Minimum operations to make Array elements 0 by decrementing pair or single element
Given an array arr[] of size N, the task is to find the minimum number of operations required to reduce all three elements of the array to zero. Following operations are allowed:
- Reduce 2 different array elements by one.
- Reduce a single array element by one.
Example:
Input: arr[] = {1, 2, 3}, N = 3
Output: 3
Explanation : Operation 1: reduce 3 and 2 to get {1, 1, 2}
Operation 2: reduce 1 and 2 to get {1, 0, 1}
Operation 3: reduce both 1s to get {0, 0, 0}Input: arr[] = {5, 1, 2, 9, 8}, N = 5
Output: 13
Approach:
This problem can be solved using greedy approach. The idea is to reduce the 2 largest elements at a time or (if not possible) 1 at a time. As we need the largest elements in each step, we can use a max heap.
The following steps can be taken to solve this approach:
- Initiate a count variable as 0.
- Insert all the elements in a max heap.
- Reduce the two largest elements.
- Insert the reduced values again into the heap.
- Repeat above mentioned steps until all array elements become zero and increase the count at each iteration.
- Stop when all array elements are zero.
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
// C++ program to reduce array to zero in minimum steps
int reduceArray(int arr[], int N)
{
int count = 0;
priority_queue<int>pq;
for (int i = 0; i < N; i++) {
pq.push(arr[i] * -1);
}
while (pq.size() > 1) {
int temp1 = pq.top();
pq.pop();
int temp2 = pq.top();
pq.pop();
count++;
temp1++;
temp2++;
if (temp1 != 0)
pq.push(temp1);
if (temp2 != 0)
pq.push(temp2);
}
if (pq.size() > 0){
count -= pq.top();
pq.pop();
}
return count-1;
}
// Driver Code
int main() {
int arr[] = { 1, 2, 3 };
int N = 3;
int count = reduceArray(arr, N);
cout << count;
return 0;
}
// This code is contributed by satwik4409.
Java
// Java program to reduce array to zero in minimum steps
import java.util.*;
class GFG {
public static int reduceArray(int arr[], int N)
{
int count = 0;
PriorityQueue<Integer> pq = new PriorityQueue<>();
for (int i = 0; i < N; i++) {
pq.add(arr[i] * -1);
}
while (pq.size() > 1) {
int temp1 = pq.poll();
int temp2 = pq.poll();
count++;
temp1++;
temp2++;
if (temp1 != 0)
pq.add(temp1);
if (temp2 != 0)
pq.add(temp2);
}
if (pq.size() > 0)
count -= pq.poll();
return count;
}
// Driver Code
public static void main(String[] args)
{
int arr[] = { 1, 2, 3 };
int N = 3;
int count = reduceArray(arr, N);
System.out.println(count);
}
}
Python3
# Python program to reduce array to zero in minimum steps
from queue import PriorityQueue
def reduceArray(arr, N):
count = 0
pq = PriorityQueue()
for i in range(N):
pq.put(arr[i] * -1)
while (pq.qsize() > 1):
temp1 = pq.get()
temp2 = pq.get()
count += 1
temp1 += 1
temp2 += 1
if (temp1 != 0):
pq.put(temp1)
if (temp2 != 0):
pq.put(temp2)
if (pq.qsize() > 0):
count -= pq.get()
return count
# Driver Code
arr = [1, 2, 3]
N = 3
count = reduceArray(arr, N)
print(count)
# This code is contributed by hrithikgarg03188.
C#
// C# implementation of above approach
using System;
using System.Collections.Generic;
class GFG {
public static int reduceArray(int[] arr, int N)
{
int count = 0;
List<int> pq = new List<int>();
for (int i = 0; i < N; i++) {
pq.Add(arr[i] * -1);
}
while (pq.Count > 1) {
int temp1 = pq[0];
pq.RemoveAt(0);
int temp2 = pq[0];
pq.RemoveAt(0);
count++;
temp1++;
temp2++;
if (temp1 != 0)
pq.Add(temp1);
if (temp2 != 0)
pq.Add(temp2);
}
if (pq.Count > 0)
count -= pq[0];
pq.RemoveAt(0);
return count-1;
}
// Driver Code
public static void Main()
{
int[] arr = { 1, 2, 3 };
int N = 3;
int count = reduceArray(arr, N);
Console.Write(count);
}
}
// This code is contributed by sanjoy_62.
Javascript
<script>
// Javascript Priority Queue implementation
function PriorityQueue () {
let collection = [];
this.printCollection = function() {
(console.log(collection));
};
this.enqueue = function(element){
if (this.isEmpty()){
collection.push(element);
} else {
let added = false;
for (let i=0; i<collection.length; i++){
if (element[1] < collection[i][1]){ //checking priorities
collection.splice(i,0,element);
added = true;
break;
}
}
if (!added){
collection.push(element);
}
}
};
this.dequeue = function() {
let value = collection.shift();
return value[0];
};
this.top = function() {
return collection[0];
};
this.size = function() {
return collection.length;
};
this.isEmpty = function() {
return (collection.length === 0);
};
}
// Javascript program to reduce array to zero in minimum steps
function reduceArray(arr, N)
{
let count = 0;
let pq = new PriorityQueue();
for (let i = 0; i < N; i++) {
pq.enqueue(arr[i] * -1);
}
while (pq.size() > 1) {
let temp1 = pq.top();
pq.dequeue();
let temp2 = pq.top();
pq.dequeue();
count++;
temp1++;
temp2++;
if (temp1 != 0)
pq.enqueue(temp1);
if (temp2 != 0)
pq.enqueue(temp2);
}
if (pq.size() > 0){
count -= pq.top();
pq.dequeue();
}
return count-1;
}
// Driver Code
let arr = [ 1, 2, 3 ];
let N = 3;
let count = reduceArray(arr, N);
console.log(count);
// This code is contributed by akashish__
</script>
Output
3
Time Complexity: O(N * logN)
Auxiliary Space: O(N)
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