二分查找变种

php/16_binary/binary.php

@@ -0,0 +1,191 @@
+<?php
+
+/**
+ * 找到第一个=value的元素
+ * @param array $numbers
+ *
+ * @return void
+ * @date 2018/11/27
+ * @author yuanliandu <[email protected]>
+ */
+function findFirstEqual(array $numbers,$find) {
+    $length = count($numbers);
+    $low = 0;
+    $high = $length - 1;
+    while($low <= $high) {
+        $mid = $low + (($high-$low)>>1);
+        if($numbers[$mid] > $find) {
+            $high = $mid - 1;
+        }else if($numbers[$mid] < $find) {
+            $low = $mid + 1;
+        }else {
+            /**
+             * 如果是第一个元素，或之前一个元素不等于我们要找的值
+             * 我们就找到了第一个=find的element
+             */
+            if($mid==0 || $numbers[$mid-1]!=$find) {
+                return $mid;
+            }else {
+                $high = $mid - 1;
+            }
+        }
+    }
+
+    return -1;
+}
+
+/**
+ * 找到最后一个=find的元素
+ * @param array $numbers
+ * @param [type] $find
+ *
+ * @return void
+ * @date 2018/11/27
+ * @author yuanliandu <[email protected]>
+ */
+function findLastEqual(array $numbers,$find) {
+    $length = count($numbers);
+    $low = 0;
+    $high = $length - 1;
+    while($low <= $high) {
+        $mid = $low + (($high-$low)>>1);
+        if($numbers[$mid] > $find) {
+            $high = $mid - 1;
+        }else if($numbers[$mid] < $find) {
+            $low = $mid + 1;
+        }else {
+            /**
+             * 如果mid是最后一个元素的index
+             * 或mid后一个元素!=我们要找的值
+             * 则找到了最后一个=find的value
+             */
+            if($mid==$length-1 || $numbers[$mid+1]!=$find) {
+                return $mid;
+            }else {
+                $low = $mid + 1;
+            }
+        }
+    }
+
+    return -1;
+}
+
+/**
+ * 找到第一个大于等于find的元素
+ * @param array $numbers
+ * @param [type] $find
+ *
+ * @return void
+ * @date 2018/11/27
+ * @author yuanliandu <[email protected]>
+ */
+function findFirstGreaterEqual(array $numbers,$find) {
+    $length = count($numbers);
+    $low = 0;
+    $high = $length - 1;
+    while($low <= $high) {
+        $mid = $low + (($high-$low)>>1);
+        if($numbers[$mid] >= $find) {
+            if ($mid == 0 || $numbers[$mid-1] < $find) {
+                return $mid;
+            }else {
+                $high = $mid - 1;
+            }
+        }else  {
+            $low  = $mid + 1;
+        }
+    }
+    return -1;
+}
+
+/**
+ * 找到最后一个小于等于find的元素
+ * @param array $numbers
+ * @param [type] $find
+ *
+ * @return void
+ * @date 2018/11/27
+ * @author yuanliandu <[email protected]>
+ */
+function findLastLessEqual(array $numbers,$find) {
+    $length = count($numbers);
+    $low = 0;
+    $high = $length - 1;
+    while($low <= $high) {
+        $mid = $low + (($high-$low)>>1);
+        if($numbers[$mid] <= $find) {
+           if($mid==$length-1 || $numbers[$mid+1]> $find) {
+               return $mid;
+           }
+           $low = $mid + 1;
+        }else  {
+            $high = $mid - 1;
+        }
+    }
+    return -1;
+}
+
+
+
+
+
+/**
+ * 循环数组中找指定元素
+ * @param array $numbers
+ * @param [type] $find
+ *
+ * @return void
+ * @date 2018/11/27
+ * @author yuanliandu <[email protected]>
+ */
+function searchCircularArray(array $numbers,$find) {
+    $length = count($numbers);
+    $low = 0;
+    $high = $length - 1;
+
+    while($low <= $high) {
+        $mid = $low + (($high-$low)>>1);
+        if($numbers[$mid] === $find) {
+            return $mid;
+        }
+
+        if($numbers[$low] > $numbers[$mid]) {
+            // 后半部分是有序数组
+           if(($numbers[$mid] < $find) && ($numbers[$high] >= $find)) {
+               if($numbers[$high] === $find)  return $high;
+                //在后半个区间内
+                $low = $mid + 1;
+           }else {
+               $high = $mid - 1;
+           }
+        }else {
+           // 前半部分是有序的
+           if(($numbers[$low] <= $find) && ($numbers[$mid] > $find)) {
+               // 在有序区间内
+               if($numbers[$low] === $find)  return $low;
+               $high = $mid - 1;
+           }else {
+               $low = $mid + 1;
+           }
+        }
+
+    }
+    return -1;
+}
+
+/***
+ * 测试
+ */
+$numbers = [1,2,3,3,3,4,5,6,8,11,13];
+$find = 3;
+
+var_dump(findFirstEqual($numbers,$find));//找到第一个等于find的元素
+var_dump(findFirstGreaterEqual($numbers,$find));//找到第一个大于等于find的元素
+var_dump(findLastEqual($numbers,$find));//找到最后一个=find的元素
+var_dump(findLastLessEqual($numbers,$find));//找到最后一个小于等于find的元素
+
+
+//测试在循环数组中找到指定数字
+$numbers = [9,10,1,2,3,4,5,6,7,8];
+$find = 2;
+var_dump(searchCircularArray($numbers,$find));