Hello Everyone,
Given an array of positive and negative numbers, arrange them in an alternate fashion such that every positive number is followed by negative and vice-versa maintaining the order of appearance.
Number of positive and negative numbers need not be equal. If there are more positive numbers they appear at the end of the array. If there are more negative numbers, they too appear in the end of the array.
Examples :
Input: arr[] = {1, 2, 3, -4, -1, 4} Output: arr[] = {-4, 1, -1, 2, 3, 4} Input: arr[] = {-5, -2, 5, 2, 4, 7, 1, 8, 0, -8} output: arr[] = {-5, 5, -2, 2, -8, 4, 7, 1, 8, 0}
Naive Approach :
The above problem can be easily solved if O(n) extra space is allowed. It becomes interesting due to the limitations that O(1) extra space and order of appearances.
The idea is to process array from left to right. While processing, find the first out of place element in the remaining unprocessed array. An element is out of place if it is negative and at odd index, or it is positive and at even index. Once we find an out of place element, we find the first element after it with opposite sign. We right rotate the subarray between these two elements (including these two).
Following is the implementation of above idea.
- C++
/* C++ program to rearrange
positive and negative integers
in alternate fashion while keeping
the order of positive and negative numbers. */
#include <assert.h>
#include <iostream>
using
namespace
std;
// Utility function to right rotate all elements between
// [outofplace, cur]
void
rightrotate(
int
arr[],
int
n,
int
outofplace,
int
cur)
{
char
tmp = arr[cur];
for
(
int
i = cur; i > outofplace; i--)
arr[i] = arr[i - 1];
arr[outofplace] = tmp;
}
void
rearrange(
int
arr[],
int
n)
{
int
outofplace = -1;
for
(
int
index = 0; index < n; index++)
{
if
(outofplace >= 0)
{
// find the item which must be moved into the
// out-of-place entry if out-of-place entry is
// positive and current entry is negative OR if
// out-of-place entry is negative and current
// entry is negative then right rotate
//
// [...-3, -4, -5, 6...] --> [...6, -3, -4,
// -5...]
// ^ ^
// | |
// outofplace --> outofplace
//
if
(((arr[index] >= 0) && (arr[outofplace] < 0))
|| ((arr[index] < 0)
&& (arr[outofplace] >= 0)))
{
rightrotate(arr, n, outofplace, index);
// the new out-of-place entry is now 2 steps
// ahead
if
(index - outofplace >= 2)
outofplace = outofplace + 2;
else
outofplace = -1;
}
}
// if no entry has been flagged out-of-place
if
(outofplace == -1) {
// check if current entry is out-of-place
if
(((arr[index] >= 0) && (!(index & 0x01)))
|| ((arr[index] < 0) && (index & 0x01))) {
outofplace = index;
}
}
}
}
// A utility function to print an array 'arr[]' of size 'n'
void
printArray(
int
arr[],
int
n)
{
for
(
int
i = 0; i < n; i++)
cout << arr[i] <<
" "
;
cout << endl;
}
// Driver code
int
main()
{
int
arr[] = { -5, -2, 5, 2,
4, 7, 1, 8, 0, -8 };
int
n =
sizeof
(arr) /
sizeof
(arr[0]);
cout <<
"Given array is \n"
;
printArray(arr, n);
rearrange(arr, n);
cout <<
"Rearranged array is \n"
;
printArray(arr, n);
return
0;
}
Output
Given array is -5 -2 5 2 4 7 1 8 0 -8 Rearranged array is -5 5 -2 2 -8 4 7 1 8 0
Time Complexity : O(N^2)
Space Complexity : O(1)
Efficient Approach :
We first sort the array in non-increasing order.Then we will count the number of poitive and negative integers. Then we will swap the one negative and one positive
number till we reach our condition. This will rearrange the array elements because we are sorting the array and accessing the element from left to right according to our need.
- Java
// Below is the implementation of the above approach
import
java.io.*;
import
java.lang.*;
import
java.util.*;
public
class
Main {
// function which works in the condition when number of
// negative numbers are lesser or equal than positive
// numbers
static
void
fill1(
int
a[],
int
neg,
int
pos)
{
if
(neg %
2
==
1
) {
for
(
int
i =
1
; i < neg; i +=
2
) {
int
c = a[i];
int
d = a[i + neg];
int
temp = c;
a[i] = d;
a[i + neg] = temp;
}
}
else
{
for
(
int
i =
1
; i <= neg; i +=
2
) {
int
c = a[i];
int
d = a[i + neg -
1
];
int
temp = c;
a[i] = d;
a[i + neg -
1
] = temp;
}
}
}
// function which works in the condition when number of
// negative numbers are greater than positive numbers
static
void
fill2(
int
a[],
int
neg,
int
pos)
{
if
(pos %
2
==
1
) {
for
(
int
i =
1
; i < pos; i +=
2
) {
int
c = a[i];
int
d = a[i + pos];
int
temp = c;
a[i] = d;
a[i + pos] = temp;
}
}
else
{
for
(
int
i =
1
; i <= pos; i +=
2
) {
int
c = a[i];
int
d = a[i + pos -
1
];
int
temp = c;
a[i] = d;
a[i + pos -
1
] = temp;
}
}
}
static
void
reverse(
int
a[],
int
n)
{
int
i, k, t;
for
(i =
0
; i < n /
2
; i++) {
t = a[i];
a[i] = a[n - i -
1
];
a[n - i -
1
] = t;
}
}
static
void
print(
int
a[],
int
n)
{
for
(
int
i =
0
; i < n; i++)
System.out.print(a[i] +
" "
);
System.out.println();
}
public
static
void
main(String[] args)
throws
java.lang.Exception
{
// Given array
int
[] arr = { -
5
, -
2
,
5
,
2
,
4
,
7
,
1
,
8
,
0
, -
8
};
int
n = arr.length;
int
neg =
0
, pos =
0
;
for
(
int
i =
0
; i < n; i++) {
if
(arr[i] <
0
)
neg++;
else
pos++;
}
// Sort the array
Arrays.sort(arr);
if
(neg <= pos) {
fill1(arr, neg, pos);
}
else
{
// reverse the array in this condition
reverse(arr, n);
fill2(arr, neg, pos);
}
print(arr, n);
}
}
Output
-8 1 -2 0 -5 2 4 5 7 8
Time Complexity: O(N*logN)
Space Complexity: O(1)