Array.prototype.sliceByIndex = function(idxs){
	var items = this;
	var slicedVals = idxs.map(function(idx){
		return items[idx];
	});
	return slicedVals;
}

var range = function(min,max){
	var nums = [];
	for (var num = min; num <= max; num++){
		nums.push(num);
	}
	return nums;
}

Array.prototype.permutation = function(n){
	var items = this;
	var length = items.length;

	var idxs = range(0,length-1);
	var idxPerms = idxs.map(function(idx){
		return [idx];
	});

	for (var i = 0; i < n-1; i++){
		var nextIdxPerms = [];
		idxPerms.forEach(function(idxPerm){
			var nextIdxs = idxs.filter(function(idx){
				return idxPerm.indexOf(idx) === -1; //
			});

			nextIdxs.forEach(function(nextIdx){
				var nextIdxPerm = idxPerm.slice(0);
				nextIdxPerm.push(nextIdx);
				nextIdxPerms.push(nextIdxPerm);
			});
		});
		idxPerms = nextIdxPerms.slice(0);
	}

	perms = idxPerms.map(function(idxPerm){
		return items.sliceByIndex(idxPerm);
	});
	return perms;
}

Array.prototype.repeatedPermutation = function(n){
	var items = this;
	var length = items.length;

	var idxs = range(0,length-1);
	var idxPerms = idxs.map(function(idx){
		return [idx];
	});

	for (var i = 0; i < n-1; i++){
		var nextIdxPerms = [];
		idxPerms.forEach(function(idxPerm){
			idxs.forEach(function(idx){
				var nextIdxPerm = idxPerm.slice(0);
				nextIdxPerm.push(idx);
				nextIdxPerms.push(nextIdxPerm);
			});
		});
		idxPerms = nextIdxPerms.slice(0);
	}

	perms = idxPerms.map(function(idxPerm){
		return items.sliceByIndex(idxPerm);
	});
	return perms;
}

Array.prototype.powerSet = function(){
	var items = this;
	var length = items.length;

	var binarys = [true,false].repeatedPermutation(length);
	var trueIdxs = binarys.map(function(binary){
		return binary.allIndexOf(true);
	});
	var subsets = trueIdxs.map(function(trueIdx){
		return items.sliceByIndex(trueIdx);
	});
	return subsets;
}

Array.prototype.combination = function(n){
	var items = this;
	var length = items.length;

	var idxs = range(0,length-1);
	var idxPerms = idxs.map(function(idx){
		return [idx];
	});

	for (var idxsIdx = 0; idxsIdx < n-1; idxsIdx++){
		var nextIdxPerms = [];
		idxPerms.forEach(function(idxPerm){
			var lastIdx = idxPerm[idxsIdx];
			var nextIdxs = idxs.filter(function(idx){
				return lastIdx < idx;
			});
			nextIdxs.forEach(function(nextIdx){
					var nextIdxPerm = idxPerm.slice(0);
					nextIdxPerm.push(nextIdx);
					nextIdxPerms.push(nextIdxPerm);
			});
		});
		idxPerms = nextIdxPerms.slice(0);
	}

	perms = idxPerms.map(function(idxPerm){
		return items.sliceByIndex(idxPerm);
	});
	return perms;
}


Array.prototype.repeatedCombination = function(n){
	var items = this;
	var length = items.length;

	var idxs = range(0,length-1);
	var idxPerms = idxs.map(function(idx){
		return [idx];
	});

	for (var idxsIdx = 0; idxsIdx < n-1; idxsIdx++){
		var nextIdxPerms = [];
		idxPerms.forEach(function(idxPerm){
			var lastIdx = idxPerm[idxsIdx];
			var nextIdxs = idxs.filter(function(idx){
				return lastIdx <= idx;
			});
			nextIdxs.forEach(function(nextIdx){
					var nextIdxPerm = idxPerm.slice(0);
					nextIdxPerm.push(nextIdx);
					nextIdxPerms.push(nextIdxPerm);
			});
		});
		idxPerms = nextIdxPerms.slice(0);
	}

	perms = idxPerms.map(function(idxPerm){
		return items.sliceByIndex(idxPerm);
	});
	return perms;
}