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krahets
@ -1466,7 +1466,7 @@ Quadratic order means the number of operations grows quadratically with the inpu
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def quadratic(n: int) -> int:
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def quadratic(n: int) -> int:
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"""平方阶"""
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"""平方阶"""
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count = 0
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count = 0
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# 循环次数与数组长度成平方关系
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# 循环次数与数据大小 n 成平方关系
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for i in range(n):
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for i in range(n):
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for j in range(n):
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for j in range(n):
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count += 1
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count += 1
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@ -1479,7 +1479,7 @@ Quadratic order means the number of operations grows quadratically with the inpu
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/* 平方阶 */
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/* 平方阶 */
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int quadratic(int n) {
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int quadratic(int n) {
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int count = 0;
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int count = 0;
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// 循环次数与数组长度成平方关系
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// 循环次数与数据大小 n 成平方关系
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for (int i = 0; i < n; i++) {
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < n; j++) {
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for (int j = 0; j < n; j++) {
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count++;
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count++;
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@ -1495,7 +1495,7 @@ Quadratic order means the number of operations grows quadratically with the inpu
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/* 平方阶 */
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/* 平方阶 */
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int quadratic(int n) {
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int quadratic(int n) {
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int count = 0;
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int count = 0;
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// 循环次数与数组长度成平方关系
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// 循环次数与数据大小 n 成平方关系
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for (int i = 0; i < n; i++) {
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < n; j++) {
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for (int j = 0; j < n; j++) {
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count++;
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count++;
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@ -1511,7 +1511,7 @@ Quadratic order means the number of operations grows quadratically with the inpu
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/* 平方阶 */
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/* 平方阶 */
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int Quadratic(int n) {
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int Quadratic(int n) {
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int count = 0;
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int count = 0;
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// 循环次数与数组长度成平方关系
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// 循环次数与数据大小 n 成平方关系
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for (int i = 0; i < n; i++) {
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < n; j++) {
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for (int j = 0; j < n; j++) {
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count++;
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count++;
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@ -1527,7 +1527,7 @@ Quadratic order means the number of operations grows quadratically with the inpu
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/* 平方阶 */
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/* 平方阶 */
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func quadratic(n int) int {
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func quadratic(n int) int {
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count := 0
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count := 0
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// 循环次数与数组长度成平方关系
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// 循环次数与数据大小 n 成平方关系
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for i := 0; i < n; i++ {
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for i := 0; i < n; i++ {
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for j := 0; j < n; j++ {
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for j := 0; j < n; j++ {
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count++
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count++
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@ -1543,7 +1543,7 @@ Quadratic order means the number of operations grows quadratically with the inpu
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/* 平方阶 */
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/* 平方阶 */
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func quadratic(n: Int) -> Int {
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func quadratic(n: Int) -> Int {
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var count = 0
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var count = 0
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// 循环次数与数组长度成平方关系
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// 循环次数与数据大小 n 成平方关系
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for _ in 0 ..< n {
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for _ in 0 ..< n {
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for _ in 0 ..< n {
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for _ in 0 ..< n {
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count += 1
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count += 1
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@ -1559,7 +1559,7 @@ Quadratic order means the number of operations grows quadratically with the inpu
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/* 平方阶 */
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/* 平方阶 */
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function quadratic(n) {
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function quadratic(n) {
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let count = 0;
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let count = 0;
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// 循环次数与数组长度成平方关系
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// 循环次数与数据大小 n 成平方关系
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for (let i = 0; i < n; i++) {
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for (let i = 0; i < n; i++) {
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for (let j = 0; j < n; j++) {
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for (let j = 0; j < n; j++) {
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count++;
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count++;
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@ -1575,7 +1575,7 @@ Quadratic order means the number of operations grows quadratically with the inpu
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/* 平方阶 */
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/* 平方阶 */
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function quadratic(n: number): number {
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function quadratic(n: number): number {
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let count = 0;
