pits.js

// http://hastebin.com/ubagequlal.pas
// pit bro
// find deepest pit (which is also the widest due to constraints given in the problem around strict ordering).

function Pit(start, middle, end) {
  return {start: start, middle: middle, end: end};
}

var NoPit = Pit(-1, -1, -1);

function until(pred, arr, start) {
  // returns last index until pred becomes false.
  var n = arr.length;
  var prevIndex = start;
  var prev = arr[prevIndex];
  for (var i = start + 1; i < n; i++) {
    var curr = arr[i];
    if (!pred(prev, curr)) {
      break;
    }
    prevIndex = i;
    prev = curr;
  } 
  return prevIndex;
}

function lessThan(prev, curr) { return curr < prev; }
function greaterThan(prev, curr) { return curr > prev; }

function findPit(arr, start) {
  // returns Pit

  var n = arr.length;

  // silde down
  var middle = until(lessThan, arr, start);
  if (middle <= start) {
    return NoPit;
  }

  // ride up
  var end = until(greaterThan, arr, middle);
  if (end <= middle) {
    return NoPit;
  }

  return Pit(start, middle, end);
}

function allPits(arr) {
  var start = 0;
  var n = arr.length;
  var pits = [];
  while (start < n - 3) {
    var pit = findPit(arr, start);
    if (pit === NoPit) {
      break;
    }
    pits.push(pit);
    start = pit.end;
  }
  return pits;
}

function sizeOfPit(arr, pit) {
  return Math.min(arr[pit.start] - arr[pit.middle], arr[pit.end] - arr[pit.middle]);
}

function largestPit(arr) {
  var pits = allPits(arr);
  if (pits.length < 1) {
    return;
  }
  var largest = pits[0];
  for (var i = 1; i < pits.length; i++) {
    if (sizeOfPit(pits[i]) > sizeOfPit(largest)) {
      largest = pits[i];
    }
  }
  return largest;
}