Maximize weighted sum with disjoint adjacent swaps
Problem Description
You are given an integer array arr of length n (0-indexed).
Define the weighted sum S as:
S = Σ_{i=0..n-1} arr[i] * (i + 1).
You may perform any number of adjacent swaps of the form swap(arr[i], arr[i+1]). A critical constraint is that each array position can be involved in at most one swap. This implies that any chosen swaps must be non-overlapping; if arr[i] and arr[i+1] are swapped, then arr[i-1] cannot be involved in a swap with arr[i], nor arr[i+1] with arr[i+2].
Your task is to return the maximum possible value of S after performing such swaps.
Constraints
1 ≤ n ≤ 2e5|arr[i]|fits within a 32-bit signed integer.- The final weighted sum
Smay require a 64-bit integer type.
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Core dilemma
Optimally deciding whether to perform an adjacent swap at each possible position, given the strict non-overlapping constraint, to maximize a weighted sum. This is a classic dynamic programming problem where local choices impact future options.
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Maximize weighted sum with disjoint adjacent swaps
Problem Description
You are given an integer array arr of length n (0-indexed).
Define the weighted sum S as:
S = Σ_{i=0..n-1} arr[i] * (i + 1).
You may perform any number of adjacent swaps of the form swap(arr[i], arr[i+1]). A critical constraint is that each array position can be involved in at most one swap. This implies that any chosen swaps must be non-overlapping; if arr[i] and arr[i+1] are swapped, then arr[i-1] cannot be involved in a swap with arr[i], nor arr[i+1] with arr[i+2].
Your task is to return the maximum possible value of S after performing such swaps.
Constraints
1 ≤ n ≤ 2e5|arr[i]|fits within a 32-bit signed integer.- The final weighted sum
Smay require a 64-bit integer type.