Labeling common segments of multiple sets of segments

There are three different sets of segments. It is necessary to determine all the areas where they intersect, mark such intersections as separate new segments (for example, the intersection of the green and yellow sets is marked as a new segment – see exampleResult4), cut them out of the original sets, and output the sequence of the resulting segments in the range from 0 to 100.

// Segment mnemonics
const Task4 = () => {
    type IMnemo = "green" | "yellow" | "red"
    // Type for a segment - start and end
    interface IInterval {
        start: number,
        end: number
    }
    type ISourceIntervals = Record<IMnemo, IInterval[]>

    // Response type
    interface IExpectedResult extends IInterval {
        mnemo: IMnemo[],
    }
    // Source segments
    const sourceData: ISourceIntervals = {
        green: [{ start: 0, end: 30 }, { start: 90, end: 100 }],
        yellow: [{ start: 20, end: 40 }, { start: 50, end: 70 }],
        red: [{ start: 10, end: 50 }, { start: 70, end: 90 }],
    }

    // Expected result
    const expectedResult: IExpectedResult[] = [
        { "mnemo": ["green"], start: 0, end: 10 },
        { "mnemo": ["green", "red"], start: 10, end: 20 },
        { "mnemo": ["green", "yellow", "red"], start: 20, end: 30 },
        { "mnemo": ["yellow", "red"], start: 30, end: 40 },
        { "mnemo": ["red"], start: 40, end: 50 },
        { "mnemo": ["yellow"], start: 50, end: 70 },
        { "mnemo": ["red"], start: 70, end: 90 },
        { "mnemo": ["green"], start: 90, end: 100 },
    ]

    // Implement this function optimally, only one iteration over the source array is allowed!
    // Additional arrays/objects can be created.
    const getResult = (sourceIntervals: ISourceIntervals): IExpectedResult[] => {
        return expectedResult
    }

    // This will output the result of its work on the right
    return { expectedResult: expectedResult, result: getResult(sourceData) }
}

//Helper functions
const showTaskResult =(task: number, taskResult: {result: any, expectedResult: any}) => {
    console.log(`---Result of task ${task}---`)
    console.log('Expected: ', taskResult.expectedResult)
    console.log('From function: ', taskResult.result)
    console.log('')
}


showTaskResult(4, Task4())