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Complexidade de Algoritmos Recursivos

Complexidade de Algoritmos Recursivos. Alex F. V. Machado. Recursividade. Implementação recursiva int fatorial (int N) ‏ { if (N<= 1) ‏ return(1); else return( N * fatorial(N-1)); }. Recursividade. X= fatorial (4) ‏ return( 4* fatorial(3) ) ‏

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Complexidade de Algoritmos Recursivos

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  1. Complexidade de Algoritmos Recursivos Alex F. V. Machado

  2. Recursividade • Implementação recursiva int fatorial (int N)‏ { if (N<= 1)‏ return(1); else return( N * fatorial(N-1)); }

  3. Recursividade • X= fatorial (4)‏ • return( 4* fatorial(3) )‏ • return( 3* fatorial(2) )‏ • return( 2* fatorial(1) )‏ • return( 1 )‏

  4. Análise de Recursividade • T(n)‏ • tempo de processar o algoritmo para entrada n • número de passos ou operações dominantes • Fatorial • T(n) = 1, se n = 0 • = T(n-1) +1, se n > 0 • mas quanto é T(n-1)?

  5. T(n) - Fatorial • = (T(n-1)) + 1 • = (T(n-2) + 1) + 1 • = T(n-2) + 2 • = (T(n-3) + 1) + 2 • = T(n-3) + 3 • ..... • forma geral, T(n) = T(n-k) + k, 1  k  n • fazendo n = k, reduzimos a T(n) = n

  6. void merge(int vec[], int vecSize) { int mid; int i, j, k; int* tmp; mid = vecSize / 2; i = 0; j = mid; k = 0; while (i < mid && j < vecSize) { if (vec[i] > vec[j]) { tmp[k] = vec[i]; ++i; } else { tmp[k] = vec[j]; ++j; } ++k; } if (i == mid) { while (j < vecSize) { tmp[k] = vec[j]; ++j; ++k; } } else { while (i < mid) { tmp[k] = vec[i]; ++i; ++k; } } for (i = 0; i < vecSize; ++i) { vec[i] = tmp[i]; } } void mergeSort(int vec[], int vecSize) { int mid; if (vecSize > 1) { mid = vecSize / 2; mergeSort(vec, mid); mergeSort(vec + mid, vecSize - mid); merge(vec, vecSize); } }

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