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let count = 0;
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// 循环次数与数组长度成平方关系
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// 循环次数与数据大小 n 成平方关系
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for (let i = 0; i < n; i++) {
|
for (let i = 0; i < n; i++) {
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for (let j = 0; j < n; j++) {
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for (let j = 0; j < n; j++) {
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count++;
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count++;
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@ -1591,7 +1591,7 @@ Quadratic order means the number of operations grows quadratically with the inpu
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/* 平方阶 */
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/* 平方阶 */
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int quadratic(int n) {
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int quadratic(int n) {
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int count = 0;
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int count = 0;
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// 循环次数与数组长度成平方关系
|
// 循环次数与数据大小 n 成平方关系
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for (int i = 0; i < n; i++) {
|
for (int i = 0; i < n; i++) {
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for (int j = 0; j < n; j++) {
|
for (int j = 0; j < n; j++) {
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count++;
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count++;
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@ -1607,7 +1607,7 @@ Quadratic order means the number of operations grows quadratically with the inpu
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/* 平方阶 */
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/* 平方阶 */
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fn quadratic(n: i32) -> i32 {
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fn quadratic(n: i32) -> i32 {
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let mut count = 0;
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let mut count = 0;
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// 循环次数与数组长度成平方关系
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// 循环次数与数据大小 n 成平方关系
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for _ in 0..n {
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for _ in 0..n {
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for _ in 0..n {
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for _ in 0..n {
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count += 1;
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count += 1;
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@ -1623,7 +1623,7 @@ Quadratic order means the number of operations grows quadratically with the inpu
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/* 平方阶 */
|
/* 平方阶 */
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int quadratic(int n) {
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int quadratic(int n) {
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int count = 0;
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int count = 0;
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// 循环次数与数组长度成平方关系
|
// 循环次数与数据大小 n 成平方关系
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for (int i = 0; i < n; i++) {
|
for (int i = 0; i < n; i++) {
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for (int j = 0; j < n; j++) {
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for (int j = 0; j < n; j++) {
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count++;
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count++;
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@ -1640,7 +1640,7 @@ Quadratic order means the number of operations grows quadratically with the inpu
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fn quadratic(n: i32) i32 {
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fn quadratic(n: i32) i32 {
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var count: i32 = 0;
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var count: i32 = 0;
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var i: i32 = 0;
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var i: i32 = 0;
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// 循环次数与数组长度成平方关系
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// 循环次数与数据大小 n 成平方关系
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while (i < n) : (i += 1) {
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while (i < n) : (i += 1) {
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var j: i32 = 0;
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var j: i32 = 0;
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while (j < n) : (j += 1) {
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while (j < n) : (j += 1) {
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@ -1653,8 +1653,8 @@ Quadratic order means the number of operations grows quadratically with the inpu
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|
|
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??? pythontutor "Code Visualization"
|
??? pythontutor "Code Visualization"
|
||||||
|
|
||||||
<div style="height: 477px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20quadratic%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%B9%B3%E6%96%B9%E9%98%B6%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%E5%BE%AA%E7%8E%AF%E6%AC%A1%E6%95%B0%E4%B8%8E%E6%95%B0%E7%BB%84%E9%95%BF%E5%BA%A6%E6%88%90%E5%B9%B3%E6%96%B9%E5%85%B3%E7%B3%BB%0A%20%20%20%20for%20i%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E8%BE%93%E5%85%A5%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%3D%22,%20n%29%0A%0A%20%20%20%20count%20%3D%20quadratic%28n%29%0A%20%20%20%20print%28%22%E5%B9%B3%E6%96%B9%E9%98%B6%E7%9A%84%E6%93%8D%E4%BD%9C%E6%95%B0%E9%87%8F%20%3D%22,%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
|
<div style="height: 477px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20quadratic%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%B9%B3%E6%96%B9%E9%98%B6%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%E5%BE%AA%E7%8E%AF%E6%AC%A1%E6%95%B0%E4%B8%8E%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%E6%88%90%E5%B9%B3%E6%96%B9%E5%85%B3%E7%B3%BB%0A%20%20%20%20for%20i%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E8%BE%93%E5%85%A5%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%3D%22,%20n%29%0A%0A%20%20%20%20count%20%3D%20quadratic%28n%29%0A%20%20%20%20print%28%22%E5%B9%B3%E6%96%B9%E9%98%B6%E7%9A%84%E6%93%8D%E4%BD%9C%E6%95%B0%E9%87%8F%20%3D%22,%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
|
||||||
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20quadratic%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%B9%B3%E6%96%B9%E9%98%B6%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%E5%BE%AA%E7%8E%AF%E6%AC%A1%E6%95%B0%E4%B8%8E%E6%95%B0%E7%BB%84%E9%95%BF%E5%BA%A6%E6%88%90%E5%B9%B3%E6%96%B9%E5%85%B3%E7%B3%BB%0A%20%20%20%20for%20i%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E8%BE%93%E5%85%A5%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%3D%22,%20n%29%0A%0A%20%20%20%20count%20%3D%20quadratic%28n%29%0A%20%20%20%20print%28%22%E5%B9%B3%E6%96%B9%E9%98%B6%E7%9A%84%E6%93%8D%E4%BD%9C%E6%95%B0%E9%87%8F%20%3D%22,%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Full Screen ></a></div>
|
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20quadratic%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%B9%B3%E6%96%B9%E9%98%B6%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%E5%BE%AA%E7%8E%AF%E6%AC%A1%E6%95%B0%E4%B8%8E%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%E6%88%90%E5%B9%B3%E6%96%B9%E5%85%B3%E7%B3%BB%0A%20%20%20%20for%20i%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E8%BE%93%E5%85%A5%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%3D%22,%20n%29%0A%0A%20%20%20%20count%20%3D%20quadratic%28n%29%0A%20%20%20%20print%28%22%E5%B9%B3%E6%96%B9%E9%98%B6%E7%9A%84%E6%93%8D%E4%BD%9C%E6%95%B0%E9%87%8F%20%3D%22,%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Full Screen ></a></div>
|
||||||
|
|
||||||
The following image compares constant order, linear order, and quadratic order time complexities.
