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In the Cangjie language programming practice of HarmonyOS Next, loop structure is the core way to implement repetitive tasks. The while and do-while loops have their own characteristics, and their performance in different scenarios also varies.As a technician who has been studying this field for a long time, I will combine practical cases to deeply analyze the principles, characteristics and optimization strategies of these two cycle structures.
1. The principle of circular structure
(I) Accuracy control strategy for square roots in dichotomy
Finding square roots in dichotomy is a classic case of using while loops to implement iterative calculations.In this algorithm, the true square root value is gradually approached by continuously narrowing the value range of the root.Take the calculation of the square root of the number 2 as an example:
main() {
var root = 0.0
var min = 1.0
var max = 2.0
var error = 1.0
let tolerance = 0.1 ** 10
while (error ** 2 > tolerance) {
root = (min + max) / 2.0
error = root ** 2 - 2.0
if (error > 0.0) {
max = root
} else {
min = root
}
}
println("2's square root is approximately equal to: ${root}")
}
In the above code, tolerance is used to control the precision, which determines when the loop stops.In each loop, calculate the error error between the currently guessed root root and the real square root. If the square of the error is greater than tolerance, continue to adjust the values of minandmaxto narrow the value range of the root.This accuracy control strategy ensures the accuracy of the calculation results, but it also requires the reasonable setting of the value oftoleranceaccording to actual needs.If thetolerance` is set too small, it will increase the number of cycles and the calculation time will become longer; if the setting is too large, the accuracy of the calculation result will be affected.In practical applications, trade-offs need to be made between precision and performance.
2. Do-while features
(I) Rational analysis that must be performed once in the Monte Carlo algorithm
Monte Carlo algorithms are often used to estimate numerical values through random simulations, in which the do-while loop plays a unique role.Take the estimation of pi as an example:
cj
import std.random.*
main() {
let random = Random()
var totalPoints = 0
var hitPoints = 0
do {
let x = random.nextFloat64()
let y = random.nextFloat64()
if ((x - 0.5) ** 2 + (y - 0.5) ** 2 < 0.25) {
hitPoints++
}
totalPoints++
} while (totalPoints < 1000000)
let pi = 4.0 * Float64(hitPoints) / Float64(totalPoints)
println("P approximate value is: ${pi}")
}
In this example, the do-while loop ensures that the loop body will be executed at least once.This makes sense in Monte Carlo algorithms, because we need to do at least one random sampling to get the initial data.If you use a while loop, in some special cases (for example, the initial condition is not met), the loop body may not be executed at once, resulting in inaccurate results.The characteristics of the do-while loop ensure that no matter the initial conditions, a random point generation and judgment can be performed, providing basic data for subsequent calculations, making the algorithm more robust and reliable.
3. Circular optimization suggestions
(I) Mathematical modeling of error tolerance
In loop algorithms, error tolerance tolerance has a crucial impact on performance, and reasonable mathematical modeling can help us better choose the value of tolerance.Taking the dichotomy method to find the square root as an example, suppose we hope to improve the calculation efficiency as much as possible while ensuring a certain accuracy.We can determine the relationship between tolerance and the number of cycles through mathematical analysis.
Let tolerance be the error tolerance, and the value range of the root in each loop is reduced by half.Assume that the initial range is [a, b], and after n cycles, the range is reduced to [(a + b) / 2^n, (a + b) / 2^n].To meet the accuracy requirements, we want (b - a) / 2^n <= tolerance.Through logarithmic operation, you can get n >= log2((b - a) / tolerance).For example, when calculating the square root of the number 2, the initial range [1, 2], if tolerance = 0.1 ** 10, the number of cycles can be roughly estimated by calculation, thereby evaluating the time complexity of the algorithm.According to this relationship, we can choose the appropriate tolerance value according to actual needs and performance requirements, and while ensuring calculation accuracy, we can optimize cycle performance, avoid unnecessary cyclical calculations, and improve the operation efficiency of the program.
