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Split Array Largest Sum in C++
Suppose we have an array of positive integers and one value m. We can divide this array into m number of contiguous subarrays. We have to devise an algorithm to minimize the largest sum among these m subarrays.
So if the array is say [7,2,4,10,9], and m = 2, then the sum will be 19, as we can make two subarrays like [7,2,4] and [10,9], then the subarray with largest sum is 19.
To solve this, we will follow these steps −
- Define a function splitArray(), this will take an array v, m,
- n := size of v
- make one array dp of size
- make another array sum of size n
- sum[0] := v[0]
- for initialize i := 1, when i < n, update (increase i by 1), do −
- sum[i] := sum[i - 1] + v[i]
- dp[0] := sum[n - 1]
- for initialize i := 1, when i < n, update (increase i by 1), do −
- dp[i] := sum[n - 1] - sum[i - 1]
- for initialize i := 1, when i < m, update (increase i by 1), do −
- for initialize start := 0, when start < n - i, update (increase start by 1), do −
- for initialize end := start + 1, when end <= n - i, update (increase end by 1), do −
- dp[start] := minimum of dp[start] and maximum of (sum[end - 1] when start is 0, otherwise sum[end - 1] - sum[start - 1]) and dp[end]
- for initialize start := 0, when start < n - i, update (increase start by 1), do −
- return dp[0]
Let us see the following implementation to get better understanding −
Example
#include <bits/stdc++.h>
using namespace std;
typedef long long int lli;
class Solution {
public:
int splitArray(vector<int>& v, int m) {
int n = v.size();
vector <long long int > dp(n);
vector <long long int> sum(n);
sum[0] = v[0];
for(int i =1;i<n;i++)sum[i] =sum[i-1]+v[i];
dp[0] = sum[n-1];
for(int i =1;i<n;i++){
dp[i] = sum[n-1] - sum[i-1];
}
for(int i =1;i<m;i++){
for(int start = 0;start<n-i;start++){
for(int end = start+1;end<=n-i;end++){
dp[start] = min(dp[start],max((start==0?sum[end-1]:sum[end-1]-sum[start-1]),dp[end]));
}
}
}
return dp[0];
}
};
main(){
Solution ob;
vector<int> v = {7,2,4,10,9};
cout << (ob.splitArray(v, 2));
}Input
[7,2,4,10,9] 2
Output
19
Updated on: 01-Jun-2020
283 Views
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