// Get all k-combinations from array
function combinations(arr, k){
  if (k==1) return arr;
  var ret = [];
  arr.forEach(function(d,i) {
    combinations(arr.slice(i+1, arr.length), k-1)
    .forEach(function(sub) {
      var next = [].concat(sub);
      next.unshift(d);
      ret.push( next );
    });
  });
  return ret;
}

// Generate a LaTex fraction
function frac(a,b) {
  if (!b || b == 1) return a;
  return '\\frac{'+(a || 1)+'}{'+b+'}';
}

// Main calculation - callback to the JSONP request
function main(input) {
  input = input.query.results.json;

  // Build rates matrix
  var rates = {};
  Object.keys(input).forEach(function(key) {
    var numerator = key.slice(0,3),
        denominator = key.slice(4);
    if (!rates[numerator]) rates[numerator]  = {};
    rates[numerator][denominator] = input[key];
  });

  // List FX rates
  fx = Object.keys(rates);

  var levels = {};


  // Determine the bid/offer from input data using high/low
  fx.forEach(function(A) {
    levels[A] = {};
    fx.forEach(function(B) {
      if (A == B) return;
      var first = rates[A][B],
          second = 1/rates[B][A];

      levels[A][B] = {
        offer : Math.max(first,second),
        bid : Math.min(first,second)
      };
      $("#prices").append('$$ '+frac(A,B)+'='+levels[A][B].bid+' / '+levels[A][B].offer+' $$');
    });
  });


  // Go through all triangular combinations
  combinations(fx,3).forEach(function(c) {
    ['bid','offer'].forEach(function(side) {
      var result = 1,
          txtFx = [],
          txtPrice =[],
          msg;
      c.forEach(function(base,i) {
        var other = c[i+1] || c[0];
        var price = levels[base][other][side];
        result *= price;
        txtFx.push(frac(base+'^{\\text{'+side+'}}',other));
        txtPrice.push(price);
      });

      if (side == 'bid') msg = (result < 1) ? '(result < 1 = No Arbitrage)' : '(result > 1 = Arbitrage)';
      else msg = (result > 1) ? '(result > 1 = No Arbitrage)' : '(result < 1 = Arbitrage)';

      $("#triangular").append('$$ '+txtFx.join(' \\cdot ')+'='+txtPrice.join(' \\cdot ')+' = '+result+' \\text{'+msg+'}$$');
    });
  });
}