JSFiddle - React, Tailwind, and code Playground

JavaScript

let data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 80,
  11, 12, 13, 14, 15, 16, 17, 18, 19, 81,
  21, 22, 23, 24, 25, 26, 27, 28, 29, 82,
  31, 32, 33, 34, 35, 36, 37, 38, 39, 83,
  41, 42, 43, 44, 45, 46, 47, 48, 49, 84,
  51, 52, 53, 54, 55, 56, 57, 58, 59, 85,
  61, 62, 63, 64, 65, 66, 67, 68, 69, 86,
  71, 72, 73, 74, 75, 76, 77, 78, 79, 87,
  81, 82, 83, 84, 85, 86, 87, 80
];

function getCycleCount(adjacency) {
  let i = 0, count = 0;
  while(adjacency[i] >= 0) {
    let j = adjacency[i];
    adjacency[i] = -adjacency[i] - 1;
    i = j;
  }
  while(adjacency[i] < 0) {
    adjacency[i] = -adjacency[i] - 1;
    i = adjacency[i];
    count++;
  }
  for (i = 0; adjacency[i] < 0; i = adjacency[i])
  	adjacency[i] = -adjacency[i] - 1;
  return count;
}

document.body.innerHTML = getCycleCount(data) + '<br>' + data;