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The following image compares constant order, linear order, and quadratic order time complexities.
|
||||||
|
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||||||
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File diff suppressed because one or more lines are too long
@ -4,74 +4,134 @@ comments: true
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# 16.3 术语表
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# 16.3 术语表
|
||||||
|
|
||||||
表 16-1 列出了书中出现的重要术语。建议读者同时记住它们的中英文叫法，以便阅读英文文献。
|
表 16-1 列出了书中出现的重要术语，值得注意以下几点。
|
||||||
|
|
||||||
|
- 部分名词在简体中文和繁体中文下的叫法不同。
|
||||||
|
- 建议记住名词的英文叫法，以便阅读英文文献。
|
||||||
|
|
||||||
<p align="center"> 表 16-1 数据结构与算法的重要名词 </p>
|
<p align="center"> 表 16-1 数据结构与算法的重要名词 </p>
|
||||||
|
|
||||||
<div class="center-table" markdown>
|
<div class="center-table" markdown>
|
||||||
|
|
||||||
| 中文 | English | 中文 | English |
|
| English | 简体中文 | 繁体中文 |
|
||||||
| -------------- | ------------------------------ | -------------- | --------------------------- |
|
| ------------------------------ | -------------- | -------------- |
|
||||||
| 算法 | algorithm | AVL 树 | AVL tree |
|
| algorithm | 算法 | 算法 |
|
||||||
| 数据结构 | data structure | 红黑树 | red-black tree |
|
| data structure | 数据结构 | 資料結構 |
|
||||||
| 渐近复杂度分析 | asymptotic complexity analysis | 层序遍历 | level-order traversal |
|
| asymptotic complexity analysis | 渐近复杂度分析 | 漸近複雜度分析 |
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||||||
| 时间复杂度 | time complexity | 广度优先遍历 | breadth-first traversal |
|
| time complexity | 时间复杂度 | 時間複雜度 |
|
||||||
| 空间复杂度 | space complexity | 深度优先遍历 | depth-first traversal |
|
| space complexity | 空间复杂度 | 空間複雜度 |
|
||||||
| 迭代 | iteration | 二叉搜索树 | binary search tree |
|
| iteration | 迭代 | 迭代 |
|
||||||
| 递归 | recursion | 平衡二叉搜索树 | balanced binary search tree |
|
| recursion | 递归 | 遞迴 |
|
||||||
| 尾递归 | tail recursion | 平衡因子 | balance factor |
|
| tail recursion | 尾递归 | 尾遞迴 |
|
||||||
| 递归树 | recursion tree | 堆 | heap |
|
| recursion tree | 递归树 | 遞迴樹 |
|
||||||
| 大 $O$ 记号 | big-$O$ notation | 大顶堆 | max heap |
|
| big-$O$ notation | 大 $O$ 记号 | 大 $O$ 記號 |
|
||||||
| 渐近上界 | asymptotic upper bound | 小顶堆 | min heap |
|
| asymptotic upper bound | 渐近上界 | 漸近上界 |
|
||||||
| 原码 | sign-magnitude | 优先队列 | priority queue |
|
| sign-magnitude | 原码 | 原碼 |
|
||||||
| 反码 | 1’s complement | 堆化 | heapify |
|
| 1’s complement | 反码 | 反碼 |
|
||||||
| 补码 | 2’s complement | Top-$k$ 问题 | Top-$k$ problem |
|
| 2’s complement | 补码 | 補碼 |
|
||||||
| 数组 | array | 图 | graph |
|
| array | 数组 | 陣列 |
|
||||||
| 索引 | index | 顶点 | vertex |
|
| index | 索引 | 索引 |
|
||||||
| 链表 | linked list | 无向图 | undirected graph |
|
| linked list | 链表 | 連結串列 |
|
||||||
| 链表节点 | linked list node, list node | 有向图 | directed graph |
|
| linked list node, list node | 链表节点 | 連結串列節點 |
