Update README_EN.md

Author: Nothing-avil

solution/3000-3099/3008.Find Beautiful Indices in the Given Array II/README_EN.md

@@ -55,4 +55,72 @@ Thus we return [0] as the result.
 
 ## Solutions
 
+```cpp
+class Solution {
+public:
+    vector<int> beautifulIndices(string s, string patternA, string patternB, int k) {
+        vector<int> beautifulIndicesA = kmpSearch(s, patternA);
+        vector<int> beautifulIndicesB = kmpSearch(s, patternB);
+
+        sort(beautifulIndicesB.begin(), beautifulIndicesB.end());
+
+        vector<int> result;
+        for (int indexA : beautifulIndicesA) {
+            int left = lower_bound(beautifulIndicesB.begin(), beautifulIndicesB.end(), indexA - k) - beautifulIndicesB.begin();
+            int right = lower_bound(beautifulIndicesB.begin(), beautifulIndicesB.end(), indexA + k + patternB.length()) - beautifulIndicesB.begin();
+
+            left = (left >= 0) ? left : -(left + 1);
+            right = (right >= 0) ? right : -(right + 1);
+
+            for (int indexB = left; indexB < right; indexB++) {
+                if (abs(beautifulIndicesB[indexB] - indexA) <= k) {
+                    result.push_back(indexA);
+                    break;
+                }
+            }
+        }
+
+        return result;
+    }
+
+private:
+    vector<int> kmpSearch(string text, string pattern) {
+        vector<int> indices;
+        vector<int> pi = computePrefixFunction(pattern);
+
+        int q = 0;
+        for (int i = 0; i < text.length(); i++) {
+            while (q > 0 && pattern[q] != text[i]) {
+                q = pi[q - 1];
+            }
+            if (pattern[q] == text[i]) {
+                q++;
+            }
+            if (q == pattern.length()) {
+                indices.push_back(i - q + 1);
+                q = pi[q - 1];
+            }
+        }
+
+        return indices;
+    }
+
+    vector<int> computePrefixFunction(string pattern) {
+        int m = pattern.length();
+        vector<int> pi(m, 0);
+        int k = 0;
+        for (int q = 1; q < m; q++) {
+            while (k > 0 && pattern[k] != pattern[q]) {
+                k = pi[k - 1];
+            }
+            if (pattern[k] == pattern[q]) {
+                k++;
+            }
+            pi[q] = k;
+        }
+        return pi;
+    }
+};
+```
+
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