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Improved task 3441 #1942

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Mar 13, 2025
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Improved task 3441 #1942

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197 changes: 53 additions & 144 deletions src/main/java/g3401_3500/s3441_minimum_cost_good_caption/Solution.java
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Original file line number Diff line number Diff line change
@@ -1,160 +1,69 @@
package g3401_3500.s3441_minimum_cost_good_caption;

// #Hard #String #Dynamic_Programming #2025_02_04_Time_48_ms_(96.00%)_Space_56.50_MB_(89.33%)
// #Hard #String #Dynamic_Programming #2025_03_13_Time_20_ms_(100.00%)_Space_46.12_MB_(96.53%)

@SuppressWarnings({"java:S107", "java:S6541"})
public class Solution {
private static final int INF = Integer.MAX_VALUE / 2;
import java.util.Arrays;

public class Solution {
public String minCostGoodCaption(String caption) {
int n = caption.length();
if (n < 3) {
return "";
}
char[] arr = caption.toCharArray();
int[][] prefixCost = new int[n + 1][26];
for (int i = 0; i < n; i++) {
int orig = arr[i] - 'a';
for (int c = 0; c < 26; c++) {
prefixCost[i + 1][c] = prefixCost[i][c] + Math.abs(orig - c);
}
}
int[] dp = new int[n + 1];
int[] nextIndex = new int[n + 1];
int[] nextChar = new int[n + 1];
int[] blockLen = new int[n + 1];
for (int i = 0; i < n; i++) {
dp[i] = INF;
nextIndex[i] = -1;
nextChar[i] = -1;
blockLen[i] = 0;
}
dp[n] = 0;
for (int i = n - 1; i >= 0; i--) {
for (int l = 3; l <= 5; l++) {
if (i + l <= n) {
int bestLetter = 0;
int bestCost = INF;
for (int c = 0; c < 26; c++) {
int costBlock = prefixCost[i + l][c] - prefixCost[i][c];
if (costBlock < bestCost) {
bestCost = costBlock;
bestLetter = c;
}
}
int costCandidate = dp[i + l] + bestCost;
if (costCandidate < dp[i]) {
dp[i] = costCandidate;
nextIndex[i] = i + l;
nextChar[i] = bestLetter;
blockLen[i] = l;
} else if (costCandidate == dp[i]) {
int cmp =
compareSolutions(
nextChar[i],
blockLen[i],
nextIndex[i],
bestLetter,
l,
(i + l),
nextIndex,
nextChar,
blockLen,
n);
if (cmp > 0) {
nextIndex[i] = i + l;
nextChar[i] = bestLetter;
blockLen[i] = l;
}
}
byte[] s = caption.getBytes();
int[] f = new int[n + 1];
f[n - 1] = f[n - 2] = Integer.MAX_VALUE / 2;
byte[] t = new byte[n + 1];
byte[] size = new byte[n];
for (int i = n - 3; i >= 0; i--) {
byte[] sub = Arrays.copyOfRange(s, i, i + 3);
Arrays.sort(sub);
byte a = sub[0];
byte b = sub[1];
byte c = sub[2];
byte s3 = t[i + 3];
int res = f[i + 3] + (c - a);
int mask = b << 24 | s3 << 16 | s3 << 8 | s3;
size[i] = 3;
if (i + 4 <= n) {
byte[] sub4 = Arrays.copyOfRange(s, i, i + 4);
Arrays.sort(sub4);
byte a4 = sub4[0];
byte b4 = sub4[1];
byte c4 = sub4[2];
byte d4 = sub4[3];
byte s4 = t[i + 4];
int res4 = f[i + 4] + (c4 - a4 + d4 - b4);
int mask4 = b4 << 24 | b4 << 16 | s4 << 8 | s4;
if (res4 < res || res4 == res && mask4 < mask) {
res = res4;
mask = mask4;
size[i] = 4;
}
}
}
if (dp[0] >= INF) {
return "";
}
StringBuilder builder = new StringBuilder(n);
int idx = 0;
while (idx < n) {
int len = blockLen[idx];
int c = nextChar[idx];
for (int k = 0; k < len; k++) {
builder.append((char) ('a' + c));
}
idx = nextIndex[idx];
}
return builder.toString();
}

private int compareSolutions(
int oldLetter,
int oldLen,
int oldNext,
int newLetter,
int newLen,
int newNext,
int[] nextIndex,
int[] nextChar,
int[] blockLen,
int n) {
int offsetOld = 0;
int offsetNew = 0;
int curOldPos;
int curNewPos;
int letOld = oldLetter;
int letNew = newLetter;
int lenOld = oldLen;
int lenNew = newLen;
int nxtOld = oldNext;
int nxtNew = newNext;
while (true) {
if (letOld != letNew) {
return (letOld < letNew) ? -1 : 1;
}
int remainOld = lenOld - offsetOld;
int remainNew = lenNew - offsetNew;
int step = Math.min(remainOld, remainNew);
offsetOld += step;
offsetNew += step;
if (offsetOld == lenOld && offsetNew == lenNew) {
if (nxtOld == n && nxtNew == n) {
return 0;
}
if (nxtOld == n) {
return -1;
if (i + 5 <= n) {
byte[] sub5 = Arrays.copyOfRange(s, i, i + 5);
Arrays.sort(sub5);
byte a5 = sub5[0];
byte b5 = sub5[1];
byte c5 = sub5[2];
byte d5 = sub5[3];
byte e5 = sub5[4];
int res5 = f[i + 5] + (d5 - a5 + e5 - b5);
int mask5 = c5 << 24 | c5 << 16 | c5 << 8 | t[i + 5];
if (res5 < res || res5 == res && mask5 < mask) {
res = res5;
mask = mask5;
size[i] = 5;
}
if (nxtNew == n) {
return 1;
}
curOldPos = nxtOld;
letOld = nextChar[curOldPos];
lenOld = blockLen[curOldPos];
nxtOld = nextIndex[curOldPos];
offsetOld = 0;
curNewPos = nxtNew;
letNew = nextChar[curNewPos];
lenNew = blockLen[curNewPos];
nxtNew = nextIndex[curNewPos];
offsetNew = 0;
} else if (offsetOld == lenOld) {
if (nxtOld == n) {
return -1;
}
curOldPos = nxtOld;
letOld = nextChar[curOldPos];
lenOld = blockLen[curOldPos];
nxtOld = nextIndex[curOldPos];
offsetOld = 0;
} else if (offsetNew == lenNew) {
if (nxtNew == n) {
return 1;
}
curNewPos = nxtNew;
letNew = nextChar[curNewPos];
lenNew = blockLen[curNewPos];
nxtNew = nextIndex[curNewPos];
offsetNew = 0;
}
f[i] = res;
t[i] = (byte) (mask >> 24);
}
StringBuilder ans = new StringBuilder(n);
for (int i = 0; i < n; i += size[i]) {
ans.append(String.valueOf((char) t[i]).repeat(Math.max(0, size[i])));
}
return ans.toString();
}
}