Adds a color attribute to the objects to implement breadth first search algorithm.

homework.js

/*  A  ----  B  ----- C
    |        |
    |        |
    D ------ E ------ F    */

var allNodes = {
        A : { "color": "WHITE" , "value": 20, "neighbours": ["D","B"] },
        B : { "color": "WHITE" , "value": 10, "neighbours": ["A","E","C"] },
        C : { "color": "WHITE" , "value": 30, "neighbours": ["B"] },
        D : { "color": "WHITE" , "value": 20, "neighbours": ["A","E"] },
        E : { "color": "WHITE" , "value": 90, "neighbours": ["D","B","F"] },
        F : { "color": "WHITE" , "value": 90, "neighbours": ["E"] }
};

function getMaxValue(root){
    var visited_nodes;
    var max = 0;

    if( allNodes[root]["value"] > max ){
        max = allNodes[root]["value"];
    }

    // Implements breadth first search algorithm to traverse the graph
    // For given problem, running time is big-O(# edges in the graph )
     
    allNodes[root]["color"] = "GRAY";
    visited_nodes = [];
    visited_nodes.push( allNodes[root] );
    
    while( visited_nodes.length != 0 ){
        var u = visited_nodes.pop( );

        for(i = 0; i < u["neighbours"].length; i++){
            var v = allNodes[ u["neighbours"][i] ];
            if( v["color"]==="WHITE"){
                v["color"] = "GRAY";
                visited_nodes.push( v );

                if( v["value"] > max ){
                    max = v["value"];
                }
            }    
        }         
        u["color"]="BLACK";
    }
    reset(allNodes);
    return max;
 }

function reset(nodes){
    for (var key in nodes) {
             nodes[key].color = "WHITE";
        };     
};

var r = getMaxValue('A');
document.getElementById('text').innerHTML = "Maximum is : " + r;

index.html

<div id="text"></div>