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RecursiveComplexity.js
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RecursiveComplexity.js
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function fact(n) {
// Base case
if(n == 1) return 1;
let assume = fact(n-1); // that fact of n-1 is correct
return n*assume;; // self work
}
// TC = #ofrecursivecalls * Time of one call
// TC = O(n)
function power(a, b) {
if(b == 0) return 1; // base case
let assume = power(a, b-1); // assumption
return a*assume;
}
// TC = O(b)
function friends(n) {
if(n == 1) return 1;
if(n == 2) return 2;
// let a = friends(n-1); // nth friend goes along
// let b = friends(n-2); // nth friend makes a pair
return friends(n-1) + (n-1)*friends(n-2);
}
// O(2^n)
function print_dec(n) {
// base case
if(n == 1) {
console.log(1);
return;
}
console.log(n);
print_dec(n-1);
}
// TC = O(n)
function tile(n) {
if(n == 1) return 1;
if(n == 2) return 2;
return tile(n-1) + tile(n-2);
}
// O(2^n)
function f(n) {
if(n == 1) return 0;
if(n == 2 || n == 3) return 1;
let inf = Number.MAX_SAFE_INTEGER;
return 1 + Math.min((n%3 == 0) ? f(n/3) : inf, (n%2 == 0) ? f(n/2) : inf, f(n-1));
}
// O(3^n)
function isSorted(arr, idx) {
if(idx == arr.length - 1) {
return true;
}
let assume = isSorted(arr, idx+1);
return assume && (arr[idx] <= arr[idx+1]);
}
// TC = O(n)
function f(i, j, n, m) {
// base case
if(i == n-1 && j == m-1) {
// found one possible way
return 1;
}
if(i >= n || j >= m) return 0; // if you go outside the grid, there is no possible way
return f(i, j+1, n, m) + f(i+1, j, n, m);
}
// TC = O(2^(nm))
function f(n) {
// base case
if(n == 0) {
return 1;
}
let ans = 0;
/*
ans = f(n-1) + f(n-2) + f(n-3) + f(n-4) + f(n-5) + f(n-6)
*/
for(let k = 1; k <= 6; k++) {
if(n - k >= 0) {
ans += f(n-k);
}
}
return ans;
}
// TC = O(6^n)
function f(x, coins) {
// base case
if(x == 0) {
return 0;
}
let ans = Number.MAX_SAFE_INTEGER;
for(let i = 0; i < coins.length; i++) {
if(x-coins[i] >= 0) {
ans = Math.min(ans, f(x-coins[i], coins));
}
}
return 1+ans;
}
// TC = O(coins_length*(coins_length^x))
function subset(arr, res, i) {
if(i == arr.length) {
console.log(res);
return;
}
subset(arr, res + " " + arr[i], i+1);
subset(arr, res, i+1);
}
// TC = O(2^(arr.length))