How to script a character to move in any direction with a running/walking animation using mecanim?

how would I get my character to do free form motion(running in any direction with out a strafing animation) with a walk and a run animation using mecanim??

here are some examples

videos: [MEDIA=youtube]aH6AYuqQo90[/MEDIA]

https://www.youtube.com/watch?v=aH6AYuqQo90

on the above like go to seconds 12 and watch it until you see it hit 19 seconds the character runs forwards, backwards, left, and right with the same running animation with no strafing animations what so ever

link #2: [MEDIA=youtube]GormUcBjsns[/MEDIA]

https://www.youtube.com/watch?v=GormUcBjsns

the above video is what I wan't to achieve a walking and running animation that has no strafing and you can run in any direction how do you script it here's what i've scripted so far

script

 using UnityEngine;
 using System.Collections;
 
 public class PlayerMovement : MonoBehaviour {
     Transform mainCamera;
     private Animator anim;
     private float vertical;
     private float horizontal;
 
     // Use this for initialization
     void Start () {
         anim = GetComponent <Animator> ();
     }
     
     // Update is called once per frame
     void Update ()
     {
     
     }
 }