Main problem in their code is that it is made, well... for one slideshow, and when you try to apply it to multiple slideshows, some serious problems arise, as you have experienced. They used global vars (index, n), which is not problem when you have one slideshow, but with more slideshows - hard to handle stuff, and it is hard to get reference to current slideshow div with existing concept.
And, yes, this is plain javascript slideshow, NO jQuery here. I've changed slightly your HTML and CSS (dots div is INSIDE slideshow div, just for easier targetting), also, i've removed inline event handlers, just to make things little easier and cleaner.
This could be solved on many ways, i've choosed this one:
(function() {
init(); //on page load - show first slide, hidethe rest
function init() {
parents = document.getElementsByClassName('slideshow-container');
for (j = 0; j < parents.length; j++) {
var slides = parents[j].getElementsByClassName("mySlides");
var dots = parents[j].getElementsByClassName("dot");
slides[0].classList.add('active-slide');
dots[0].classList.add('active');
}
}
dots = document.getElementsByClassName('dot'); //dots functionality
for (i = 0; i < dots.length; i++) {
dots[i].onclick = function() {
slides = this.parentNode.parentNode.getElementsByClassName("mySlides");
for (j = 0; j < this.parentNode.children.length; j++) {
this.parentNode.children[j].classList.remove('active');
slides[j].classList.remove('active-slide');
if (this.parentNode.children[j] == this) {
index = j;
}
}
this.classList.add('active');
slides[index].classList.add('active-slide');
}
}
//prev/next functionality
links = document.querySelectorAll('.slideshow-container a');
for (i = 0; i < links.length; i++) {
links[i].onclick = function() {
current = this.parentNode;
var slides = current.getElementsByClassName("mySlides");
var dots = current.getElementsByClassName("dot");
curr_slide = current.getElementsByClassName('active-slide')[0];
curr_dot = current.getElementsByClassName('active')[0];
curr_slide.classList.remove('active-slide');
curr_dot.classList.remove('active');
if (this.className == 'next') {
if (curr_slide.nextElementSibling.classList.contains('mySlides')) {
curr_slide.nextElementSibling.classList.add('active-slide');
curr_dot.nextElementSibling.classList.add('active');
} else {
slides[0].classList.add('active-slide');
dots[0].classList.add('active');
}
}
if (this.className == 'prev') {
if (curr_slide.previousElementSibling) {
curr_slide.previousElementSibling.classList.add('active-slide');
curr_dot.previousElementSibling.classList.add('active');
} else {
slides[slides.length - 1].classList.add('active-slide');
dots[slides.length - 1].classList.add('active');
}
}
}
}
})();
/* Slideshow container */
.slideshow-container {
max-width: 1000px;
position: relative;
margin: auto;
}
/* Next & previous buttons */
.prev, .next {
cursor: pointer;
position: absolute;
top: 50%;
width: auto;
margin-top: -22px;
padding: 16px;
color: white;
font-weight: bold;
font-size: 18px;
transition: 0.6s ease;
border-radius: 0 3px 3px 0;
}
/* Position the "next button" to the right */
.next {
right: 0;
border-radius: 3px 0 0 3px;
}
/* On hover, add a black background color with a little bit see-through */
.prev:hover, .next:hover {
background-color: rgba(0,0,0,0.8);
}
/* Caption text */
.text {
color: #f2f2f2;
font-size: 15px;
padding: 8px 12px;
position: absolute;
bottom:20px;
width: 100%;
text-align: center;
}
.mySlides {
display:none;
}
.active-slide {
display:block;
}
/* Number text (1/3 etc) */
.numbertext {
color: #f2f2f2;
font-size: 12px;
padding: 8px 12px;
position: absolute;
top: 0;
}
/* The dots/bullets/indicators */
.dot {
cursor:pointer;
height: 13px;
width: 13px;
margin: 0 2px;
background-color: #bbb;
border-radius: 50%;
display: inline-block;
transition: background-color 0.6s ease;
}
.active, .dot:hover {
background-color: #717171;
}
/* Fading animation */
.fade {
-webkit-animation-name: fade;
-webkit-animation-duration: 1.5s;
animation-name: fade;
animation-duration: 1.5s;
}
@-webkit-keyframes fade {
from {opacity: .4}
to {opacity: 1}
}
@keyframes fade {
from {opacity: .4}
to {opacity: 1}
}
<div class="slideshow-container">
<div class="mySlides fade">
<div class="numbertext">1 / 4</div>
<img src="http://www.w3schools.com/howto/img_mountains_wide.jpg" style="width:100%">
<div class="text">Caption Text</div>
</div>
<div class="mySlides fade">
<div class="numbertext">2 / 4</div>
<img src="http://www.w3schools.com/howto/img_fjords_wide.jpg" style="width:100%">
<div class="text">Caption Two</div>
</div>
<div class="mySlides fade">
<div class="numbertext">3 / 4</div>
<img src="http://www.w3schools.com/howto/img_nature_wide.jpg" style="width:100%">
<div class="text">Caption Three</div>
</div>
<div class="mySlides fade">
<div class="numbertext">4 / 4</div>
<img src="http://placehold.it/1000x350" style="width:100%">
<div class="text">Caption Four</div>
</div>
<a class="prev">❮</a>
<a class="next">❯</a>
<div style="text-align:center">
<span class="dot"></span>
<span class="dot" ></span>
<span class="dot" ></span>
<span class="dot"></span>
</div>
</div>
<br>
<div class="slideshow-container">
<div class="mySlides fade">
<div class="numbertext">1 / 3</div>
<img src="http://www.w3schools.com/howto/img_mountains_wide.jpg" style="width:100%">
<div class="text">Caption Text</div>
</div>
<div class="mySlides fade">
<div class="numbertext">2 / 3</div>
<img src="http://www.w3schools.com/howto/img_fjords_wide.jpg" style="width:100%">
<div class="text">Caption Two</div>
</div>
<div class="mySlides fade">
<div class="numbertext">3 / 3</div>
<img src="http://www.w3schools.com/howto/img_nature_wide.jpg" style="width:100%">
<div class="text">Caption Three</div>
</div>
<a class="prev" >❮</a>
<a class="next">❯</a>
<div style="text-align:center">
<span class="dot"></span>
<span class="dot"></span>
<span class="dot"></span>
</div>
</div>
<br>
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