My Learning Blog

Algorithm-70,322 - 1/21/2024

Backtracking with memo

70:You are climbing a staircase. It takes n steps to reach the top. Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

function climbStairs(n: number): number {
    const memo = new Map<number,number>()
    function dfs(steps:number, total:number){
        if(steps === total) return 1
        if (steps > total) return 0
        if (memo.has(steps)) return memo.get(steps)
        let ans = 0
        for( const step of [1,2]){
          ans = ans+ dfs(step + steps ,total)
        memo.set(steps, ans)
       return ans
    return dfs(0, n)

322:You are given an integer array coins representing coins of different denominations and an integer amount representing a total amount of money.

Return the fewest number of coins that you need to make up that amount. If that amount of money cannot be made up by any combination of the coins, return -1.

You may assume that you have an infinite number of each kind of coin.

Input: coins = [1,2,5], amount = 11 Output: 3 Explanation: 11 = 5 + 5 + 1

function coinChange(coins: number[], amount: number): number {
  let memo = new Map<number,number>()
  function dfs(sum: number): number {
    if (sum === amount) return 0;
    if (sum > amount) return Infinity;
    if(mem.has(sum)) return mem.get(sum)
    let ans = Infinity;
    for (let coin of coins) {
      let result = dfs(sum + coin);
      ans = Math.min(ans, result + 1);
    return ans;
  let res = dfs(0);
  return res === Infinity ? -1 : res;

139: Word Break

Given a string s and a dictionary of strings wordDict, return true if s can be segmented into a space-separated sequence of one or more dictionary words.

Note that the same word in the dictionary may be reused multiple times in the segmentation.

function wordBreak(s: string, wordDict: string[]): boolean {
    const set = new Set(wordDict)
    const memo = new Map<number, boolean>()

    function dfs(start: number) {
        if (start === s.length) return true

        if (memo.has(start)) return memo.get(start)

        for (let i = start; i < s.length; i++) {
            const pre = s.slice(start, i + 1)
            if (set.has(pre)) {
                if (dfs(i + 1)) {
                    memo.set(start, true)
                    return true
        return false

    return dfs(0)

function wordBreak(s: string, wordDict: string[]): boolean {
    let ans = false
    const memo = new Map()
    function dfs(start: number){
        if(start === s.length) return true
        if(start > s.length) return false
        if(memo.has(start)) return memo.get(start)
        for(const item of wordDict){
                ans = ans ||dfs(start + item.length)
        return ans

    return ans