In the development of HarmonyOS Next, a deep understanding of the principles and characteristics of while and do-while loops, and rationally using precision control strategies and mathematical modeling of error tolerance can help developers write efficient and stable loop code to improve the performance and quality of applications.
1. The principle of circular structure
(I) Accuracy control strategy for square roots in dichotomy
Finding square roots in dichotomy is a classic case of using while loops to implement iterative calculations.In this algorithm, the true square root value is gradually approached by continuously narrowing the value range of the root.Take the calculation of the square root of the number 2 as an example:
main() {
var root = 0.0
var min = 1.0
var max = 2.0
var error = 1.0
let tolerance = 0.1 ** 10
while (error ** 2 > tolerance) {
root = (min + max) / 2.0
error = root ** 2 - 2.0
if (error > 0.0) {
max = root
} else {
min = root
}
}
println("2's square root is approximately equal to: ${root}")
}
In the above code, tolerance is used to control the precision, which determines when the loop stops.In each loop, calculate the error error between the currently guessed root root and the real square root. If the square of the error is greater than tolerance, continue to adjust the values of minandmaxto narrow the value range of the root.This accuracy control strategy ensures the accuracy of the calculation results, but it also requires the reasonable setting of the value oftoleranceaccording to actual needs.If thetolerance` is set too small, it will increase the number of cycles and the calculation time will become longer; if the setting is too large, the accuracy of the calculation result will be affected.In practical applications, trade-offs need to be made between precision and performance.
2. Do-while features
(I) Rational analysis that must be performed once in the Monte Carlo algorithm
Monte Carlo algorithms are often used to estimate numerical values through random simulations, in which the do-while loop plays a unique role.Take the estimation of pi as an example:
cj
import std.random.*
main() {
let random = Random()
var totalPoints = 0
var hitPoints = 0
do {
let x = random.nextFloat64()
let y = random.nextFloat64()
if ((x - 0.5) ** 2 + (y - 0.5) ** 2 < 0.25) {
hitPoints++
}
totalPoints++
} while (totalPoints < 1000000)
let pi = 4.0 * Float64(hitPoints) / Float64(totalPoints)
println("P approximate value is: ${pi}")
}
In this example, the do-while loop ensures that the loop body will be executed at least once.This makes sense in Monte Carlo algorithms, because we need to do at least one random sampling to get the initial data.If you use a while loop, in some special cases (for example, the initial condition is not met), the loop body may not be executed at once, resulting in inaccurate results.The characteristics of the do-while loop ensure that no matter the initial conditions, a random point generation and judgment can be performed, providing basic data for subsequent calculations, making the algorithm more robust and reliable.
3. Circular optimization suggestions
(I) Mathematical modeling of error tolerance
In loop algorithms, error tolerance tolerance has a crucial impact on performance, and reasonable mathematical modeling can help us better choose the value of tolerance.Taking the dichotomy method to find the square root as an example, suppose we hope to improve the calculation efficiency as much as possible while ensuring a certain accuracy.We can determine the relationship between tolerance and the number of cycles through mathematical analysis.
Let tolerance be the error tolerance, and the value range of the root in each loop is reduced by half.Assume that the initial range is [a, b], and after n cycles, the range is reduced to [(a + b) / 2^n, (a + b) / 2^n].To meet the accuracy requirements, we want (b - a) / 2^n <= tolerance.Through logarithmic operation, you can get n >= log2((b - a) / tolerance).For example, when calculating the square root of the number 2, the initial range [1, 2], if tolerance = 0.1 ** 10, the number of cycles can be roughly estimated by calculation, thereby evaluating the time complexity of the algorithm.According to this relationship, we can choose the appropriate tolerance value according to actual needs and performance requirements, and while ensuring calculation accuracy, we can optimize cycle performance, avoid unnecessary cyclical calculations, and improve the operation efficiency of the program.
In the development of HarmonyOS Next, a deep understanding of the principles and characteristics of while and do-while loops, and rationally using precision control strategies and mathematical modeling of error tolerance can help developers write efficient and stable loop code to improve the performance and quality of applications.