// Interval graph coloring algorithm, by Twal

class IntervalColoration {
    constructor (intervals) {
        this.intervals = intervals;
        this.n = this.intervals.length;
        this.computeInterferenceGraph();
        this.computePEO();
        this.computeColoration();
    }

    computeInterferenceGraph() {
        this.adj = new Array(this.n);
        for (let i = 0; i < this.n; ++i) {
            this.adj[i] = [];
        }
        for (let i = 0; i < this.n; ++i) {
            for (let j = 0; j < i; ++j) {
                let inti = this.intervals[i];
                let intj = this.intervals[j];
                if (inti[0] < intj[1] && intj[0] < inti[1]) {
                    this.adj[i].push(j);
                    this.adj[j].push(i);
                }
            }
        }
    }

    //Perfect elimination order using Maximum Cardinality Search
    //Runs in O(n^2), could be optimized in O(n log n)
    computePEO() {
        let marked = new Array(this.n);
        let nbMarkedNeighbor = new Array(this.n);
        this.perm = new Array(this.n);
        for (let i = 0; i < this.n; ++i) {
            marked[i] = false;
            nbMarkedNeighbor[i] = 0;
        }
        for (let k = this.n-1; k >= 0; --k) {
            let maxi = -1;
            for (let i = 0; i < this.n; ++i) {
                if (!marked[i] && (maxi == -1 || nbMarkedNeighbor[i] >= nbMarkedNeighbor[maxi])) {
                    maxi = i;
                }
            }
            for (let i = 0; i < this.adj[maxi].length; ++i) {
                nbMarkedNeighbor[this.adj[maxi][i]] += 1;
            }
            this.perm[maxi] = k;
            marked[maxi] = true;
        }
        // console.log(this.perm);
    }

    computeColoration() {
        this.colors = new Array(this.n);
        let isColorUsed = new Array(this.n);
        for (let i = 0; i < this.n; ++i) {
            this.colors[i] = -1;
            isColorUsed[i] = false;
        }
        for (let i = 0; i < this.n; ++i) {
            let ind = this.perm[i];
            for (let j = 0; j < this.adj[ind].length; ++j) {
                let neigh = this.adj[ind][j];
                if (this.colors[neigh] >= 0) {
                    isColorUsed[this.colors[neigh]] = true;
                }
            }
            for (let j = 0; j < this.n; ++j) {
                if (!isColorUsed[j]) {
                    this.colors[ind] = j;
                    break;
                }
            }
            for (let j = 0; j < this.adj[ind].length; ++j) {
                let neigh = this.adj[ind][j];
                if (this.colors[neigh] >= 0) {
                    isColorUsed[this.colors[neigh]] = false;
                }
            }
        }
    }
}