My dp array contains positions that can successfully cut the string.

```
public class Solution {
public boolean wordBreak(String s, Set<String> dict) {
int n = s.length();
int[] dp = new int[n + 1];
dp[0] = 0;
for (int i = 1; i <= n; i++) {
boolean f = false;
for (int j = i - 1; j >= 0; j--) {
if (dict.contains( s.substring(dp[j], i) )) {
f = true;
break;
}
if (dp[j] == 0) break;
j = dp[j];
}
if (f) dp[i] = i;
else dp[i] = dp[i - 1];
}
return dp[n] == n ? true : false;
}
}
```