See: https://leetcode.com/problems/insert-interval/

insertInterval.js

function insertValue(array, index, value) {
  const newArray = [...array];
  newArray.splice(index, 0, value);
  return newArray;
}

function replaceValue(array, start, end, value) {
  const newArray = [...array];
  newArray.splice(start, 1 + (end - start), value);
  return newArray;
}

/**
 * @param {number[][]} intervals
 * @param {number[]} newInterval
 * @return {number[][]}
 */
var insert = function(intervals, newInterval) {
  if (intervals.length === 0) {
    return [newInterval];
  }
  
  let start;
  let end;
  for (let i = 0; i < intervals.length; i++) {
    const current = intervals[i];
    const next = intervals[i + 1];
    
    if (start === undefined) {
      const afterCurrentRangeButNotOverlapping = newInterval[0] > current[1] && (!next || newInterval[1] < next[0]);
      if (afterCurrentRangeButNotOverlapping) {
        return insertValue(intervals, i + 1, newInterval);
      }
      
      const beforeCurrentRangeButNotOverlapping = newInterval[0] < current[0] && newInterval[1] < current[0];
      if (beforeCurrentRangeButNotOverlapping) {
        return insertValue(intervals, i, newInterval);
      }

      const startsInsideCurrentRange = newInterval[0] >= current[0] && newInterval[0] <= current[1];
      const startsBeforeCurrentRangeButContinuesInside = newInterval[0] <= current[0] && newInterval[1] >= current[0];
      const overlappingCurrentRange = startsInsideCurrentRange || startsBeforeCurrentRangeButContinuesInside;
      if (overlappingCurrentRange) {
        start = i;
        end = i;
        continue;
      }
    } else {
      const endsInsideOrAfterCurrentRange = newInterval[1] >= current[0];
      if (endsInsideOrAfterCurrentRange) {
        end = i;
        continue;
      }
    }
  }
  
  const lengthenedInterval = [
    Math.min(newInterval[0], intervals[start][0]),
    Math.max(newInterval[1], intervals[end][1])
  ];
  return replaceValue(intervals, start, end, lengthenedInterval);
};