|
||||||
| 头节点 | head node | 连通图 | connected graph |
|
| head node | 头节点 | 頭節點 |
|
||||||
| 尾节点 | tail node | 非连通图 | disconnected graph |
|
| tail node | 尾节点 | 尾節點 |
|
||||||
| 列表 | list | 有权图 | weighted graph |
|
| list | 列表 | 列表 |
|
||||||
| 动态数组 | dynamic array | 邻接 | adjacency |
|
| dynamic array | 动态数组 | 動態陣列 |
|
||||||
| 硬盘 | hard disk | 路径 | path |
|
| hard disk | 硬盘 | 硬碟 |
|
||||||
| 内存 | random-access memory (RAM) | 入度 | in-degree |
|
| random-access memory (RAM) | 内存 | 內存 |
|
||||||
| 缓存 | cache memory | 出度 | out-degree |
|
| cache memory | 缓存 | 快取 |
|
||||||
| 缓存未命中 | cache miss | 邻接矩阵 | adjacency matrix |
|
| cache miss | 缓存未命中 | 快取未命中 |
|
||||||
| 缓存命中率 | cache hit rate | 邻接表 | adjacency list |
|
| cache hit rate | 缓存命中率 | 快取命中率 |
|
||||||
| 栈 | stack | 广度优先搜索 | breadth-first search |
|
| stack | 栈 | 堆疊 |
|
||||||
| 栈顶 | top of the stack | 深度优先搜索 | depth-first search |
|
| top of the stack | 栈顶 | 堆疊頂 |
|
||||||
| 栈底 | bottom of the stack | 二分查找 | binary search |
|
| bottom of the stack | 栈底 | 堆疊底 |
|
||||||
| 队列 | queue | 搜索算法 | searching algorithm |
|
| queue | 队列 | 佇列 |
|
||||||
| 双向队列 | double-ended queue | 排序算法 | sorting algorithm |
|
| double-ended queue | 双向队列 | 雙向佇列 |
|
||||||
| 队首 | front of the queue | 选择排序 | selection sort |
|
| front of the queue | 队首 | 佇列首 |
|
||||||
| 队尾 | rear of the queue | 冒泡排序 | bubble sort |
|
| rear of the queue | 队尾 | 佇列尾 |
|
||||||
| 哈希表 | hash table | 插入排序 | insertion sort |
|
| hash table | 哈希表 | 雜湊表 |
|
||||||
| 桶 | bucket | 快速排序 | quick sort |
|
| bucket | 桶 | 桶 |
|
||||||
| 哈希函数 | hash function | 归并排序 | merge sort |
|
| hash function | 哈希函数 | 雜湊函式 |
|
||||||
| 哈希冲突 | hash collision | 堆排序 | heap sort |
|
| hash collision | 哈希冲突 | 雜湊衝突 |
|
||||||
| 负载因子 | load factor | 桶排序 | bucket sort |
|
| load factor | 负载因子 | 負載因子 |
|
||||||
| 链式地址 | separate chaining | 计数排序 | counting sort |
|
| separate chaining | 链式地址 | 鏈結位址 |
|
||||||
| 开放寻址 | open addressing | 基数排序 | radix sort |
|
| open addressing | 开放寻址 | 開放定址 |
|
||||||
| 线性探测 | linear probing | 分治 | divide and conquer |
|
| linear probing | 线性探测 | 線性探查 |
|
||||||
| 懒删除 | lazy deletion | 汉诺塔问题 | hanota problem |
|
| lazy deletion | 懒删除 | 懶刪除 |
|
||||||
| 二叉树 | binary tree | 回溯算法 | backtracking algorithm |
|
| binary tree | 二叉树 | 二元樹 |
|
||||||
| 树节点 | tree node | 约束 | constraint |
|
| tree node | 树节点 | 樹節點 |
|
||||||
| 左子节点 | left-child node | 解 | solution |
|
| left-child node | 左子节点 | 左子節點 |
|
||||||
| 右子节点 | right-child node | 状态 | state |
|
| right-child node | 右子节点 | 右子節點 |
|
||||||
| 父节点 | parent node | 剪枝 | pruning |
|
| parent node | 父节点 | 父節點 |
|
||||||
| 左子树 | left subtree | 全排列问题 | permutations problem |
|
| left subtree | 左子树 | 左子樹 |
|
||||||
| 右子树 | right subtree | 子集和问题 | subset-sum problem |
|
| right subtree | 右子树 | 右子樹 |
|
||||||
| 根节点 | root node | n 皇后问题 | n-queens problem |
