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| 1 | +// https://leetcode.com/problems/perfect-squares |
| 2 | +// T: O(N * k) k = size of perfect squares array which is constant |
| 3 | +// S: O(N + k) |
| 4 | + |
| 5 | +public class PerfectSquares { |
| 6 | + private static final int[] PERFECT_SQUARES = { |
| 7 | + 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, |
| 8 | + 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, |
| 9 | + 1936, 2025, 2116, 2209, 2304, 2401, 2500, 2601, 2704, 2809, 2916, 3025, 3136, 3249, 3364, 3481, 3600, 3721, |
| 10 | + 3844, 3969, 4096, 4225, 4356, 4489, 4624, 4761, 4900, 5041, 5184, 5329, 5476, 5625, 5776, 5929, 6084, 6241, |
| 11 | + 6400, 6561, 6724, 6889, 7056, 7225, 7396, 7569, 7744, 7921, 8100, 8281, 8464, 8649, 8836, 9025, 9216, 9409, |
| 12 | + 9604, 9801, 10000, 10_201 |
| 13 | + }; |
| 14 | + |
| 15 | + public int numSquares(int n) { |
| 16 | + final int[] dp = new int[n + 1]; |
| 17 | + dp[0] = dp[1] = 1; |
| 18 | + for (int i = 2 ; i < dp.length ; i++) { |
| 19 | + dp[i] = numSquares(i, dp); |
| 20 | + } |
| 21 | + return dp[dp.length - 1]; |
| 22 | + } |
| 23 | + |
| 24 | + private int numSquares(int n, int[] dp) { |
| 25 | + int result = Integer.MAX_VALUE, square; |
| 26 | + for (int i = 0 ; PERFECT_SQUARES[i] <= n ; i++) { |
| 27 | + square = PERFECT_SQUARES[i]; |
| 28 | + result = Math.min(result, dp[square] + dp[n - square]); |
| 29 | + } |
| 30 | + return result; |
| 31 | + } |
| 32 | +} |
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