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<meta name="description" content="LeetCode、剑指Offer、程序员面试金典题解">
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<style>
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}
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</body>
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solution/0600-0699/0699.Falling Squares/README.md

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**方法一:线段树**
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线段树将整个区间分割为多个不连续的子区间,子区间的数量不超过 `log(width)`。更新某个元素的值,只需要更新 `log(width)` 个区间,并且这些区间都包含在一个包含该元素的大区间内。区间修改时,需要使用**懒标记**保证效率。
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线段树将整个区间分割为多个不连续的子区间,子区间的数量不超过 $log(width)$。更新某个元素的值,只需要更新 $log(width)$ 个区间,并且这些区间都包含在一个包含该元素的大区间内。区间修改时,需要使用**懒标记**保证效率。
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- 线段树的每个节点代表一个区间;
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- 线段树具有唯一的根节点,代表的区间是整个统计范围,如 `[1, N]`
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- 线段树的每个叶子节点代表一个长度为 1 的元区间 `[x, x]`
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- 对于每个内部节点 `[l, r]`,它的左儿子是 `[l, mid]`,右儿子是 `[mid + 1, r]`, 其中 `mid = ⌊(l + r) / 2⌋` (即向下取整)。
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- 线段树具有唯一的根节点,代表的区间是整个统计范围,如 $[1, N]$
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- 线段树的每个叶子节点代表一个长度为 1 的元区间 $[x, x]$
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- 对于每个内部节点 $[l, r]$,它的左儿子是 $[l, mid]$,右儿子是 $[mid + 1, r]$, 其中 $mid = ⌊(l + r) / 2⌋$ (即向下取整)。
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对于本题,线段树节点维护的信息有:
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1. 区间中方块的最大高度 v
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1. 懒标记 add
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1. 区间中方块的最大高度 $v$
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1. 懒标记 $add$
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另外,由于数轴范围很大,达到 10^8,因此我们采用动态开点。
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另外,由于数轴范围很大,达到 $10^8$,因此我们采用动态开点。
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