|
| root node | 根节点 | 根節點 |
|
||||||
| 叶节点 | leaf node | 动态规划 | dynamic programming |
|
| leaf node | 叶节点 | 葉節點 |
|
||||||
| 边 | edge | 初始状态 | initial state |
|
| edge | 边 | 邊 |
|
||||||
| 层 | level | 状态转移方程 | state-trasition equation |
|
| level | 层 | 層 |
|
||||||
| 度 | degree | 背包问题 | knapsack problem |
|
| degree | 度 | 度 |
|
||||||
| 高度 | height | 编辑距离问题 | edit distance problem |
|
| height | 高度 | 高度 |
|
||||||
| 深度 | depth | 贪心算法 | greedy algorithm |
|
| depth | 深度 | 深度 |
|
||||||
| 完美二叉树 | perfect binary tree | | |
|
| perfect binary tree | 完美二叉树 | 完美二元樹 |
|
||||||
| 完全二叉树 | complete binary tree | | |
|
| complete binary tree | 完全二叉树 | 完全二元樹 |
|
||||||
| 完满二叉树 | full binary tree | | |
|
| full binary tree | 完满二叉树 | 完滿二元樹 |
|
||||||
| 平衡二叉树 | balanced binary tree | | |
|
| balanced binary tree | 平衡二叉树 | 平衡二元樹 |
|
||||||
|
| AVL tree | AVL 树 | AVL 樹 |
|
||||||
|
| red-black tree | 红黑树 | 紅黑樹 |
|
||||||
|
| level-order traversal | 层序遍历 | 層序走訪 |
|
||||||
|
| breadth-first traversal | 广度优先遍历 | 廣度優先走訪 |
|
||||||
|
| depth-first traversal | 深度优先遍历 | 深度優先走訪 |
|
||||||
|
| binary search tree | 二叉搜索树 | 二元搜尋樹 |
|
||||||
|
| balanced binary search tree | 平衡二叉搜索树 | 平衡二元搜尋樹 |
|
||||||
|
| balance factor | 平衡因子 | 平衡因子 |
|
||||||
|
| heap | 堆 | 堆 |
|
||||||
|
| max heap | 大顶堆 | 大頂堆 |
|
||||||
|
| min heap | 小顶堆 | 小頂堆 |
|
||||||
|
| priority queue | 优先队列 | 優先佇列 |
|
||||||
|
| heapify | 堆化 | 堆化 |
|
||||||
|
| top-$k$ problem | Top-$k$ 问题 | Top-$k$ 問題 |
|
||||||
|
| graph | 图 | 圖 |
|
||||||
|
| vertex | 顶点 | 頂點 |
|
||||||
|
| undirected graph | 无向图 | 無向圖 |
|
||||||
|
| directed graph | 有向图 | 有向圖 |
|
||||||
|
| connected graph | 连通图 | 連通圖 |
|
||||||
|
| disconnected graph | 非连通图 | 非連通圖 |
|
||||||
|
| weighted graph | 有权图 | 有權圖 |
|
||||||
|
| adjacency | 邻接 | 鄰接 |
|
||||||
|
| path | 路径 | 路徑 |
|
||||||
|
| in-degree | 入度 | 入度 |
|
||||||
|
| out-degree | 出度 | 出度 |
|
||||||
|
| adjacency matrix | 邻接矩阵 | 鄰接矩陣 |
|
||||||
|
| adjacency list | 邻接表 | 鄰接表 |
|
||||||
|
| breadth-first search | 广度优先搜索 | 廣度優先搜尋 |
|
||||||
|
| depth-first search | 深度优先搜索 | 深度優先搜尋 |
|
||||||
|
| binary search | 二分查找 | 二分查找 |
|
||||||
|
| searching algorithm | 搜索算法 | 搜尋演算法 |
|
||||||
|
| sorting algorithm | 排序算法 | 排序演算法 |
|
||||||
|
| selection sort | 选择排序 | 選擇排序 |
|
||||||
|
| bubble sort | 冒泡排序 | 泡沫排序 |
|
||||||
|
| insertion sort | 插入排序 | 插入排序 |
|
||||||
|
| quick sort | 快速排序 | 快速排序 |
|
||||||
|
| merge sort | 归并排序 | 合併排序 |
|
||||||
|
| heap sort | 堆排序 | 堆排序 |
|
||||||
|
| bucket sort | 桶排序 | 桶排序 |
|
||||||
|
| counting sort | 计数排序 | 計數排序 |
|
||||||
|
| radix sort | 基数排序 | 基數排序 |
|
||||||
|
| divide and conquer | 分治 | 分治 |
|
||||||
|
| hanota problem | 汉诺塔问题 | 漢諾塔問題 |
|
||||||
|
| backtracking algorithm | 回溯算法 | 回溯演算法 |
|
||||||
|
| constraint | 约束 | 約束 |
|
||||||
|
| solution | 解 | 解 |
|
||||||
|
| state | 状态 | 狀態 |
|
||||||
