给定一个数组arr[] ,任务是找到排除其最大元素后具有最大总和的子数组的开始和结束索引。
例子:
Input: arr[] = {5, -2, 10, -1, 4}
Output: 1 5
Explanation:
Subarray[1:5] = {5, -2, 10, -1, 4}
Sum of subarray excluding maximum element = 5 + (-2) + (-1) + 4 = 6
Input: arr[] = {5, 2, 5, 3, -30, -30, 6, 9}
Output: 1 4
Explanation:
Subarray[1:4] = {5, 2, 5, 3}
Sum of subarray excluding maximum element = 5 + 2 + 3 = 10
做法:思路是用Kadane算法来解决这个问题。
- 在这个问题中,我们必须选择一个元素,它是子数组中的最大值。
- 因此,我们可以从数组中选择所有正元素,并且每次我们可以将大于该元素的元素设置为INT_MIN,这样它就不会被包含在数组中。
- 最后,应用 Kadane 算法找到最大和子数组。
- 如果数组中没有正元素,那么我们可以从数组中选择任何一个元素,以获得最大和为 0。
下面是上述方法的实现:
C++
// C++ implementation to find the
// maximum sum subarray such by
// excluding the maximum element
// from the subarray
#include
using namespace std;
// Function to find the maximum sum
// subarray by excluding the maximum
// element from the array
void maximumSumSubarray(int arr[], int n)
{
unordered_map mp;
// Loop to store all the positive
// elements in the map
for (int i = 0; i < n; i++) {
if (arr[i] >= 0
&& mp.find(arr[i])
== mp.end())
mp[arr[i]] = 1;
}
int first = 0;
int last = 0;
int ans = 0;
int INF = 1e6;
// Loop to iterating over the map
// and considering as the maximum
// element of the current including
// subarray
for (auto i : mp) {
// Make the current
// element maximum
int mx = i.first;
int curr = 0;
int curr_start;
// Iterate through array and
// apply kadane's algorithm
for (int j = 0; j < n; j++) {
if (curr == 0)
curr_start = j;
// Condition if current element is
// greater than mx then make
// the element -infinity
int val = arr[j] > mx
? -INF
: arr[j];
curr += val;
if (curr < 0)
curr = 0;
if (curr > ans) {
ans = curr;
// Store the indices
// in some variable
first = curr_start;
last = j;
}
}
}
cout << first + 1
<< " " << last + 1;
}
// Driver Code
int main()
{
int arr[] = { 5, -2, 10, -1, 4 };
int size = sizeof(arr) / sizeof(arr[0]);
// Function Call
maximumSumSubarray(arr, size);
return 0;
}
Java
// Java implementation to find the
// maximum sum subarray such by
// excluding the maximum element
// from the subarray
import java.util.*;
class GFG{
// Function to find the maximum sum
// subarray by excluding the maximum
// element from the array
static void maximumSumSubarray(int arr[], int n)
{
Map mp = new HashMap<>();
// Loop to store all the positive
// elements in the map
for(int i = 0; i < n; i++)
{
if (arr[i] >= 0)
mp.put(arr[i], 1);
}
int first = 0;
int last = 0;
int ans = 0;
int INF = (int)1e6;
// Loop to iterating over the map
// and considering as the maximum
// element of the current including
// subarray
for (Map.Entry i : mp.entrySet())
{
// Make the current
// element maximum
int mx = i.getKey();
int curr = 0;
int curr_start = -1;
// Iterate through array and
// apply kadane's algorithm
for(int j = 0; j < n; j++)
{
if (curr == 0)
curr_start = j;
// Condition if current element is
// greater than mx then make
// the element -infinity
int val = arr[j] > mx ? -INF : arr[j];
curr += val;
if (curr < 0)
curr = 0;
if (curr > ans)
{
ans = curr;
// Store the indices
// in some variable
first = curr_start;
last = j;
}
}
}
System.out.print((first + 1) + " " +
(last + 1));
}
// Driver code
public static void main(String[] args)
{
int arr[] = { 5, -2, 10, -1, 4 };
int size = arr.length;
// Function call
maximumSumSubarray(arr, size);
}
}
// This code is contributed by offbeat
Python3
# Python3 implementation to find
# the maximum sum subarray such
# by excluding the maximum
# element from the subarray
# Function to find the maximum sum
# subarray by excluding the maximum
# element from the array
def maximumSumSubarray(arr, n):
mp = {}
# Loop to store all the positive
# elements in the map
for i in range(n):
if (arr[i] >= 0 and
arr[i] not in mp):
mp[arr[i]] = 1
first = 0
last = 0
ans = 0
INF = 1e6
# Loop to iterating over the map
# and considering as the maximum
# element of the current including
# subarray
for i in mp:
# Make the current
# element maximum
mx = i
curr = 0
# Iterate through array and
# apply kadane's algorithm
for j in range(n):
if (curr == 0):
curr_start = j
# Condition if current element
# is greater than mx then make
# the element -infinity
if arr[j] > mx:
val =- INF
else:
val= arr[j];
curr += val
if (curr < 0):
curr = 0
if (curr > ans):
ans = curr
# Store the indices
# in some variable
first = curr_start
last = j
print(first + 1, last + 1)
# Driver Code
if __name__ == "__main__":
arr = [ 5, -2, 10, -1, 4 ]
size = len(arr)
# Function Call
maximumSumSubarray(arr, size)
# This code is contributed by chitranayal
C#
// C# implementation to find the
// maximum sum subarray such by
// excluding the maximum element
// from the subarray
using System;
using System.Collections.Generic;
class GFG{
// Function to find the maximum sum
// subarray by excluding the maximum
// element from the array
static void maximumSumSubarray(int []arr,
int n)
{
Dictionary mp = new Dictionary();
// Loop to store all the positive
// elements in the map
for(int i = 0; i < n; i++)
{
if (arr[i] >= 0)
mp.Add(arr[i], 1);
}
int first = 0;
int last = 0;
int ans = 0;
int INF = (int)1e6;
// Loop to iterating over the map
// and considering as the maximum
// element of the current including
// subarray
foreach (KeyValuePair i in mp)
{
// Make the current
// element maximum
int mx = i.Key;
int curr = 0;
int curr_start = -1;
// Iterate through array and
// apply kadane's algorithm
for(int j = 0; j < n; j++)
{
if (curr == 0)
curr_start = j;
// Condition if current element is
// greater than mx then make
// the element -infinity
int val = arr[j] > mx ?
-INF : arr[j];
curr += val;
if (curr < 0)
curr = 0;
if (curr > ans)
{
ans = curr;
// Store the indices
// in some variable
first = curr_start;
last = j;
}
}
}
Console.Write((first + 1) + " " +
(last + 1));
}
// Driver code
public static void Main(String[] args)
{
int []arr = {5, -2, 10, -1, 4};
int size = arr.Length;
// Function call
maximumSumSubarray(arr, size);
}
}
// This code is contributed by shikhasingrajput
Javascript
输出:
1 5
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