C ++程序使用二进制搜索方法查找最大子数组和
二进制搜索是一种运行时间复杂度为O（log n）的快速搜索算法。这种搜索算法基于分而治之的原理。为了使该算法正常工作，数据收集应采用排序形式。
二进制搜索通过比较集合中最中间的项来查找特定项。如果发生匹配，则返回项目的索引。如果中间项目大于该项目，则在中间项目左侧的子数组中搜索该项目。否则，将在中间项目右侧的子数组中搜索该项目。该过程也将在子数组上继续进行，直到子数组的大小减小到零为止。
这是使用二进制搜索方法查找最大子数组总和的程序。
演算法
BeginDeclare an integer function maximum() to find the maximum of two integers.
Declare val1, val2 to the integer datatype.
Pass them as parameter.
Check the maximum between val1 and val2.
Return the maximum value.
End
Begin
Declare an integer function MCS() to find the maximum sum sub-array which includes medium of the sub-array.
Declare an array array[] and variable l, m, h to the integer datatype.
Pass them as parameter.
Declare variable s, sum_of_left_part to the integer datatype.
Initialize s = 0.
Initialize sum_of_left_part = -1.
for (int i = m; i >= l; i--)
s = s + array[i].
if (s > sum_of_left_part) then
sum_of_left_part = s.
s = 0
Declare variable sum_of_right_part to the integer datatype.
Initialize sum_of_right_part = -1.
for (int i = m+1; i <= h; i++)
s = s + array[i].
if (s > sum_of_right_part) then
sum_of_right_part = s.
return sum_of_left_part + sum_of_right_part.
End
Begin
Declare an integer function MaximumSum_of_SubArray().
Declare an array array[] and variable l, h to the integer datatype.
Pass them as parameter.
Declare m to the integer datatype.
if (l == h) then
return array[l].
m = (l + h)/2;
return maximum(maximum(MaximumSum_of_SubArray(array, l, m), MaximumSum_of_SubArray(array, m+1, h)), MCS(array, l, m, h)).
Declare number_of_elements and i to the integer datatype.
Print “Enter the number of elements of array: ”.
Enter the value of number_of_elements.
Declare an array a[number_of_elements] to the integer datatype.
for(i = 0; i < n; i++)
Print “Enter the element of”.
Enter the data element of array.
Print “Maximum sum of Sub-Array is: ” .
Print the result of MaximumSum_of_SubArray(a, 0, n-1).
End.
示例
#include<iostream>using namespace std;
int maximum(int val1, int val2) // find the maximum of two integers {
return (val1 > val2)? val1:val2;
}
int MCS(int array[], int l, int m, int h) // find the maximum sum sub-array which includes medium of the sub-array. {
int s = 0;
int sum_of_left_part = -1;
for (int i = m; i >= l; i--) {
s = s + array[i];
if (s > sum_of_left_part)
sum_of_left_part = s;
}
s = 0;
int sum_of_right_part = -1;
for (int i = m+1; i <= h; i++) {
s = s + array[i];
if (s > sum_of_right_part)
sum_of_right_part = s;
}
return sum_of_left_part + sum_of_right_part; // Return sum of elements on left and right of medium.
}
int MaximumSum_of_SubArray(int array[], int l, int h) {
int m;
if (l == h)
return array[l];
m = (l + h)/2;
return maximum(maximum(MaximumSum_of_SubArray(array, l, m), MaximumSum_of_SubArray(array, m+1, h)), MCS(array, l, m, h));
}
int main() {
int number_of_elements, i;
cout<<"Enter the number of elements of array: ";
cin>> number_of_elements;
cout<<endl;
int a[number_of_elements];
for(i = 0; i < number_of_elements; i++) {
cout<<"Enter the element of "<<i+1<<": ";
cin>>a[i];
}
cout<<"\nMaximum sum of Sub-Array is: "<<MaximumSum_of_SubArray(a, 0, number_of_elements -1); // Print the maximum sum sub-array.
return 0;
}
输出结果
Enter the number of elements of array: 5Enter the element of 1: 12
Enter the element of 2: 45
Enter the element of 3: 56
Enter the element of 4: 48
Enter the element of 5: 75
Maximum sum of Sub-Array is: 236
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