二分法(Binary Search)介绍

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本文介绍了二分法的概念，并通过实例讲解如何在代码中实现二分法。特别提到在Android开发中，二分法的应用可能因为历史遗留问题导致阅读难度增加。

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二分法，是常用的方法，下面这里有个实例，讲述如何使用二分法写代码。

// Implementation of binary search
#include <iostream>
#include <string>
#include "vector.h"
using namespace std;

void initCityNames(Vector<string> & cities);
int findInSortedVector(string key, Vector<string> & vec);
int binarySearch(string key, Vector<string> & vec, int p1, int p2);

// 不停地使用二分法查找。
int main() {
   Vector<string> cities;
   initCityNames(cities);
   for (string city : cities) {
      int index = findInSortedVector(city, cities);
      cout << city << " == " << cities[index] << endl;
   }
   return 0;
}

void initCityNames(Vector<string> & cities) {
   cities += "Amsterdam", "Angora", "Athina", "Barcelona", "Berlin",
             "Brest", "Brindisi", "Bruxelles", "Bucuresti", "Budapest",
             "Cadiz", "Constantinople", "Danzig", "Dieppe", "Edinburgh",
             "Erzurum", "Essen", "Frankfurt", "Kharkov", "Kobenhavn",
             "Kyiv", "Lisboa", "London", "Madrid", "Marseille", "Moskva",
             "Munchen", "Palermo", "Pamplona", "Paris", "Petrograd",
             "Riga", "Roma", "Rostov", "Sarajevo", "Sevastopol",
             "Smolensk", "Smyrna", "Sochi", "Sofia", "Stockholm",
             "Venezia", "Warszawa", "Wien", "Wilno", "Zagrab", "Zurich";
};

int findInSortedVector(string key, Vector<string> & vec) {
    return binarySearch(key, vec, 0, vec.size() - 1);
}

// Searches for the specified key in the Vector<string> vec, looking
// only at indices between p1 and p2, inclusive. The function returns
// the index of a matching element, or -1 if no match is found.

int binarySearch(string key, Vector<string> & vec, int p1, int p2) {
    if (p1 > p2) return -1;
    int mid = (p1 + p2) / 2;
    if (key == vec[mid]) return mid;
    if (key < vec[mid]) {
        return binarySearch(key, vec, p1, mid - 1);
    } else {
        return binarySearch(key, vec, mid+1, p2);
    }
}

实现的代码，这里的Vector是本地写的一个头文件，和标准库的中vector的用法基本上是一样的。

可能是因为历史原因，当时的vector不支持遍历。

android中有处用到二分法，读起来比较晦涩。

ssize_t SortedVectorImpl::indexOf(const void* item) const
{
    return _indexOrderOf(item);
}

size_t SortedVectorImpl::orderOf(const void* item) const
{
    size_t o;
    _indexOrderOf(item, &o);
    return o;
}

ssize_t SortedVectorImpl::_indexOrderOf(const void* item, size_t* order) const
{
    if (order) *order = 0;
    if (isEmpty()) {
        return NAME_NOT_FOUND;
    }
    // binary search
    ssize_t err = NAME_NOT_FOUND;
    ssize_t l = 0;
    ssize_t h = size()-1;
    ssize_t mid;
    const void* a = arrayImpl();
    const size_t s = itemSize();
    while (l <= h) {
        mid = l + (h - l)/2;
        const void* const curr = reinterpret_cast<const char *>(a) + (mid*s);
	ALOGE("wangrl VectorImpl curr = %s", curr);
        const int c = do_compare(curr, item);
        if (c == 0) {
            err = l = mid;
            break;
        } else if (c < 0) {
            l = mid + 1;
        } else {
            h = mid - 1;
        }
    }
    if (order) *order = l;
    return err;
}