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| 1 | +# 🔥 Range Sum Query - Immutable 🔥 || 3 Solutions || Simple Fast and Easy || with Explanation |
| 2 | + |
| 3 | +## Solution - 1 |
| 4 | + |
| 5 | +```dart |
| 6 | +class NumArray { |
| 7 | + late List<int> prefixSum; |
| 8 | +
|
| 9 | + NumArray(List<int> nums) { |
| 10 | + if (nums == 0) { |
| 11 | + throw ArgumentError("Panic: Input is Empty"); |
| 12 | + } |
| 13 | +
|
| 14 | + this.prefixSum = List.filled(nums.length + 1, 0); |
| 15 | +
|
| 16 | + for (int i = 1; i <= nums.length; i++) { |
| 17 | + prefixSum[i] = prefixSum[i - 1] + nums[i - 1]; |
| 18 | + } |
| 19 | + } |
| 20 | +
|
| 21 | + int sumRange(int left, int right) { |
| 22 | + if (left < 0 || right >= prefixSum.length - 1) { |
| 23 | + throw RangeError("Panic: Input indices are out of bounds"); |
| 24 | + } |
| 25 | +
|
| 26 | + // Here both left and right are inclusive. |
| 27 | + // right maps to right+1 in prefixSum. left maps to left+1 in prefixSum. |
| 28 | + // To get the result subtract the prefixSum before left index from prefixSum at |
| 29 | + // right index. |
| 30 | + return prefixSum[right + 1] - prefixSum[left]; |
| 31 | + } |
| 32 | +} |
| 33 | +``` |
| 34 | + |
| 35 | +## Solution - 2 |
| 36 | + |
| 37 | +```dart |
| 38 | +class NumArray { |
| 39 | + late List<int> nums; |
| 40 | + late List<int> prefixSum; |
| 41 | + NumArray(List<int> nums) { |
| 42 | + this.nums = nums; |
| 43 | + this.prefixSum = getPrefixSum(); |
| 44 | + } |
| 45 | +
|
| 46 | + int sumRange(int left, int right) { |
| 47 | + if (left == 0) return prefixSum[right]; |
| 48 | + return prefixSum[right] - prefixSum[left - 1]; |
| 49 | + } |
| 50 | +
|
| 51 | + List<int> getPrefixSum() { |
| 52 | + int sum = 0; |
| 53 | + List<int> ans = List.filled(nums.length, 0); |
| 54 | +
|
| 55 | + for (int i = 0; i < nums.length; i++) { |
| 56 | + sum += nums[i]; |
| 57 | + ans[i] = sum; |
| 58 | + } |
| 59 | +
|
| 60 | + return ans; |
| 61 | + } |
| 62 | +} |
| 63 | +``` |
| 64 | + |
| 65 | +## Solution - 3 |
| 66 | + |
| 67 | +```dart |
| 68 | +
|
| 69 | +class NumArray { |
| 70 | + List<int> arr = []; |
| 71 | + NumArray(List<int> nums) { |
| 72 | + this.arr = nums; |
| 73 | + } |
| 74 | +
|
| 75 | + int sumRange(int left, int right) { |
| 76 | + int sum = 0; |
| 77 | + for (int i = left; i <= right; i++) sum += this.arr[i]; |
| 78 | + return sum; |
| 79 | + } |
| 80 | +} |
| 81 | +``` |
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