ORIGINAL CODING QUESTION
Fewest square-valued tokens
Return the minimum number of positive perfect squares that sum to x. Squares may repeat; x=0 needs zero tokens.
Original exercise · medium. Editorial role relevance does not imply a company has asked this question.
Input and output
One nonnegative integer x.
Constraints
0 ≤ x ≤ 1000.
Example 1
Input
12
Output
3
Three value-4 tokens suffice.
Example 2
Input
13
Output
2
Values 4 and 9 use two tokens.
Explain your approach
Explain your time and auxiliary space complexity. Which input makes your algorithm work hardest?
Private grading inputs, expected outputs and canonical reference implementations are withheld. Authored expected outputs were cross-checked with independent reference oracles; compiler/runtime behavior still needs a verified execution provider.
Hint 1
Every square defines a possible last token.
Hint 2
Store the fewest tokens for each smaller sum.
Hint 3
dp[s]=min(dp[s-square]+1) over valid squares.
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