We framed the principle of optimality as every sub-solution of an optimal solution is optimal. But...

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We framed the principle of optimality as "every sub-solution of an optimal solution is optimal". But we can relax this definition into "even optimal solution can be synthesized from optimal sub- solutions". This latter definition is sufficient to derive a recurrence relation that relates a solution to its sub-solutions. Since the recurrence relation is all that matters, the second definition is fine. In this problem, you will see an instance where this second definition is what you need. Let A[1:n] be a real array, k an integer, 1 ≤k≤n. A k-partition of A is any sequence of subarrays A[1: n₁], A[n₁ + 1:n₂], A[n₂ + 1: N3], ..., A[nk-1 +1:n], for some ₁, ₂,...,nk-1, where I≤n₁ < n₂ <...<n. The weight of this k-partition is defined to be Max(Σ=1 A[i], Σān,+1A[i], ..., Σ=n–1+1A[i]). definition of the POO is satisfied, and derive a recurrence relation. as the weight of the minimum-weight r-partition of the array A[1:j].) Prove that the second (Notation hint: Take W We framed the principle of optimality as "every sub-solution of an optimal solution is optimal". But we can relax this definition into "even optimal solution can be synthesized from optimal sub- solutions". This latter definition is sufficient to derive a recurrence relation that relates a solution to its sub-solutions. Since the recurrence relation is all that matters, the second definition is fine. In this problem, you will see an instance where this second definition is what you need. Let A[1:n] be a real array, k an integer, 1 ≤k≤n. A k-partition of A is any sequence of subarrays A[1: n₁], A[n₁ + 1:n₂], A[n₂ + 1: N3], ..., A[nk-1 +1:n], for some ₁, ₂,...,nk-1, where I≤n₁ < n₂ < ...<n. The weight of this k-partition is defined to be Max(Σ=1 A[i], Σān,+1A[i], ..., Σ=n–1+1A[i]). definition of the POO is satisfied, and derive a recurrence relation. as the weight of the minimum-weight r-partition of the array A[1:j].) Prove that the second (Notation hint: Take W We framed the principle of optimality as "every sub-solution of an optimal solution is optimal". But we can relax this definition into "even optimal solution can be synthesized from optimal sub- solutions". This latter definition is sufficient to derive a recurrence relation that relates a solution to its sub-solutions. Since the recurrence relation is all that matters, the second definition is fine. In this problem, you will see an instance where this second definition is what you need. Let A[1:n] be a real array, k an integer, 1 ≤k≤n. A k-partition of A is any sequence of subarrays A[1: n₁], A[n₁ + 1:n₂], A[n₂ + 1: N3], ..., A[nk-1 +1:n], for some ₁, ₂,...,nk-1, where I≤n₁ < n₂ <...<n. The weight of this k-partition is defined to be Max(Σ=1 A[i], Σān,+1A[i], ..., Σ=n–1+1A[i]). definition of the POO is satisfied, and derive a recurrence relation. as the weight of the minimum-weight r-partition of the array A[1:j].) Prove that the second (Notation hint: Take W We framed the principle of optimality as "every sub-solution of an optimal solution is optimal". But we can relax this definition into "even optimal solution can be synthesized from optimal sub- solutions". This latter definition is sufficient to derive a recurrence relation that relates a solution to its sub-solutions. Since the recurrence relation is all that matters, the second definition is fine. In this problem, you will see an instance where this second definition is what you need. Let A[1:n] be a real array, k an integer, 1 ≤k≤n. A k-partition of A is any sequence of subarrays A[1: n₁], A[n₁ + 1:n₂], A[n₂ + 1: N3], ..., A[nk-1 +1:n], for some ₁, ₂,...,nk-1, where I≤n₁ < n₂ < ...<n. The weight of this k-partition is defined to be Max(Σ=1 A[i], Σān,+1A[i], ..., Σ=n–1+1A[i]). definition of the POO is satisfied, and derive a recurrence relation. as the weight of the minimum-weight r-partition of the array A[1:j].) Prove that the second (Notation hint: Take W