12 islanders balancing problem

islanders.ts

// Random Integer from  m to n excluding e
const randInt = (m: number, n: number, e?: number): number =>  {
    const result = Math.floor(Math.random() * m) + n;
    return e == undefined ? result :
           result == e ? randInt(m, n, e) : 
           result
}

class Person { constructor(public weight: number) {} }

const weight = (ps: Person[]) => ps.reduce((sum, next) => next.weight + sum, 0)

function findDifferentPerson(population: Person[]): Person | undefined {
    if(population.length != 12)
        return undefined

    // split the population into three even groups (generalized as an odd number of even membered groups?)
    const group1 = population.slice(0,4),
          group2 = population.slice(4,8),
          group3 = population.slice(8,12);

    // 1. Weigh the first two groups
    const wg1 = weight(group1),
          wg2 = weight(group2)

    if(wg1 == wg2) {
        // Then group3 contains the candidate and every person in group1, group2 have the same weight
        // Comparing group3 in its entirety to group1 or group2 will not gain us any additional information
        // as the individual could weigh more or less. By the same argument we can't split group 3 in half 
        // and weigh as we don't know if the candidate is heavier or lighter

        const [p1,p2,p3,  ] = group1,
              [q1,q2,q3,q4] = group3

        // 2. choose 3 from the known group1 and candidate group3 to weigh
        const weightG1 = weight([p1,p2,p3]),
              weightG3 = weight([q1,q2,q3])

        if(weightG1 == weightG3) {
            // since every member of group1 has the same weight, the odd man out must be the one not weighed from group3
            return q4 
        } else {
            // The candidate must be one of (q1, q2, q3) since we know everyone in group1 has equal weight
            // and the scale is unbalanced with the exclusion of q4.

            // 3. weigh two of the candidate group3 against each other
            const w1 = q1.weight,
                  w2 = q2.weight

            if(w1 == w2) {
                return q3 // scales balance so it must be the unweighed person
            } else {
                if(weightG1 < weightG3) // If the candidate group weighs more than the known group
                    return w1 < w2 ? q2 : q1 // then the heavier of q1 and q2 is the individual
                else // Inversely, if the candidate group weighs less than the known group
                    return w1 < w2 ? q1 : q2 //  then the lighter of q1 and q2 is the individual
            }
        }
    } else {
        // We now know that the unmeasured group3 contains people of equal weight
        // we'll shuffle 3 of the people in each group to see if we can get the scales to change

        const [p1,p2,p3,p4] = group1,
              [q1,q2,q3,q4] = group2,
              [  ,r2,r3,r4] = group3
        
        const newGroup1 = [p1,q2,q3,q4], // remove 3 people from group1 and add 3 people from group2
              newGroup2 = [q1,r2,r3,r4] // Add 3 people from the known group3

        // 2. weigh the new groups
        const weightG1 = weight(newGroup1),
              weightG2 = weight(newGroup2)

        if(weightG1 == weightG2) {
            // By making the scales equal, we know the candidate is in the removed group: (p2,p3,p4)

            // 3. weigh two of the remaining against each other:
            const w2 = p2.weight,
                  w3 = p3.weight
            
            if(w2 == w3) {
                return p4 // scales balance so it must be the unweighed person
            } else {
                if(wg1 < wg2) // if group1 is lighter than group2
                    return w2 < w3 ? p3 : p2; // The heavier person is the candidate
                else // if group1 is heavier than group2
                    return w2 < w3 ? p2 : p3; // The lighter person is the candidate
            }
        } else {
            if(wg1 > wg2 && weightG1 > weightG2) {
                // if we shuffled the group and the weight didn't change then one of the unmoved people is the candidate (p1 or q1)

                // 3. weigh the remaining two
                const wp1 = p1.weight,
                      pq1 = q1.weight
                
                if(weightG1 < weightG2) // If the candidate group weighs more than the known group
                    return wp1 < pq1 ? q1 : p1 // it's the heavier person
                else // Inversely, if the candidate group weighs less than the known group
                    return wp1 < pq1 ? p1 : q1 // it's the lighter person
            } else  {
                // we shuffled the groups and the weights swapped. The candidate must be in moved subgroup (q2,q3,q4)

                // 3. weigh two of the candidate group3 against each other
                const w2 = q2.weight,
                      w3 = q3.weight

                if(w2 == w3) {
                    return q4 // scales balance so it must be the unweighed person
                } else {
                    if(weightG1 < weightG2) // If the candidate group weighs more than the known group
                        return w2 < w3 ? q3 : q2 // then the heavier of q1 and q2 is the individual
                    else // Inversely, if the candidate group weighs less than the known group
                        return w2 < w3 ? q2 : q3 //  then the lighter of q1 and q2 is the individual
                }
            }
        }
    }
}

// The population of the island
const population = Array.from({length: 12}, () => new Person(160));

// One person has a different weight
population[randInt(0,11)].weight = randInt(140,280, 160)

// Find the different person
console.log(findDifferentPerson(population))