ACM：二分查找，以及利用二分法来找上下界

（一）二分的模版：

int binary_search(int *array, int length, int key) {
	int start = 0, end = length - 1;
	while(end >= start) {
		int middle = start + (end - start) / 2;
		int tmp = array[middle];
		if(tmp < key) start = middle + 1;
		else if (tmp > key) end = middle - 1;
		else return middle;
	}
	return -1;
}

（二）

#include<stdio.h>
#include<assert.h>

int A[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11};

int bsearch(int* A, int x, int y, int v) {
  int m;
  while(x < y) {
    m = x+(y-x)/2;
    if(A[m] == v) return m;
    else if(A[m] > v) y = m;
    else x = m+1;
  }
  return -1;
}

int main() {
  int i;
  for(i = 1; i <= 11; i++)
    assert(bsearch(A, 0, 11, i) == i-1);
  printf("Ok!\n");
  return 0;
}

（三）利用二分法找上下界

#include<stdio.h>
#include<assert.h>
#include <iostream>
using namespace std;

int A[] = {1, 2, 3, 3, 3, 3, 3, 5, 6};

int lower_bound(int *array, int length, int v) {
  int start = 0, end = length - 1;
  while(start <= end) {
    int middle = start + (end - start) / 2;
    int tmp = array[middle];
    if(array[middle] >= v) end = middle - 1;
    else start = middle + 1;
  }
  return start;
}

int upper_bound(int *array, int length, int v) {
  int start = 0, end = length-1;
  while(start <= end) {
    int middle = start + (end - start) / 2;
    int tmp = array[middle];
    if(array[middle] <= v) start = middle + 1;
    else end = middle - 1;
  }
  return start;
}

int main() {
  cout << lower_bound(A, 9, 3) << endl
	   << upper_bound(A, 9, 3) << endl;
  return 0;
}

ACM：二分查找，以及利用二分法来找上下界