|
| pruning | 剪枝 | 剪枝 |
|
||||||
|
| permutations problem | 全排列问题 | 全排列問題 |
|
||||||
|
| subset-sum problem | 子集和问题 | 子集合問題 |
|
||||||
|
| $n$-queens problem | $n$ 皇后问题 | $n$ 皇后問題 |
|
||||||
|
| dynamic programming | 动态规划 | 動態規劃 |
|
||||||
|
| initial state | 初始状态 | 初始狀態 |
|
||||||
|
| state-trasition equation | 状态转移方程 | 狀態轉移方程 |
|
||||||
|
| knapsack problem | 背包问题 | 背包問題 |
|
||||||
|
| edit distance problem | 编辑距离问题 | 編輯距離問題 |
|
||||||
|
| greedy algorithm | 贪心算法 | 貪心演算法 |
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|||||||
@ -1470,7 +1470,7 @@ $$
|
|||||||
def quadratic(n: int) -> int:
|
def quadratic(n: int) -> int:
|
||||||
"""平方阶"""
|
"""平方阶"""
|
||||||
count = 0
|
count = 0
|
||||||
# 循环次数与数组长度成平方关系
|
# 循环次数与数据大小 n 成平方关系
|
||||||
for i in range(n):
|
for i in range(n):
|
||||||
for j in range(n):
|
for j in range(n):
|
||||||
count += 1
|
count += 1
|
||||||
@ -1483,7 +1483,7 @@ $$
|
|||||||
/* 平方阶 */
|
/* 平方阶 */
|
||||||
int quadratic(int n) {
|
int quadratic(int n) {
|
||||||
int count = 0;
|
int count = 0;
|
||||||
// 循环次数与数组长度成平方关系
|
// 循环次数与数据大小 n 成平方关系
|
||||||
for (int i = 0; i < n; i++) {
|
for (int i = 0; i < n; i++) {
|
||||||
for (int j = 0; j < n; j++) {
|
for (int j = 0; j < n; j++) {
|
||||||
count++;
|
count++;
|
||||||
@ -1499,7 +1499,7 @@ $$
|
|||||||
/* 平方阶 */
|
/* 平方阶 */
|
||||||
int quadratic(int n) {
|
int quadratic(int n) {
|
||||||
int count = 0;
|
int count = 0;
|
||||||
// 循环次数与数组长度成平方关系
|
// 循环次数与数据大小 n 成平方关系
|
||||||
for (int i = 0; i < n; i++) {
|
for (int i = 0; i < n; i++) {
|
||||||
for (int j = 0; j < n; j++) {
|
for (int j = 0; j < n; j++) {
|
||||||
count++;
|
count++;
|
||||||
@ -1515,7 +1515,7 @@ $$
|
|||||||
/* 平方阶 */
|
/* 平方阶 */
|
||||||
int Quadratic(int n) {
|
int Quadratic(int n) {
|
||||||
int count = 0;
|
int count = 0;
|
||||||
// 循环次数与数组长度成平方关系
|
// 循环次数与数据大小 n 成平方关系
|
||||||
for (int i = 0; i < n; i++) {
|
for (int i = 0; i < n; i++) {
|
||||||
for (int j = 0; j < n; j++) {
|
for (int j = 0; j < n; j++) {
|
||||||
count++;
|
count++;
|
||||||
@ -1531,7 +1531,7 @@ $$
|
|||||||
/* 平方阶 */
|
/* 平方阶 */
|
||||||
func quadratic(n int) int {
|
func quadratic(n int) int {
|
||||||
count := 0
|
count := 0
|
||||||
// 循环次数与数组长度成平方关系
|
// 循环次数与数据大小 n 成平方关系
|
||||||
for i := 0; i < n; i++ {
|
for i := 0; i < n; i++ {
|
||||||
for j := 0; j < n; j++ {
|
for j := 0; j < n; j++ {
|
||||||
count++
|
count++
|
||||||
@ -1547,7 +1547,7 @@ $$
|
|||||||
/* 平方阶 */
|
/* 平方阶 */
|
||||||
func quadratic(n: Int) -> Int {
|
func quadratic(n: Int) -> Int {
|
||||||
var count = 0
|
var count = 0
|
||||||
// 循环次数与数组长度成平方关系
|
// 循环次数与数据大小 n 成平方关系
|
||||||
for _ in 0 ..< n {
|
for _ in 0 ..< n {
|
||||||
for _ in 0 ..< n {
|
for _ in 0 ..< n {
|
||||||
count += 1
|
count += 1
|
||||||
@ -1563,7 +1563,7 @@ $$
|
|||||||
/* 平方阶 */
|
/* 平方阶 */
|
||||||
function quadratic(n) {
