算法分析与设计课件.ppt

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2019-08-02 发布于山东
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算法分析与设计课件.ppt

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Analyzing merge sort P51 Divide-and-conquer approach Recurrence for merge sort Θ(1) if n = 1 T(n) = 2T(n/2) + Θ(n) if n 1. Recursion tree Solve T(n) = 2T(n/2) + cn, where c 0 is constant. Solve T(n) = 2T(n/2) + cn, where c 0 is constant. T(n) P35 举例说明 let us pit a faster computer (computer A) running insertion sort against a slower computer (computer B) running merge sort. Efficiency Practical Complexity Practical Complexity Practical Complexity Practical Complexity Practical Complexity Homework 2.3-1 2.3-5 An Example: Insertion Sort InsertionSort(A, n) {for i = 2 to n { key = A[i] j = i - 1; while (j 0) and (A[j] key) { A[j+1] = A[j] j = j - 1 } A[j+1] = key} } 10 30 40 20 1 2 3 4 i = 4 j = 3 key = 20A[j] = 40 A[j+1] = 20 An Example: Insertion Sort InsertionSort(A, n) {for i = 2 to n { key = A[i] j = i - 1; while (j 0) and (A[j] key) { A[j+1] = A[j] j = j - 1 } A[j+1] = key} } 10 30 40 20 1 2 3 4 i = 4 j = 3 key = 20A[j] = 40 A[j+1] = 20 An Example: Insertion Sort InsertionSort(A, n) {for i = 2 to n { key = A[i] j = i - 1; while (j 0) and (A[j] key) { A[j+1] = A[j] j = j - 1 } A[j+1] = key} } 10 30 40 40 1 2 3 4 i = 4 j = 3 key = 20A[j] = 40 A[j+1] = 40 An Example: Insertion Sort InsertionSort(A, n) {for i = 2 to n { key = A[i] j = i - 1; while (j 0) and (A[j] key) { A[j+1] = A[j] j = j - 1 } A[j+1] = key} } 10 30 40 40 1 2 3 4 i = 4 j = 3 key = 20A[j] = 40 A[j+1] = 40 An Example: Insertion Sort InsertionSort(A, n) {for i = 2 to n { key = A[i] j = i - 1; while (j 0) and (A[j] key) { A[j+1] = A[j] j = j - 1 } A[j+1] = key} } 10 30 40 40 1 2 3 4 i = 4 j = 3 key = 20A[j] = 40 A[j+1] = 40 An Example: Insertion Sort InsertionSort(A, n) {for i = 2 to n { key = A[i] j = i - 1; while (j 0) and (A[j] key) { A[j+1] = A[j] j = j - 1 } A[j+1] = key} } 10 30 40 40 1 2 3 4 i = 4 j = 2 key = 20A[j] = 30