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Filename : parent-dummy-chains.js
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var _ = require("./lodash");

module.exports = parentDummyChains;

function parentDummyChains(g) {
  var postorderNums = postorder(g);

  _.forEach(g.graph().dummyChains, function(v) {
    var node = g.node(v);
    var edgeObj = node.edgeObj;
    var pathData = findPath(g, postorderNums, edgeObj.v, edgeObj.w);
    var path = pathData.path;
    var lca = pathData.lca;
    var pathIdx = 0;
    var pathV = path[pathIdx];
    var ascending = true;

    while (v !== edgeObj.w) {
      node = g.node(v);

      if (ascending) {
        while ((pathV = path[pathIdx]) !== lca &&
               g.node(pathV).maxRank < node.rank) {
          pathIdx++;
        }

        if (pathV === lca) {
          ascending = false;
        }
      }

      if (!ascending) {
        while (pathIdx < path.length - 1 &&
               g.node(pathV = path[pathIdx + 1]).minRank <= node.rank) {
          pathIdx++;
        }
        pathV = path[pathIdx];
      }

      g.setParent(v, pathV);
      v = g.successors(v)[0];
    }
  });
}

// Find a path from v to w through the lowest common ancestor (LCA). Return the
// full path and the LCA.
function findPath(g, postorderNums, v, w) {
  var vPath = [];
  var wPath = [];
  var low = Math.min(postorderNums[v].low, postorderNums[w].low);
  var lim = Math.max(postorderNums[v].lim, postorderNums[w].lim);
  var parent;
  var lca;

  // Traverse up from v to find the LCA
  parent = v;
  do {
    parent = g.parent(parent);
    vPath.push(parent);
  } while (parent &&
           (postorderNums[parent].low > low || lim > postorderNums[parent].lim));
  lca = parent;

  // Traverse from w to LCA
  parent = w;
  while ((parent = g.parent(parent)) !== lca) {
    wPath.push(parent);
  }

  return { path: vPath.concat(wPath.reverse()), lca: lca };
}

function postorder(g) {
  var result = {};
  var lim = 0;

  function dfs(v) {
    var low = lim;
    _.forEach(g.children(v), dfs);
    result[v] = { low: low, lim: lim++ };
  }
  _.forEach(g.children(), dfs);

  return result;
}