64 lines
721 B
Plaintext
64 lines
721 B
Plaintext
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12
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1 4 9
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build perfect squares up to n
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12-9=3
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3-1=2
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2-1=1
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12=9+1+1+1 -> 4
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12=4+4+4 -> 3
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1 -> 1 (1)
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2 -> 2 (1+1)
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3 -> 3 (1+1+1)
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4 -> 1 (4)
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5 -> 2 (4+1)
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6 -> 3 (4+1+1)
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7 -> 4 4+1+1+1
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8 -> 2 4+4
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f(1) = 1
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f(2) = f(1) + f(1) = 1+1=2
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f(7) = f(4) + f(3) = 1+3=4
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f(8) = f(4) + f(4) = 1+1=2
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f(12) = f(8) + f(4) = 2+1=3
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identify subproblems?
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https://leetcode.com/problems/perfect-squares/discuss/696436/Python-Simple-DP-Solution
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n=7
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square_sums = [0,1,4]
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dp = [0, inf, inf, inf, inf, inf, inf, inf]
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0 1 2 3 4 5 6 7
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dp = [0, 1, 2, 3, 1, 2, 3, 4]
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dp = [0, 1, inf, inf, 1, inf, inf, inf]
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i: 1->n
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iter all squares
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min( dp[i], dp[i-square] )
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f(1)=1
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f(2)=2
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f(12)=
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these are the candidates
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