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1 | 1 | package g3201_3300.s3213_construct_string_with_minimum_cost; |
2 | 2 |
|
3 | 3 | // #Hard #Array #String #Dynamic_Programming #Suffix_Array |
4 | | -// #2024_07_09_Time_182_ms_(100.00%)_Space_61.4_MB_(72.97%) |
| 4 | +// #2024_07_13_Time_1907_ms_(5.01%)_Space_100.9_MB_(5.09%) |
5 | 5 |
|
| 6 | +import java.util.ArrayList; |
6 | 7 | import java.util.Arrays; |
| 8 | +import java.util.Collections; |
| 9 | +import java.util.HashMap; |
| 10 | +import java.util.List; |
| 11 | +import java.util.Map; |
7 | 12 |
|
8 | 13 | public class Solution { |
9 | | - private static int invalid = Integer.MAX_VALUE; |
10 | | - |
11 | | - private static class Node { |
12 | | - int cost = -1; |
13 | | - Node[] chd = new Node[26]; |
| 14 | + List<Integer> buildKmpPrefix(String target) { |
| 15 | + List<Integer> w = new ArrayList<>(Collections.nCopies(target.length(), 0)); |
| 16 | + int k = 0; |
| 17 | + int i = 1; |
| 18 | + while (i < target.length()) { |
| 19 | + if (target.charAt(i) == target.charAt(k)) { |
| 20 | + k++; |
| 21 | + w.set(i, k); |
| 22 | + i++; |
| 23 | + } else { |
| 24 | + if (k != 0) { |
| 25 | + k = w.get(k - 1); |
| 26 | + } else { |
| 27 | + i++; |
| 28 | + } |
| 29 | + } |
| 30 | + } |
| 31 | + return w; |
14 | 32 | } |
15 | 33 |
|
16 | | - private Node rt; |
| 34 | + List<List<Integer>> find(List<Integer> prefix, String target, String w) { |
| 35 | + List<List<Integer>> result = new ArrayList<>(); |
| 36 | + int m = target.length(); |
| 37 | + int n = w.length(); |
| 38 | + int i = 0; |
| 39 | + int k = 0; |
| 40 | + while (i < m) { |
| 41 | + if (target.charAt(i) == w.charAt(k)) { |
| 42 | + i++; |
| 43 | + k++; |
| 44 | + } |
| 45 | + if (k == n) { |
| 46 | + result.add(Arrays.asList(i - k, i)); |
| 47 | + k = prefix.get(k - 1); |
| 48 | + } else if (i < m && target.charAt(i) != w.charAt(k)) { |
| 49 | + if (k != 0) { |
| 50 | + k = prefix.get(k - 1); |
| 51 | + } else { |
| 52 | + i++; |
| 53 | + } |
| 54 | + } |
| 55 | + } |
| 56 | + return result; |
| 57 | + } |
17 | 58 |
|
18 | 59 | public int minimumCost(String target, String[] words, int[] costs) { |
19 | | - rt = new Node(); |
20 | | - int m = words.length; |
21 | | - int n = target.length(); |
22 | | - for (int i = 0; i < m; ++i) { |
23 | | - if (words[i].length() <= n) { |
24 | | - insert(words[i], costs[i]); |
| 60 | + List<Integer> targetPrefix = buildKmpPrefix(target); |
| 61 | + Node root = new Node(); |
| 62 | + for (int j = 0; j < words.length; j++) { |
| 63 | + String x = words[j]; |
| 64 | + if (x.length() < 320) { |
| 65 | + Node p = root; |
| 66 | + for (int i = 0; i < x.length(); i++) { |
| 67 | + char c = x.charAt(i); |
| 68 | + p.children.putIfAbsent(c, new Node()); |
| 69 | + p = p.children.get(c); |
| 70 | + if (i == x.length() - 1) { |
| 71 | + if (p.cost == null) { |
| 72 | + p.cost = costs[j]; |
| 73 | + } else { |
| 74 | + p.cost = Math.min(costs[j], p.cost); |
| 75 | + } |
| 76 | + } |
| 77 | + } |
25 | 78 | } |
26 | 79 | } |
27 | | - int[] dp = new int[n + 1]; |
28 | | - Arrays.fill(dp, invalid); |
| 80 | + Map<Integer, Map<Integer, Integer>> dm = |
| 81 | + getIntegerMapMap(target, words, costs, targetPrefix); |
| 82 | + List<NodeCostPair> d = new ArrayList<>(); |
| 83 | + d.add(new NodeCostPair(root, 0)); |
| 84 | + int[] dp = new int[target.length() + 1]; |
| 85 | + Arrays.fill(dp, -1); |
29 | 86 | dp[0] = 0; |
30 | | - for (int i = 0; i < n; ++i) { |
31 | | - if (dp[i] == invalid) { |
32 | | - continue; |
