From 85771ea74fdeaf7756b87c7fadcb7884ac6a7a32 Mon Sep 17 00:00:00 2001
From: feng liu <fengxliu@gmail.com>
Date: Sun, 1 Oct 2017 17:26:05 -0600
Subject: [PATCH 1/2] prevent (ub+lb) overflow

---
 Searches/BinarySearch.java | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Searches/BinarySearch.java b/Searches/BinarySearch.java
index 3949f6a86f02..535442c87409 100644
--- a/Searches/BinarySearch.java
+++ b/Searches/BinarySearch.java
@@ -23,7 +23,7 @@ public static <T extends Comparable<T>> int BS(T array[], T key, int lb, int ub)
         if ( lb > ub)
             return -1;
 
-        int mid = (ub+lb)/2;
+        int mid = (ub+lb) >>> 1;
         int comp = key.compareTo(array[mid]);
 
         if (comp < 0)

From 79a73aebb41df045c8aed286171b8051cd886554 Mon Sep 17 00:00:00 2001
From: feng liu <fengxliu@gmail.com>
Date: Sun, 1 Oct 2017 17:45:16 -0600
Subject: [PATCH 2/2] KMP algorithm

---
 Misc/KMP.java | 55 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 55 insertions(+)
 create mode 100644 Misc/KMP.java

diff --git a/Misc/KMP.java b/Misc/KMP.java
new file mode 100644
index 000000000000..c97c248b480a
--- /dev/null
+++ b/Misc/KMP.java
@@ -0,0 +1,55 @@
+
+/*
+Implementation of Knuth–Morris–Pratt algorithm
+Usage: 
+final String T = "AAAAABAAABA";
+final String P = "AAAA";
+KMPmatcher(T, P);
+*/
+public class KMP {
+
+    // find the starting index in string T[] that matches the search word P[]
+    public void KMPmatcher(final String T, final String P) {
+        final int m = T.length();
+        final int n = P.length();
+        final int[] pi = computePrefixFunction(P);
+        int q = 0;
+        for (int i = 0; i < m; i++) {
+            while (q > 0 && T.charAt(i) != P.charAt(q)) {
+                q = pi[q - 1]; 
+            }
+
+            if (T.charAt(i) == P.charAt(q)) {
+                q++;
+            }
+
+            if (q == n) {
+                System.out.println("Pattern starts: " + (i + 1 - n));
+                q = pi[q - 1];  
+            }
+        }
+
+    }
+
+    // return the prefix function 
+    private int[] computePrefixFunction(final String P) {
+        final int n = P.length();
+        final int[] pi = new int[n];
+        pi[0] = 0;
+        int q = 0;
+        for (int i = 1; i < n; i++) {
+            while (q > 0 && P.charAt(q) != P.charAt(i)) {
+                q = pi[q - 1];
+            }
+
+            if (P.charAt(q) == P.charAt(i)) {
+                q++;
+            }
+
+            pi[i] = q;
+
+        }
+
+        return pi;
+    }
+}