|
function quadratic(n) {
|
||||||
let count = 0;
|
let count = 0;
|
||||||
// 循环次数与数组长度成平方关系
|
// 循环次数与数据大小 n 成平方关系
|
||||||
for (let i = 0; i < n; i++) {
|
for (let i = 0; i < n; i++) {
|
||||||
for (let j = 0; j < n; j++) {
|
for (let j = 0; j < n; j++) {
|
||||||
count++;
|
count++;
|
||||||
@ -1579,7 +1579,7 @@ $$
|
|||||||
/* 平方阶 */
|
/* 平方阶 */
|
||||||
function quadratic(n: number): number {
|
function quadratic(n: number): number {
|
||||||
let count = 0;
|
let count = 0;
|
||||||
// 循环次数与数组长度成平方关系
|
// 循环次数与数据大小 n 成平方关系
|
||||||
for (let i = 0; i < n; i++) {
|
for (let i = 0; i < n; i++) {
|
||||||
for (let j = 0; j < n; j++) {
|
for (let j = 0; j < n; j++) {
|
||||||
count++;
|
count++;
|
||||||
@ -1595,7 +1595,7 @@ $$
|
|||||||
/* 平方阶 */
|
/* 平方阶 */
|
||||||
int quadratic(int n) {
|
int quadratic(int n) {
|
||||||
int count = 0;
|
int count = 0;
|
||||||
// 循环次数与数组长度成平方关系
|
// 循环次数与数据大小 n 成平方关系
|
||||||
for (int i = 0; i < n; i++) {
|
for (int i = 0; i < n; i++) {
|
||||||
for (int j = 0; j < n; j++) {
|
for (int j = 0; j < n; j++) {
|
||||||
count++;
|
count++;
|
||||||
@ -1611,7 +1611,7 @@ $$
|
|||||||
/* 平方阶 */
|
/* 平方阶 */
|
||||||
fn quadratic(n: i32) -> i32 {
|
fn quadratic(n: i32) -> i32 {
|
||||||
let mut count = 0;
|
let mut count = 0;
|
||||||
// 循环次数与数组长度成平方关系
|
// 循环次数与数据大小 n 成平方关系
|
||||||
for _ in 0..n {
|
for _ in 0..n {
|
||||||
for _ in 0..n {
|
for _ in 0..n {
|
||||||
count += 1;
|
count += 1;
|
||||||
@ -1627,7 +1627,7 @@ $$
|
|||||||
/* 平方阶 */
|
/* 平方阶 */
|
||||||
int quadratic(int n) {
|
int quadratic(int n) {
|
||||||
int count = 0;
|
int count = 0;
|
||||||
// 循环次数与数组长度成平方关系
|
// 循环次数与数据大小 n 成平方关系
|
||||||
for (int i = 0; i < n; i++) {
|
for (int i = 0; i < n; i++) {
|
||||||
for (int j = 0; j < n; j++) {
|
for (int j = 0; j < n; j++) {
|
||||||
count++;
|
count++;
|
||||||
@ -1644,7 +1644,7 @@ $$
|
|||||||
fn quadratic(n: i32) i32 {
|
fn quadratic(n: i32) i32 {
|
||||||
var count: i32 = 0;
|
var count: i32 = 0;
|
||||||
var i: i32 = 0;
|
var i: i32 = 0;
|
||||||
// 循环次数与数组长度成平方关系
|
// 循环次数与数据大小 n 成平方关系
|
||||||
while (i < n) : (i += 1) {
|
while (i < n) : (i += 1) {
|
||||||
var j: i32 = 0;
|
var j: i32 = 0;
|
||||||
while (j < n) : (j += 1) {
|
while (j < n) : (j += 1) {
|
||||||
@ -1657,8 +1657,8 @@ $$
|
|||||||
|
|
||||||
??? pythontutor "可视化运行"
|
??? pythontutor "可视化运行"
|
||||||
|
|
||||||
<div style="height: 477px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20quadratic%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%B9%B3%E6%96%B9%E9%98%B6%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%E5%BE%AA%E7%8E%AF%E6%AC%A1%E6%95%B0%E4%B8%8E%E6%95%B0%E7%BB%84%E9%95%BF%E5%BA%A6%E6%88%90%E5%B9%B3%E6%96%B9%E5%85%B3%E7%B3%BB%0A%20%20%20%20for%20i%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E8%BE%93%E5%85%A5%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%3D%22,%20n%29%0A%0A%20%20%20%20count%20%3D%20quadratic%28n%29%0A%20%20%20%20print%28%22%E5%B9%B3%E6%96%B9%E9%98%B6%E7%9A%84%E6%93%8D%E4%BD%9C%E6%95%B0%E9%87%8F%20%3D%22,%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
