];
const b = [[2, 3], [4,5], [6,8], [13, 14], [16, 17]];
const rangeToArr = ([start, end]) => Array.from({ length: end - start + 1 }, (_, i) => start + i);
const flat = inputArr => inputArr.reduce((arr, elm) => arr.concat(...elm), []);
const aRange = flat(a.map(rangeToArr));
const bRange = flat(b.map(rangeToArr));
const intersection = aRange.filter(num => bRange.includes(num));
console.log(intersection);


// Have the intersection of elements
// now we have to turn the intersection back into an array of ranges again:
const { partialIntersectionRange, thisRangeStarted, lastNum }
= intersection.reduce(({ partialIntersectionRange, thisRangeStarted, lastNum }, num) => {
  // Initial iteration only: populate with initial values
  if (typeof thisRangeStarted !== 'number') {
    return { partialIntersectionRange, thisRangeStarted: num, lastNum: num };
  }
  // If this element is a continuation of the range from the last element
  // then just increment lastNum:
  if (lastNum + 1 === num) {
    return { partialIntersectionRange, thisRangeStarted, lastNum: num };
  }
  // This element is not a continuation of the previous range
  // so make a range out of [thisRangeStarted, lastNum] and push it to the range array
  // (in case thisRangeStarted === lastNum, only push a single value)
  if (thisRangeStarted !== lastNum) partialIntersectionRange.push([thisRangeStarted, lastNum]);
  else partialIntersectionRange.push([thisRangeStarted]);
  return { partialIntersectionRange, thisRangeStarted: num, lastNum: num };
}, { partialIntersectionRange: [] });
if (thisRangeStarted !== lastNum) partialIntersectionRange.push([thisRangeStarted, lastNum]);
else partialIntersectionRange.push([thisRangeStarted]);

console.log(JSON.stringify(partialIntersectionRange));

трудность заключается не в логике пересечения, а в том, чтобы отформатировать ее нужным образом.