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18 changed files with 34 additions and 28 deletions
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@ -7,7 +7,7 @@ icon: material/help-circle-outline
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<div class="center-table" markdown>
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![附录](../assets/covers/chapter_appendix.jpg){ width="70%" }
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![附录](../assets/covers/chapter_appendix.jpg){ width="600" }
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</div>
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@ -7,7 +7,7 @@ icon: material/view-list-outline
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<div class="center-table" markdown>
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![数组与链表](../assets/covers/chapter_array_and_linkedlist.jpg){ width="70%" }
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![数组与链表](../assets/covers/chapter_array_and_linkedlist.jpg){ width="600" }
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</div>
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@ -7,7 +7,7 @@ icon: material/map-marker-path
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<div class="center-table" markdown>
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![回溯](../assets/covers/chapter_backtracking.jpg){ width="70%" }
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![回溯](../assets/covers/chapter_backtracking.jpg){ width="600" }
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</div>
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@ -7,7 +7,7 @@ icon: material/timer-sand
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<div class="center-table" markdown>
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![复杂度](../assets/covers/chapter_complexity_analysis.jpg){ width="70%" }
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![复杂度](../assets/covers/chapter_complexity_analysis.jpg){ width="600" }
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</div>
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@ -7,7 +7,7 @@ icon: material/shape-outline
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<div class="center-table" markdown>
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![数据结构](../assets/covers/chapter_data_structure.jpg){ width="70%" }
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![数据结构](../assets/covers/chapter_data_structure.jpg){ width="600" }
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</div>
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@ -94,25 +94,31 @@ $$
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细心的你可能会发现:`int` 和 `float` 长度相同,都是 4 bytes,但为什么 `float` 的取值范围远大于 `int` ?这非常反直觉,因为按理说 `float` 需要表示小数,取值范围应该变小才对。
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实际上,这是因为浮点数 `float` 采用了不同的表示方式。根据 IEEE 754 标准,32-bit 长度的 `float` 由以下部分构成:
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- 符号位 $\mathrm{S}$ :占 1 bit 。
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- 指数位 $\mathrm{E}$ :占 8 bits 。
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- 分数位 $\mathrm{N}$ :占 24 bits ,其中 23 位显式存储。
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设 32-bit 二进制数的第 $i$ 位为 $b_i$ ,则 `float` 值的计算方法定义为:
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实际上,**这是因为浮点数 `float` 采用了不同的表示方式**。记一个 32-bit 长度的二进制数为:
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$$
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\text { val } = (-1)^{b_{31}} \times 2^{\left(b_{30} b_{29} \ldots b_{23}\right)_2-127} \times\left(1 . b_{22} b_{21} \ldots b_0\right)_2
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b_{31} b_{30} b_{29} \ldots b_2 b_1 b_0
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$$
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转化到十进制下的计算公式为
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根据 IEEE 754 标准,32-bit 长度的 `float` 由以下部分构成:
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- 符号位 $\mathrm{S}$ :占 1 bit ,对应 $b_{31}$ 。
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- 指数位 $\mathrm{E}$ :占 8 bits ,对应 $b_{30} b_{29} \ldots b_{23}$ 。
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- 分数位 $\mathrm{N}$ :占 23 bits ,对应 $b_{22} b_{21} \ldots b_0$ 。
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二进制数 `float` 对应的值的计算方法:
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$$
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\text { val }=(-1)^{\mathrm{S}} \times 2^{\mathrm{E} -127} \times (1 + \mathrm{N})
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\text {val} = (-1)^{b_{31}} \times 2^{\left(b_{30} b_{29} \ldots b_{23}\right)_2-127} \times\left(1 . b_{22} b_{21} \ldots b_0\right)_2
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$$
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其中各项的取值范围为
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转化到十进制下的计算公式:
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$$
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\text {val}=(-1)^{\mathrm{S}} \times 2^{\mathrm{E} -127} \times (1 + \mathrm{N})
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$$
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其中各项的取值范围:
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$$
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\begin{aligned}
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@ -8,7 +8,7 @@ status: new
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<div class="center-table" markdown>
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![分治](../assets/covers/chapter_divide_and_conquer.jpg){ width="70%" }
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![分治](../assets/covers/chapter_divide_and_conquer.jpg){ width="600" }
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</div>
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@ -8,7 +8,7 @@ status: new
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<div class="center-table" markdown>
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![动态规划](../assets/covers/chapter_dynamic_programming.jpg){ width="70%" }
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![动态规划](../assets/covers/chapter_dynamic_programming.jpg){ width="600" }
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</div>
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@ -7,7 +7,7 @@ icon: material/graphql
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<div class="center-table" markdown>
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![图](../assets/covers/chapter_graph.jpg){ width="70%" }
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![图](../assets/covers/chapter_graph.jpg){ width="600" }
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</div>
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@ -8,7 +8,7 @@ status: new
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<div class="center-table" markdown>
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![贪心](../assets/covers/chapter_greedy.jpg){ width="70%" }
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![贪心](../assets/covers/chapter_greedy.jpg){ width="600" }
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</div>
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@ -7,7 +7,7 @@ icon: material/table-search
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<div class="center-table" markdown>
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![散列表](../assets/covers/chapter_hashing.jpg){ width="70%" }
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![散列表](../assets/covers/chapter_hashing.jpg){ width="600" }
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</div>
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@ -7,7 +7,7 @@ icon: material/family-tree
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<div class="center-table" markdown>
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![堆](../assets/covers/chapter_heap.jpg){ width="70%" }
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![堆](../assets/covers/chapter_heap.jpg){ width="600" }
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</div>
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@ -7,7 +7,7 @@ icon: material/calculator-variant-outline
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<div class="center-table" markdown>
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![初识算法](../assets/covers/chapter_introduction.jpg){ width="70%" }
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![初识算法](../assets/covers/chapter_introduction.jpg){ width="600" }
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</div>
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@ -7,7 +7,7 @@ icon: material/book-open-outline
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<div class="center-table" markdown>
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![前言](../assets/covers/chapter_preface.jpg){ width="70%" }
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![前言](../assets/covers/chapter_preface.jpg){ width="600" }
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</div>
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@ -7,7 +7,7 @@ icon: material/text-search
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<div class="center-table" markdown>
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![搜索](../assets/covers/chapter_searching.jpg){ width="70%" }
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![搜索](../assets/covers/chapter_searching.jpg){ width="600" }
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</div>
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<div class="center-table" markdown>
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![排序](../assets/covers/chapter_sorting.jpg){ width="70%" }
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![排序](../assets/covers/chapter_sorting.jpg){ width="600" }
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</div>
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<div class="center-table" markdown>
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![栈与队列](../assets/covers/chapter_stack_and_queue.jpg){ width="70%" }
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![栈与队列](../assets/covers/chapter_stack_and_queue.jpg){ width="600" }
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</div>
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<div class="center-table" markdown>
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![树](../assets/covers/chapter_tree.jpg){ width="70%" }
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![树](../assets/covers/chapter_tree.jpg){ width="600" }
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</div>
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