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17. Word Break

mediumAsked at Postman

Decide whether a string can be segmented into a sequence of dictionary words.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

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. Words may be reused.

Constraints

  • 1 <= s.length <= 300
  • 1 <= wordDict.length <= 1000
  • Words consist of lowercase English letters

Examples

Example 1

Input
s = "leetcode", wordDict = ["leet","code"]
Output
true

Example 2

Input
s = "catsandog", wordDict = ["cats","dog","sand","and","cat"]
Output
false

Approaches

1. Recursive without memo

Try every prefix that is in the dictionary, recurse on the suffix; without memoization this is exponential.

Time
O(2^n)
Space
O(n)
function ok(s) {
  if (s === '') return true;
  for (const w of wordDict) if (s.startsWith(w) && ok(s.slice(w.length))) return true;
  return false;
}

Tradeoff:

2. DP over prefixes

dp[i] is true if s[0..i] is segmentable. For each i, scan back to find a j with dp[j] true and s.slice(j,i) in the dictionary set.

Time
O(n^2 + dict)
Space
O(n + dict)
function wordBreak(s, wordDict) {
  const set = new Set(wordDict);
  const dp = new Array(s.length + 1).fill(false);
  dp[0] = true;
  for (let i = 1; i <= s.length; i++) {
    for (let j = 0; j < i; j++) {
      if (dp[j] && set.has(s.slice(j, i))) { dp[i] = true; break; }
    }
  }
  return dp[s.length];
}

Tradeoff:

Postman-specific tips

Postman favors DP-over-prefixes since URL path segmentation (splitting `/users/{id}/orders/{oid}` against a route table) is the same problem in production.

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Output

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