33 | | - } |
34 | | - int nowC = dp[i]; |
35 | | - Node now = rt; |
36 | | - for (int j = i; now != null && j < n; ++j) { |
37 | | - int ch = target.charAt(j) - 'a'; |
38 | | - now = now.chd[ch]; |
39 | | - if (now != null && now.cost != -1) { |
40 | | - dp[j + 1] = Math.min(dp[j + 1], nowC + now.cost); |
| 87 | + for (int i = 0; i < target.length(); i++) { |
| 88 | + char x = target.charAt(i); |
| 89 | + List<NodeCostPair> q = new ArrayList<>(); |
| 90 | + Integer t = null; |
| 91 | + for (NodeCostPair pair : d) { |
| 92 | + Node p = pair.node; |
| 93 | + int cost = pair.cost; |
| 94 | + if (p.children.containsKey(x)) { |
| 95 | + Node w = p.children.get(x); |
| 96 | + if (w.cost != null) { |
| 97 | + t = t == null ? cost + w.cost : Math.min(t, cost + w.cost); |
| 98 | + } |
| 99 | + q.add(new NodeCostPair(w, cost)); |
41 | 100 | } |
42 | 101 | } |
| 102 | + t = getInteger(dm, i, dp, t); |
| 103 | + if (t != null) { |
| 104 | + dp[i + 1] = t; |
| 105 | + q.add(new NodeCostPair(root, t)); |
| 106 | + } |
| 107 | + d = q; |
43 | 108 | } |
| 109 | + return dp[target.length()]; |
| 110 | + } |
44 | 111 |
|
45 | | - return dp[n] == invalid ? -1 : dp[n]; |
| 112 | + private Integer getInteger(Map<Integer, Map<Integer, Integer>> dm, int i, int[] dp, Integer t) { |
| 113 | + Map<Integer, Integer> qm = dm.getOrDefault(i + 1, Collections.emptyMap()); |
| 114 | + for (Map.Entry<Integer, Integer> entry : qm.entrySet()) { |
| 115 | + int b = entry.getKey(); |
| 116 | + if (dp[b] >= 0) { |
| 117 | + t = t == null ? dp[b] + entry.getValue() : Math.min(t, dp[b] + entry.getValue()); |
| 118 | + } |
| 119 | + } |
| 120 | + return t; |
46 | 121 | } |
47 | 122 |
|
48 | | - private void insert(String wd, int cst) { |
49 | | - int len = wd.length(); |
50 | | - Node now = rt; |
51 | | - for (int i = 0; i < len; ++i) { |
52 | | - int ch = wd.charAt(i) - 'a'; |
53 | | - if (now.chd[ch] == null) { |
54 | | - now.chd[ch] = new Node(); |
| 123 | + private Map<Integer, Map<Integer, Integer>> getIntegerMapMap( |
| 124 | + String target, String[] words, int[] costs, List<Integer> targetPrefix) { |
| 125 | + Map<Integer, Map<Integer, Integer>> dm = new HashMap<>(); |
| 126 | + for (int i = 0; i < words.length; i++) { |
| 127 | + String word = words[i]; |
| 128 | + if (word.length() >= 320) { |
| 129 | + List<List<Integer>> q = find(targetPrefix, target, word); |
| 130 | + for (List<Integer> pair : q) { |
| 131 | + int b = pair.get(0); |
| 132 | + int e = pair.get(1); |
| 133 | + dm.putIfAbsent(e, new HashMap<>()); |
| 134 | + Map<Integer, Integer> qm = dm.get(e); |
| 135 | + if (qm.containsKey(b)) { |
| 136 | + qm.put(b, Math.min(qm.get(b), costs[i])); |
| 137 | + } else { |
| 138 | + qm.put(b, costs[i]); |
| 139 | + } |
| 140 | + } |
55 | 141 | } |
56 | | - now = now.chd[ch]; |
57 | 142 | } |
58 | | - if (now.cost == -1 || now.cost > cst) { |
59 | | - now.cost = cst; |
| 143 | + return dm; |
| 144 | + } |
| 145 | + |
| 146 | + private static class Node { |
| 147 | + Map<Character, Node> children; |
| 148 | + Integer cost; |
| 149 | + |
| 150 | + public Node() { |
| 151 | + this.children = new HashMap<>(); |
| 152 | + this.cost = null; |
| 153 | + } |
| 154 | + } |
| 155 | + |
| 156 | + private static class NodeCostPair { |
| 157 | + Node node; |
| 158 | + int cost; |
| 159 | + |
| 160 | + public NodeCostPair(Node node, int cost) { |
| 161 | + this.node = node; |
| 162 | + this.cost = cost; |
60 | 163 | } |
61 | 164 | } |
62 | 165 | } |
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