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<div style="height: 477px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20quadratic%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%B9%B3%E6%96%B9%E9%98%B6%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%E5%BE%AA%E7%8E%AF%E6%AC%A1%E6%95%B0%E4%B8%8E%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%E6%88%90%E5%B9%B3%E6%96%B9%E5%85%B3%E7%B3%BB%0A%20%20%20%20for%20i%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E8%BE%93%E5%85%A5%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%3D%22,%20n%29%0A%0A%20%20%20%20count%20%3D%20quadratic%28n%29%0A%20%20%20%20print%28%22%E5%B9%B3%E6%96%B9%E9%98%B6%E7%9A%84%E6%93%8D%E4%BD%9C%E6%95%B0%E9%87%8F%20%3D%22,%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
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<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20quadratic%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%B9%B3%E6%96%B9%E9%98%B6%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%E5%BE%AA%E7%8E%AF%E6%AC%A1%E6%95%B0%E4%B8%8E%E6%95%B0%E7%BB%84%E9%95%BF%E5%BA%A6%E6%88%90%E5%B9%B3%E6%96%B9%E5%85%B3%E7%B3%BB%0A%20%20%20%20for%20i%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E8%BE%93%E5%85%A5%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%3D%22,%20n%29%0A%0A%20%20%20%20count%20%3D%20quadratic%28n%29%0A%20%20%20%20print%28%22%E5%B9%B3%E6%96%B9%E9%98%B6%E7%9A%84%E6%93%8D%E4%BD%9C%E6%95%B0%E9%87%8F%20%3D%22,%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全屏观看 ></a></div>
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<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20quadratic%28n%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%B9%B3%E6%96%B9%E9%98%B6%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%E5%BE%AA%E7%8E%AF%E6%AC%A1%E6%95%B0%E4%B8%8E%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%E6%88%90%E5%B9%B3%E6%96%B9%E5%85%B3%E7%B3%BB%0A%20%20%20%20for%20i%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E8%BE%93%E5%85%A5%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%3D%22,%20n%29%0A%0A%20%20%20%20count%20%3D%20quadratic%28n%29%0A%20%20%20%20print%28%22%E5%B9%B3%E6%96%B9%E9%98%B6%E7%9A%84%E6%93%8D%E4%BD%9C%E6%95%B0%E9%87%8F%20%3D%22,%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全屏观看 ></a></div>
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图 2-10 对比了常数阶、线性阶和平方阶三种时间复杂度。
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图 2-10 对比了常数阶、线性阶和平方阶三种时间复杂度。
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Reference in New Issue
Block a user